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21 pages, 5226 KiB  
Article
Characterization and Implementation of Cocoa Pod Husk as a Reinforcing Agent to Obtain Thermoplastic Starches and Bio-Based Composite Materials
by Andrés Mauricio Holguín Posso, Juan Carlos Macías Silva, Juan Pablo Castañeda Niño, Jose Herminsul Mina Hernandez and Lety del Pilar Fajardo Cabrera de Lima
Polymers 2024, 16(11), 1608; https://doi.org/10.3390/polym16111608 - 6 Jun 2024
Cited by 1 | Viewed by 1857
Abstract
When the cocoa pod husk (CPH) is used and processed, two types of flour were obtained and can be differentiated by particle size, fine flour (FFCH), and coarse flour (CFCH) and can be used as a possible reinforcement for the development of bio-based [...] Read more.
When the cocoa pod husk (CPH) is used and processed, two types of flour were obtained and can be differentiated by particle size, fine flour (FFCH), and coarse flour (CFCH) and can be used as a possible reinforcement for the development of bio-based composite materials. Each flour was obtained from chopping, drying by forced convection, milling by blades, and sieving using the 100 mesh/bottom according to the Tyler series. Their physicochemical, thermal, and structural characterization made it possible to identify the lower presence of lignin and higher proportions of cellulose and pectin in FFCH. Based on the properties identified in FFCH, it was included in the processing of thermoplastic starch (TPS) from the plantain pulp (Musa paradisiaca) and its respective bio-based composite material using plantain peel short fiber (PPSF) as a reinforcing agent using the following sequence of processing techniques: extrusion, internal mixing, and compression molding. The influence of FFCH contributed to the increase in ultimate tensile strength (7.59 MPa) and higher matrix–reinforcement interaction when obtaining the freshly processed composite material (day 0) when compared to the bio-based composite material with higher FCP content (30%) in the absence of FFCH. As for the disadvantages of FFCH, reduced thermal stability (323.57 to 300.47 °C) and losses in ultimate tensile strength (0.73 MPa) and modulus of elasticity (142.53 to 26.17 MPa) during storage progress were identified. In the case of TPS, the strengthening action of FFCH was not evident. Finally, the use of CFCH was not considered for the elaboration of the bio-based composite material because it reached a higher lignin content than FFCH, which was expected to decrease its affinity with the TPS matrix, resulting in lower mechanical properties in the material. Full article
(This article belongs to the Special Issue Preparation and Application of Biomass-Based Materials)
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Graphical abstract
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<p>Raw materials for producing bio-based composite material: (<b>a</b>) cocoa pod husk; (<b>b</b>) plantain pulp and peel variety Dominico hartón.</p>
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<p>Raw materials are required to obtain bio-based materials. (<b>a</b>) Plantain native starch (PNS); (<b>b</b>) plantain peel short fiber (PPSF); (<b>c</b>) coarse flour from a cocoa pod husk (CFCH); (<b>d</b>) fine flour from a cocoa pod husk (FFCH).</p>
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<p>Processing of TPS and bio-based composite material. (<b>a</b>) Thermo Scientific internal torque mixer; (<b>b</b>) TPS samples made in compression molding (five test specimens).</p>
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<p>Scheme for obtaining the bio-based composite material from the cocoa pod husk and plantain.</p>
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<p>(<b>a</b>) FFCH with starch granules; (<b>b</b>) CFCH. See the yellow circles in the image.</p>
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<p>DSC thermograms for the two types of cocoa flour.</p>
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<p>Thermogravimetric analysis of FFCH and CFCH.</p>
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<p>Spectrograms of CPH flour.</p>
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<p>Diffractograms of the CPH flour.</p>
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<p>SEM micrographs of (<b>a</b>) TPS; (<b>b</b>) TPS2; (<b>c</b>) TPS + F; (<b>d</b>) TPS2 + F, at 200× and 500×.</p>
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<p>Diffractograms of TPS and bio-based composite materials.</p>
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<p>DTGA thermograms of TPS and plantain and cocoa-based composites.</p>
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12 pages, 3348 KiB  
Proceeding Paper
Evaluation of Combined Effect of Zero Flux and Convective Boundary Conditions on Magnetohydrodynamic Boundary-Layer Flow of Nanofluid over Moving Surface Using Buongiorno’s Model
by Purnima Rai and Upendra Mishra
Eng. Proc. 2023, 59(1), 245; https://doi.org/10.3390/engproc2023059245 - 10 Apr 2024
Cited by 1 | Viewed by 697
Abstract
This study explores the synergistic impact of zero flux and convective boundary conditions on the magnetohydrodynamic (MHD) boundary-layer slip flow of nanofluid over a moving surface, utilizing Buongiorno’s model. In a landscape of expanding nanofluid applications, understanding boundary condition interactions is crucial. Employing [...] Read more.
This study explores the synergistic impact of zero flux and convective boundary conditions on the magnetohydrodynamic (MHD) boundary-layer slip flow of nanofluid over a moving surface, utilizing Buongiorno’s model. In a landscape of expanding nanofluid applications, understanding boundary condition interactions is crucial. Employing a systematic approach, we varied key parameters, including surface velocity, thermophoresis, Brownian motion, Eckert number, Prandtl number, and Lewis number, systematically investigating their effects on flow and heat transfer. Numerical simulations focused on critical metrics such as skin friction coefficients; Nusselt and Sherwood numbers; and temperature, concentration, and velocity profiles. Noteworthy findings include the amplifying effect of a magnetic field and viscous dissipation on temperature profiles and the dual impact of heightened velocity slip on temperature and velocity profiles, which result in a thicker concentration boundary layer. Beyond academia, we envision our research having practical applications in optimizing high-temperature processes, bio-sensors, paints, pharmaceuticals, coatings, cosmetics, and space technology. Full article
(This article belongs to the Proceedings of Eng. Proc., 2023, RAiSE-2023)
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<p>Practical manifestation of the problem.</p>
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<p>Temperature profiles, <span class="html-italic">θ</span>(<span class="html-italic">η</span>), with different values of <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>t</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Concentration profiles, <span class="html-italic">ϕ</span>(<span class="html-italic">η</span>), with different values of <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>t</mi> </msub> </mrow> </semantics></math>..</p>
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<p>Concentration profiles, <span class="html-italic">ϕ</span>(<span class="html-italic">η</span>), with different values of <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>b</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Temperature profiles, <span class="html-italic">θ</span>(<span class="html-italic">η</span>), with different values of <span class="html-italic">M</span>.</p>
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<p>Temperature profiles, <span class="html-italic">θ</span>(<span class="html-italic">η</span>), with different values of <span class="html-italic">Ec</span>.</p>
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<p>Concentration profiles, <span class="html-italic">ϕ</span>(<span class="html-italic">η</span>), with different values of Ec.</p>
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<p>Temperature profiles, <span class="html-italic">θ</span>(<span class="html-italic">η</span>), with different values of <span class="html-italic">Pr</span>.</p>
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<p>Temperature profiles, <span class="html-italic">θ</span>(<span class="html-italic">η</span>), with different values of <math display="inline"><semantics> <mi>ε</mi> </semantics></math>.</p>
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<p>Concentration profile, <span class="html-italic">ϕ</span>(<span class="html-italic">η</span>), with different values of <math display="inline"><semantics> <mi>ε</mi> </semantics></math>.</p>
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27 pages, 853 KiB  
Article
Overlapping Grid-Based Spectral Collocation Technique for Bioconvective Flow of MHD Williamson Nanofluid over a Radiative Circular Cylindrical Body with Activation Energy
by Musawenkosi Patson Mkhatshwa
Computation 2024, 12(4), 75; https://doi.org/10.3390/computation12040075 - 5 Apr 2024
Cited by 2 | Viewed by 1247
Abstract
The amalgamation of motile microbes in nanofluid (NF) is important in upsurging the thermal conductivity of various systems, including micro-fluid devices, chip-shaped micro-devices, and enzyme biosensors. The current scrutiny focuses on the bioconvective flow of magneto-Williamson NFs containing motile microbes through a horizontal [...] Read more.
The amalgamation of motile microbes in nanofluid (NF) is important in upsurging the thermal conductivity of various systems, including micro-fluid devices, chip-shaped micro-devices, and enzyme biosensors. The current scrutiny focuses on the bioconvective flow of magneto-Williamson NFs containing motile microbes through a horizontal circular cylinder placed in a porous medium with nonlinear mixed convection and thermal radiation, heat sink/source, variable fluid properties, activation energy with chemical and microbial reactions, and Brownian motion for both nanoparticles and microbes. The flow analysis has also been considered subject to velocity slips, suction/injection, and heat convective and zero mass flux constraints at the boundary. The governing equations have been converted to a non-dimensional form using similarity variables, and the overlapping grid-based spectral collocation technique has been executed to procure solutions numerically. The graphical interpretation of various pertinent variables in the flow profiles and physical quantities of engineering attentiveness is provided and discussed. The results reveal that NF flow is accelerated by nonlinear thermal convection, velocity slip, magnetic fields, and variable viscosity parameters but decelerated by the Williamson fluid and suction parameters. The inclusion of nonlinear thermal radiation and variable thermal conductivity helps to enhance the fluid temperature and heat transfer rate. The concentration of both nanoparticles and motile microbes is promoted by the incorporation of activation energy in the flow system. The contribution of microbial Brownian motion along with microbial reactions on flow quantities justifies the importance of these features in the dynamics of motile microbes. Full article
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Figure 1
<p>Flow model and physical coordinate system.</p>
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<p>Dividing the time solution domain into <math display="inline"><semantics> <mi>ϖ</mi> </semantics></math> non-overlapping sub-intervals.</p>
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<p>Dividing the spatial solution domain into <math display="inline"><semantics> <mi>ς</mi> </semantics></math> overlapping sub-intervals.</p>
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<p>Comparison of solution errors <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>f</mi> </msub> <mo>,</mo> <msub> <mi>E</mi> <mi>θ</mi> </msub> <mo>,</mo> <msub> <mi>E</mi> <mi>ϕ</mi> </msub> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mi>χ</mi> </msub> <mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> when <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>ξ</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>ϖ</mi> <mo>=</mo> <mn>20</mn> <mo>.</mo> </mrow> </semantics></math> (<b>a</b>) Solution errors against iterations for the MD-BSLLM <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>ς</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>N</mi> <mi>η</mi> </msub> <mo>=</mo> <mn>100</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>b</b>) Solution errors against iterations for the OMD-BSLLM <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>ς</mi> <mo>&gt;</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>N</mi> <mi>η</mi> </msub> <mo>=</mo> <mn>10</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Comparison of residual error approximations for the case of MD-BSLLM <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>ς</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> and OMD-BSLLM <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>ς</mi> <mo>&gt;</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> when <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>ξ</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>ϖ</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> for different nodes (<math display="inline"><semantics> <mrow> <mrow> <mo>[</mo> <msub> <mi>N</mi> <mi>η</mi> </msub> <mo>,</mo> <mi>ς</mi> <mo>]</mo> </mrow> <mo>=</mo> <mrow> <mo>[</mo> <mn>100</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mo>[</mo> <mn>50</mn> <mo>,</mo> <mn>2</mn> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mo>[</mo> <mn>20</mn> <mo>,</mo> <mn>5</mn> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mo>[</mo> <mn>10</mn> <mo>,</mo> <mn>10</mn> <mo>]</mo> </mrow> </mrow> </semantics></math>).</p>
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<p>Dimensionless velocity profiles.</p>
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<p>Dimensionless velocity profiles.</p>
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<p>Dimensionless velocity profiles.</p>
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<p>Dimensionless temperature profiles.</p>
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<p>Dimensionless temperature profiles.</p>
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<p>Dimensionless nanoparticle concentration profiles.</p>
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<p>Dimensionless density of the motile microbe profiles.</p>
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<p>Dimensionless density of the motile microbe profiles.</p>
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<p>Dimensionless surface drag coefficient.</p>
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<p>Dimensionless surface drag coefficient.</p>
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<p>Dimensionless surface drag coefficient.</p>
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<p>Dimensionless Nusselt number.</p>
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<p>Dimensionless Nusselt number.</p>
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<p>Dimensionless density number of the motile microbes.</p>
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<p>Dimensionless density number of the motile microbes.</p>
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21 pages, 1488 KiB  
Article
Health-Promoting Properties of Processed Red Cabbage (Brassica oleracea var. capitata f. rubra): Effects of Drying Methods on Bio-Compound Retention
by Nicol Mejías, Antonio Vega-Galvez, Luis S. Gomez-Perez, Alexis Pasten, Elsa Uribe, Anielka Cortés, Gabriela Valenzuela-Barra, Javiera Camus, Carla Delporte and Giuliano Bernal
Foods 2024, 13(6), 830; https://doi.org/10.3390/foods13060830 - 8 Mar 2024
Cited by 4 | Viewed by 2295
Abstract
The aim of this work is to describe the effect of convective drying (CD), vacuum drying (VD), infrared drying (IRD), low-temperature vacuum drying (LTVD) and freeze drying (FD) on bio-compound retention of red cabbage and its beneficial health properties. The total phenolics content [...] Read more.
The aim of this work is to describe the effect of convective drying (CD), vacuum drying (VD), infrared drying (IRD), low-temperature vacuum drying (LTVD) and freeze drying (FD) on bio-compound retention of red cabbage and its beneficial health properties. The total phenolics content (TPC), flavonoids (TFC), anthocyanin (TAC) and glucosinolates (TGC) were determined by spectrophotometry. The profiles of phenolic acids, amino acids and fatty acids were determined by HPLC-UV-DAD, LC-DAD and GC-FID, respectively. Antioxidant potential was verified by DPPH and ORAC assays. The antiproliferative activity was measured in the human gastric cell line (AGS). Anti-inflammatory activity was evaluated by phorbol 12-myristate 13-acetate and arachidonic acid models. VD showed high values of TPC = 11.89 ± 0.28 mg GAE/g d.m.; TFC = 11.30 ± 0.9 mg QE/g d.m.; TAC = 0.265 ± 0.01 mg Cya3glu/g d.m.; and TGC = 51.15 ± 3.31 µmol SE/g d.m. Caffeic acid, ferulic acid and sinapic acid were identified. The predominant amino acid and fatty acid were glutamic acid and γ–linolenic acid, respectively. The antioxidant potential was dependent on drying methods for both DPPH and ORAC assays. Dried red cabbage extracts showed clear anti-inflammatory and antiproliferative activity. The dehydration process is an alternative for the retention of bio-compounds and health-promoting properties of red cabbage. Full article
(This article belongs to the Section Food Engineering and Technology)
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Graphical abstract

Graphical abstract
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<p>Antioxidant activity for samples extracts from fresh-blanched and dehydrated red cabbage. FRESH-B: fresh-blanched; VD: vacuum drying; CD: convective drying; IRD: infrared drying; LTVD: low-temperature vacuum drying; FD: freeze drying. Values are expressed as mean ± standard deviation. (<b>A</b>) is DPPH assay and (<b>B</b>) is ORAC assay. Different letters indicate significant differences (<span class="html-italic">p</span> &lt; 0.05).</p>
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<p>Anti-inflammatory activity of red cabbage extracts dehydrated by different drying methods. VD: vacuum drying; CD: convective drying; IRD: infrared drying; LTVD: low-temperature vacuum drying; FD: freeze drying. EA<sub>TPA</sub>: topical anti-inflammatory effect against phorbol 12-myristate 13-acetate; EA<sub>AA</sub>: topical anti-inflammatory effect against arachidonic acid. NIM: nimesulide; IND: indomethacin as control medicament. n.d: not determined. An asterisk (*) denotes significant differences (<span class="html-italic">p</span> &lt; 0.05) between samples with respect to the negative control (100% inflammation); n = 8.</p>
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<p>Antiproliferative activity of fresh-b and dehydrated red cabbage extracts (mg/mL) on gastric cancer cells. (<b>A</b>) Fresh-blanched, (<b>B</b>) CD: convective drying, (<b>C</b>) IRD: infrared draying, (<b>D</b>) VD: vacuum drying, (<b>E</b>) LTVD: low-temperature vacuum drying and (<b>F</b>) FD: freeze drying. Control: without red cabbage extract. The statistical analysis of AGS and GES1 was evaluated separately. Different letters indicate significant differences (<span class="html-italic">p</span> &lt; 0.05).</p>
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21 pages, 4380 KiB  
Article
Analyzing the MHD Bioconvective Eyring–Powell Fluid Flow over an Upright Cone/Plate Surface in a Porous Medium with Activation Energy and Viscous Dissipation
by Francis Peter, Paulsamy Sambath and Seshathiri Dhanasekaran
Computation 2024, 12(3), 48; https://doi.org/10.3390/computation12030048 - 4 Mar 2024
Cited by 3 | Viewed by 1818
Abstract
In the field of heat and mass transfer applications, non-Newtonian fluids are potentially considered to play a very important role. This study examines the magnetohydrodynamic (MHD) bioconvective Eyring–Powell fluid flow on a permeable cone and plate, considering the viscous dissipation (0.3 ≤ E [...] Read more.
In the field of heat and mass transfer applications, non-Newtonian fluids are potentially considered to play a very important role. This study examines the magnetohydrodynamic (MHD) bioconvective Eyring–Powell fluid flow on a permeable cone and plate, considering the viscous dissipation (0.3 ≤ Ec ≤0.7), the uniform heat source/sink (−0.1 ≤ Q0 ≤ 0.1), and the activation energy (−1 ≤ E1 ≤ 1). The primary focus of this study is to examine how MHD and porosity impact heat and mass transfer in a fluid with microorganisms. A similarity transformation (ST) changes the nonlinear partial differential equations (PDEs) into ordinary differential equations (ODEs). The Keller Box (KB) finite difference method solves these equations. Our findings demonstrate that adding MHD (0.5 ≤ M ≤ 0.9) and porosity (0.3 ≤ Γ ≤ 0.7) effects improves microbial diffusion, boosting the rates of mass and heat transfer. Our comparison of our findings to prior studies shows that they are reliable. Full article
(This article belongs to the Section Computational Engineering)
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<p>Physical model.</p>
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<p>Flowchart for Keller Box method.</p>
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<p>Consequence of <span class="html-italic">K</span> on momentum.</p>
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<p>Consequence of <span class="html-italic">M</span> over momentum.</p>
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<p>Consequence of <math display="inline"><semantics> <mi mathvariant="sans-serif">Γ</mi> </semantics></math> over momentum.</p>
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<p>Consequence of <math display="inline"><semantics> <msub> <mi>N</mi> <mi>r</mi> </msub> </semantics></math> on velocity.</p>
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<p>Consequence of <math display="inline"><semantics> <msub> <mi>R</mi> <mi>b</mi> </msub> </semantics></math> over momentum.</p>
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<p>Consequence of <span class="html-italic">K</span> over temperature.</p>
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<p>Consequence of <span class="html-italic">M</span> over thermal profile.</p>
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<p>Consequence of <math display="inline"><semantics> <mi mathvariant="sans-serif">Γ</mi> </semantics></math> on thermal profile.</p>
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<p>Consequence of <math display="inline"><semantics> <msub> <mi>E</mi> <mi>c</mi> </msub> </semantics></math> over thermal profile.</p>
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<p>Consequence of <math display="inline"><semantics> <msub> <mi>Q</mi> <mn>0</mn> </msub> </semantics></math> over thermal profile.</p>
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<p>Consequence of <math display="inline"><semantics> <msub> <mi>P</mi> <mi>r</mi> </msub> </semantics></math> over thermal profile.</p>
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<p>Consequence of <span class="html-italic">K</span> over concentration profile.</p>
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<p>Consequence of <span class="html-italic">M</span> over concentration.</p>
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<p>Consequence of <math display="inline"><semantics> <mi mathvariant="sans-serif">Γ</mi> </semantics></math> over concentration.</p>
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<p>Consequence of <math display="inline"><semantics> <msub> <mi>K</mi> <mn>0</mn> </msub> </semantics></math> over concentration.</p>
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<p>Consequence of <math display="inline"><semantics> <msub> <mi>E</mi> <mn>1</mn> </msub> </semantics></math> over concentration.</p>
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<p>Consequence of <math display="inline"><semantics> <msub> <mi>S</mi> <mi>c</mi> </msub> </semantics></math> over concentration.</p>
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<p>Consequence of <span class="html-italic">M</span> over microorganism.</p>
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<p>Consequence of <math display="inline"><semantics> <mi mathvariant="sans-serif">Γ</mi> </semantics></math> over microorganism.</p>
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<p>Consequence of <math display="inline"><semantics> <msub> <mi>K</mi> <mn>0</mn> </msub> </semantics></math> over microorganism.</p>
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<p>Consequence of <math display="inline"><semantics> <msub> <mi>E</mi> <mn>1</mn> </msub> </semantics></math> over microorganism.</p>
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<p>Consequence of <math display="inline"><semantics> <msub> <mi>P</mi> <mi>e</mi> </msub> </semantics></math> over microorganism.</p>
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<p>Consequence of <math display="inline"><semantics> <msub> <mi>L</mi> <mi>b</mi> </msub> </semantics></math> over microorganism.</p>
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43 pages, 19694 KiB  
Article
Influence of Gyrotactic Microorganisms on Bioconvection in Electromagnetohydrodynamic Hybrid Nanofluid through a Permeable Sheet
by Ahmed S. Rashed, Ehsan H. Nasr and Samah M. Mabrouk
Computation 2024, 12(1), 17; https://doi.org/10.3390/computation12010017 - 20 Jan 2024
Cited by 2 | Viewed by 1894
Abstract
Many biotechnology sectors that depend on fluids and their physical characteristics, including the phenomenon of bioconvection, have generated a great deal of discussion. The term “bioconvection” describes the organized movement of microorganisms, such as bacteria or algae. Microorganisms that participate in bioconvection display [...] Read more.
Many biotechnology sectors that depend on fluids and their physical characteristics, including the phenomenon of bioconvection, have generated a great deal of discussion. The term “bioconvection” describes the organized movement of microorganisms, such as bacteria or algae. Microorganisms that participate in bioconvection display directed movement, frequently in the form of upward or downward streaming, which can lead to the production of distinctive patterns. The interaction between the microbes’ swimming behavior and the physical forces acting on them, such as buoyancy and fluid flow, is what drives these patterns. This work considers the laminar-mixed convection incompressible flow at the stagnation point with viscous and gyrotactic microorganisms in an unsteady electrically conducting hybrid nanofluid (Fe3O4-Cu/water). In addition, hybrid nanofluid flow over a horizontal porous stretched sheet, as well as external and induced magnetic field effects, can be used in biological domains, including drug delivery and microcirculatory system flow dynamics. The governing system has been reduced to a set of ordinary differential equations (ODEs) through the use of the group technique. The current research was inspired by an examination of the impacts of multiple parameters, including Prandtl number, Pr, magnetic diffusivity, η0, shape factor, n, microorganism diffusion coefficient, Dn, Brownian motion coefficient, DB, thermophoresis diffusion coefficient,  DT, bioconvection Peclet number, Pe, temperature difference,  δt, and concentration difference,  δc. The results show that as Pr rises, temperature, heat flux, and nanoparticles all decrease. In contrast, when the η0 value increases, the magnetic field and velocity decrease. Heat flow, bacterial density, and temperature decrease as the DB value rises, yet the number of nanoparticles increases. As the DT value increases, the temperature, heat flow, and concentration of nanoparticles all rise while the density of bacteria decreases. Even though temperature, heat flux, nanoparticles, and bacterial density all decrease as δc values climb, bacterial density rises as Dn values do although bacterial density falls with increasing,  δt and Pe values; on the other hand, when n values increase, temperature and heat flow increase but the density of bacteria and nanoparticle decrease. The physical importance and behavior of the present parameters were illustrated graphically. Full article
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<p>Physical representation of the problem.</p>
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<p>Prandtl number <inline-formula><mml:math id="mm213"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, temperature comparison; dashed lines for our study, solid for <italic>H</italic>. Waqas et al. [<xref ref-type="bibr" rid="B49-computation-12-00017">49</xref>].</p>
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<p>The impact of Prandtl number <inline-formula><mml:math id="mm214"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on temperature.</p>
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<p>The impact of Prandtl number <inline-formula><mml:math id="mm215"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on heat flux.</p>
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<p>The impact of Prandtl number <inline-formula><mml:math id="mm216"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on nanoparticles.</p>
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<p>The impact of Prandtl number <inline-formula><mml:math id="mm217"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on nanoparticles gradient.</p>
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<p>The impact of Prandtl number <inline-formula><mml:math id="mm218"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria.</p>
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<p>The impact of Prandtl number <inline-formula><mml:math id="mm219"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on density gradient of bacteria.</p>
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<p>The impact of magnetic diffusivity <inline-formula><mml:math id="mm220"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on magnetic field along <italic>x</italic>-axis.</p>
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<p>The impact of magnetic diffusivity <inline-formula><mml:math id="mm221"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on magnetic field gradient along <italic>x</italic>-axis.</p>
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<p>The impact of magnetic diffusivity <inline-formula><mml:math id="mm222"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on magnetic field along <italic>y</italic>-axis.</p>
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<p>The impact of magnetic diffusivity <inline-formula><mml:math id="mm223"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on magnetic field gradient along <italic>y</italic>-axis.</p>
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<p>The impact of magnetic diffusivity <inline-formula><mml:math id="mm224"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on velocity in x-direction.</p>
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<p>The impact of magnetic diffusivity <inline-formula><mml:math id="mm225"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on shear in x-direction.</p>
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<p>The impact of magnetic diffusivity <inline-formula><mml:math id="mm226"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on velocity in y-direction.</p>
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<p>The impact of magnetic diffusivity <inline-formula><mml:math id="mm227"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on shear in y-direction.</p>
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<p>The impact of Brownian motion coefficient, <inline-formula><mml:math id="mm228"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on temperature.</p>
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<p>The impact of Brownian motion coefficient, <inline-formula><mml:math id="mm229"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on heat flux.</p>
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<p>The impact of Brownian motion coefficient, <inline-formula><mml:math id="mm230"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on nanoparticles.</p>
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<p>The impact of Brownian motion coefficient, <inline-formula><mml:math id="mm231"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on nanoparticles gradient.</p>
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<p>The impact of Brownian motion coefficient, <inline-formula><mml:math id="mm232"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria.</p>
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<p>The impact of Brownian motion coefficient, <inline-formula><mml:math id="mm233"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria gradient.</p>
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<p>The impact of thermophoresis diffusion coefficient, <inline-formula><mml:math id="mm234"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on temperature.</p>
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<p>The impact of thermophoresis diffusion coefficient, <inline-formula><mml:math id="mm235"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on heat flux.</p>
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<p>The impact of thermophoresis diffusion coefficient, <inline-formula><mml:math id="mm236"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on nanoparticles.</p>
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<p>The impact of thermophoresis diffusion coefficient, <inline-formula><mml:math id="mm237"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on nanoparticles gradient.</p>
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<p>The impact of thermophoresis diffusion coefficient, <inline-formula><mml:math id="mm238"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria.</p>
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<p>The impact of thermophoresis diffusion coefficient, <inline-formula><mml:math id="mm239"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria gradient.</p>
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<p>The impact of microorganism diffusion coefficient, <inline-formula><mml:math id="mm240"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria.</p>
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<p>The impact of microorganism diffusion coefficient, <inline-formula><mml:math id="mm241"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria gradient.</p>
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<p>The impact of concentration difference, <inline-formula><mml:math id="mm242"><mml:semantics><mml:mrow><mml:mi>δ</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on temperature.</p>
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<p>The impact of concentration difference, <inline-formula><mml:math id="mm243"><mml:semantics><mml:mrow><mml:mi>δ</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on heat flux.</p>
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<p>The impact of concentration difference, <inline-formula><mml:math id="mm244"><mml:semantics><mml:mrow><mml:mi>δ</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on nanoparticles.</p>
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<p>The impact of concentration difference, <inline-formula><mml:math id="mm245"><mml:semantics><mml:mrow><mml:mi>δ</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on nanoparticles gradient.</p>
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<p>The impact of concentration difference, <inline-formula><mml:math id="mm246"><mml:semantics><mml:mrow><mml:mi>δ</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria.</p>
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<p>The impact of concentration difference, <inline-formula><mml:math id="mm247"><mml:semantics><mml:mrow><mml:mi>δ</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria gradient.</p>
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<p>The impact of temperature difference, <inline-formula><mml:math id="mm248"><mml:semantics><mml:mrow><mml:mi>δ</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on nanoparticles.</p>
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<p>The impact of temperature difference, <inline-formula><mml:math id="mm249"><mml:semantics><mml:mrow><mml:mi>δ</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on nanoparticles gradient.</p>
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<p>The impact of temperature difference, <inline-formula><mml:math id="mm250"><mml:semantics><mml:mrow><mml:mi>δ</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria.</p>
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<p>The impact of temperature difference, <inline-formula><mml:math id="mm251"><mml:semantics><mml:mrow><mml:mi>δ</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria gradient.</p>
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<p>The impact of shape factor, <inline-formula><mml:math id="mm252"><mml:semantics><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on temperature.</p>
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<p>The impact of shape factor, <inline-formula><mml:math id="mm253"><mml:semantics><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on heat flux.</p>
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<p>The impact of shape factor, <inline-formula><mml:math id="mm254"><mml:semantics><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on nanoparticles.</p>
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<p>The impact of shape factor, <inline-formula><mml:math id="mm255"><mml:semantics><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on nanoparticles gradient.</p>
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<p>The impact of shape factor, <inline-formula><mml:math id="mm256"><mml:semantics><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria.</p>
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<p>The impact of shape factor, <inline-formula><mml:math id="mm257"><mml:semantics><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on density gradient of bacteria.</p>
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<p>The impact of bioconvection Peclet number, <inline-formula><mml:math id="mm258"><mml:semantics><mml:mrow><mml:mi>P</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on density of bacteria.</p>
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<p>The impact of bioconvection Peclet number, <inline-formula><mml:math id="mm259"><mml:semantics><mml:mrow><mml:mi>P</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula>, on density gradient of bacteria.</p>
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19 pages, 3478 KiB  
Article
Numerical Investigation of Radiative Hybrid Nanofluid Flows over a Plumb Cone/Plate
by Francis Peter, Paulsamy Sambath and Seshathiri Dhanasekaran
Mathematics 2023, 11(20), 4331; https://doi.org/10.3390/math11204331 - 18 Oct 2023
Cited by 2 | Viewed by 1177
Abstract
Non-Newtonian fluids play a crucial role in applications involving heat transfer and mass transfer. The inclusion of nanoparticles in these fluids improves the efficiency of heat and mass transfer processes. This study employs a numerical solution approach to examine the flow of non-Newtonian [...] Read more.
Non-Newtonian fluids play a crucial role in applications involving heat transfer and mass transfer. The inclusion of nanoparticles in these fluids improves the efficiency of heat and mass transfer processes. This study employs a numerical solution approach to examine the flow of non-Newtonian hybrid nanofluids over a plumb cone/plate surface, considering the effects of magnetohydrodynamics (MHD) and thermal radiation. Additionally, we investigate how heat and mass transfer are affected by a fluid containing microorganisms. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations using a similarity transformation to simplify this complex system. We then use the Keller-box finite-difference method to solve these equations. Along with a table presenting the results for skin friction, Nusselt number, Sherwood number, and microbe density number, we present graphical representations of velocity, temperature, concentration, and microorganism diffusion behavior. Our results indicate that the addition of MHD and thermal radiation improves the diffusion of microorganisms, thereby enhancing the rates of heat and mass transfer. Through a comparative analysis with prior research, we demonstrate the reliability of our conclusions. Full article
(This article belongs to the Section Probability and Statistics)
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Figure 1
<p>Physical model.</p>
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<p>Effect of <span class="html-italic">K</span> on velocity.</p>
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<p>Effect of <span class="html-italic">M</span> on velocity.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>N</mi> <mi>r</mi> </msub> </semantics></math> on momentum.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>R</mi> <mi>b</mi> </msub> </semantics></math> on velocity.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> </semantics></math> on temperature.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>2</mn> </msub> </semantics></math> on temperature.</p>
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<p>Effect of <span class="html-italic">K</span> on temperature.</p>
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<p>Effect of <span class="html-italic">M</span> on temperature.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>R</mi> <mi>d</mi> </msub> </semantics></math> on temperature.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>P</mi> <mi>r</mi> </msub> </semantics></math> on temperature.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> </semantics></math> on concentration.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>2</mn> </msub> </semantics></math> on concentration.</p>
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<p>Effect of <span class="html-italic">K</span> on concentration.</p>
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<p>Effect of <span class="html-italic">M</span> on concentration.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>K</mi> <mi>r</mi> </msub> </semantics></math> on concentration.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>S</mi> <mi>c</mi> </msub> </semantics></math> on concentration.</p>
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<p>Effect of <span class="html-italic">K</span> on microorganisms.</p>
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<p>Effect of <span class="html-italic">M</span> on microorganisms.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>K</mi> <mi>r</mi> </msub> </semantics></math> on microorganisms.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>R</mi> <mi>d</mi> </msub> </semantics></math> on microorganisms.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>P</mi> <mi>e</mi> </msub> </semantics></math> on microorganisms.</p>
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<p>Effect of <math display="inline"><semantics> <msub> <mi>L</mi> <mi>b</mi> </msub> </semantics></math> on microorganisms.</p>
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19 pages, 6138 KiB  
Article
Comparative Numerical Analysis for the Error Estimation of the Fluid Flow over an Inclined Axisymmetric Cylinder with a Gyrotactic Microbe
by Fuad A. Awwad, Emad A. A. Ismail, Waris Khan, Taza Gul and Abdul Samad Khan
Symmetry 2023, 15(10), 1811; https://doi.org/10.3390/sym15101811 - 22 Sep 2023
Cited by 1 | Viewed by 1024
Abstract
The numerical investigation of bioconvective nanofluid (NF) flow, which involves gyrotactic microbes and heat and mass transmission analysis above an inclined extending axisymmetric cylinder, is presented in this study. The study aims to investigate the bioconvection flow of nanofluid under the influence of [...] Read more.
The numerical investigation of bioconvective nanofluid (NF) flow, which involves gyrotactic microbes and heat and mass transmission analysis above an inclined extending axisymmetric cylinder, is presented in this study. The study aims to investigate the bioconvection flow of nanofluid under the influence of heat sources/sinks. Through proper transformation, all partial differential equations are transformed into a non-linear ODE scheme. A new set of variables is presented in the directive to get the first-order convectional equations and then solved numerically using bvp4c MATLAB, embedded in the function. The proposed model is validated after calculating the error estimation and obtaining the residual error. The influence of various factors on the velocity, energy, concentration, and density of motile microorganisms is examined and studied. The analysis describes and addresses all physical measures of concentration such as Skin Friction (SF), Sherwood number, the density of motile microorganisms, and Nusselt number. To validate the present study, a comparison is conducted with previous studies, and excellent correspondence is found. In addition, the ND-Solve approach is utilized to confirm the bvp4c. The mathematical model is confirmed through error analysis. This study provides the platform for industrial applications such as cooling capacity polymers, heat exchange, and chemical production sectors. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Computational Fluid Dynamics)
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<p>Configuration of the geometry and coordinates.</p>
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<p>(<b>a</b>–<b>e</b>) Assessment of bvph4c and ND-solve for <math display="inline"><semantics> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>θ</mi> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>χ</mi> <mfenced> <mi>η</mi> </mfenced> <mo> </mo> </mrow> </semantics></math>; Flow chart of bvp4c.</p>
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<p>(<b>a</b>–<b>d</b>) Error estimation for the velocity profile for different values of <math display="inline"><semantics> <mi>γ</mi> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>i</mi> </msub> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>–<b>d</b>) Error estimation for the velocity and temperature profiles with different values of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">N</mi> <mi mathvariant="bold-italic">r</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">N</mi> <mi mathvariant="bold-italic">b</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Influence of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>B</mi> <mi>L</mi> </msub> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>χ</mo> <mfenced> <mi>η</mi> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>b</b>). <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>b</mi> </msub> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>θ</mo> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>b</mi> </msub> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>ϕ</mo> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>t</mi> </msub> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>θ</mo> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math>, (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>t</mi> </msub> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>ϕ</mo> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math>, (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>t</mi> </msub> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <msup> <mi mathvariant="normal">f</mi> <mo>′</mo> </msup> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math>.</p>
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<p>Influence of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>r</mi> </msub> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>θ</mo> <mfenced> <mi>η</mi> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>r</mi> </msub> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>ϕ</mo> <mfenced> <mi>η</mi> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>c</b>)<math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>N</mi> <mi>r</mi> </msub> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>χ</mo> <mfenced> <mi>η</mi> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>e</mi> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>θ</mo> <mfenced> <mi>η</mi> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>r</mi> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>θ</mo> <mfenced> <mi>η</mi> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>r</mi> <mrow> <mo> </mo> <mi>on</mi> <mo> </mo> </mrow> <mo>ϕ</mo> <mfenced> <mi>η</mi> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>h</b>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>r</mi> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>χ</mo> <mfenced> <mi>η</mi> </mfenced> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>–<b>d</b>) Influence of <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>b</mi> </msub> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>–<b>f</b>) Influence of <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>i</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>c</mi> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>–<b>h</b>) Influence of <math display="inline"><semantics> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>α</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mi>γ</mi> </semantics></math>.</p>
Full article ">Figure 9 Cont.
<p>(<b>a</b>–<b>h</b>) Influence of <math display="inline"><semantics> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>α</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mi>γ</mi> </semantics></math>.</p>
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<p>(<b>a</b>–<b>c</b>) Influence of <math display="inline"><semantics> <mi>ξ</mi> </semantics></math> and <math display="inline"><semantics> <mi>σ</mi> </semantics></math>.</p>
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20 pages, 2190 KiB  
Article
Assessment of Bio-Compounds Content, Antioxidant Activity, and Neuroprotective Effect of Red Cabbage (Brassica oleracea var. Capitata rubra) Processed by Convective Drying at Different Temperatures
by Antonio Vega-Galvez, Luis S. Gomez-Perez, Francisca Zepeda, René L. Vidal, Felipe Grunenwald, Nicol Mejías, Alexis Pasten, Michael Araya and Kong Shun Ah-Hen
Antioxidants 2023, 12(9), 1789; https://doi.org/10.3390/antiox12091789 - 21 Sep 2023
Cited by 4 | Viewed by 2269
Abstract
Parkinson’s disease (PD) is the second most common neurodegenerative disorder, and no efficient therapy able to cure or slow down PD is available. In this study, dehydrated red cabbage was evaluated as a novel source of bio-compounds with neuroprotective capacity. Convective drying was [...] Read more.
Parkinson’s disease (PD) is the second most common neurodegenerative disorder, and no efficient therapy able to cure or slow down PD is available. In this study, dehydrated red cabbage was evaluated as a novel source of bio-compounds with neuroprotective capacity. Convective drying was carried out at different temperatures. Total phenolics (TPC), flavonoids (TFC), anthocyanins (TAC), and glucosinolates (TGC) were determined using spectrophotometry, amino acid profile by LC-DAD and fatty acid profile by GC-FID. Phenolic characterization was determined by liquid chromatography-high-resolution mass spectrometry. Cytotoxicity and neuroprotection assays were evaluated in SH-SY5Y human cells, observing the effect on preformed fibrils of α-synuclein. Drying kinetic confirmed a shorter processing time with temperature increase. A high concentration of bio-compounds was observed, especially at 90 °C, with TPC = 1544.04 ± 11.4 mg GAE/100 g, TFC = 690.87 ± 4.0 mg QE/100 g and TGC = 5244.9 ± 260.2 µmol SngE/100 g. TAC degraded with temperature. Glutamic acid and arginine were predominant. Fatty acid profiles were relatively stable and were found to be mostly C18:3n3. The neochlorogenic acid was predominant. The extracts had no cytotoxicity and showed a neuroprotective effect at 24 h testing, which can extend in some cases to 48 h. The present findings underpin the use of red cabbage as a functional food ingredient. Full article
(This article belongs to the Collection Advances in Antioxidant Ingredients from Natural Products)
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<p>Drying kinetics of red cabbage at different process temperatures. <span class="html-italic">MR</span>: Moisture ratio (dimensionless).</p>
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<p>Bio-compounds from dried and fresh red cabbage extracts. (<b>A</b>) TPC (total phenolic content), (<b>B</b>) TFC (total flavonoid content), (<b>C</b>) TAC (total anthocyanin content), and (<b>D</b>) TGC (total glucosinolate content). Different letters indicate significant differences (<span class="html-italic">p</span> &gt; 0.05).</p>
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<p>Antioxidant potential of red cabbage extracts. (<b>A</b>) DPPH assay and (<b>B</b>) ORAC assay. Different letters indicate significant differences (<span class="html-italic">p</span> &gt; 0.05).</p>
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<p>Cytotoxicity of fresh (F) and dried red cabbage extracts at different temperatures (50, 60, 70, 80 and 90 °C). Data are presented as mean and SEM of three independent experiments performed in triplicate. Statistically significant differences were detected by ordinary one-way ANOVA.</p>
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<p>Neuroprotective effects of extracts of red cabbage. (<b>A</b>) at 24 h and (<b>B</b>) at 48 h. Data are presented as mean and SEM of three independent experiments performed in triplicate. Statistically significant differences were detected by ordinary one-way ANOVA (***: <span class="html-italic">p</span> &lt; 0.001; **: <span class="html-italic">p</span> &lt; 0.01; *: <span class="html-italic">p</span> &lt; 0.05).</p>
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<p>PCA assay for all red cabbage extracts related to TPC (total phenolic content), TFC (total flavonoid content), TAC (total anthocyanin content), TGC (total glucosinolate content), ORAC and DPPH (quintupled results) grouped according to neuroprotective effect at 48 h.</p>
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23 pages, 8920 KiB  
Article
Bio-Convection Effects of MHD Williamson Fluid Flow over a Symmetrically Stretching Sheet: Machine Learning
by P. Priyadharshini, V. Karpagam, Nehad Ali Shah and Mansoor H. Alshehri
Symmetry 2023, 15(9), 1684; https://doi.org/10.3390/sym15091684 - 1 Sep 2023
Cited by 4 | Viewed by 1797
Abstract
The primary goal of this research study is to examine the influence of Brownian motion and thermophoresis diffusion with the impact of thermal radiation and the bioconvection of microorganisms in a symmetrically stretching sheet of non-Newtonian typical Williamson fluid. Structures of the momentum, [...] Read more.
The primary goal of this research study is to examine the influence of Brownian motion and thermophoresis diffusion with the impact of thermal radiation and the bioconvection of microorganisms in a symmetrically stretching sheet of non-Newtonian typical Williamson fluid. Structures of the momentum, energy, concentration, and bio-convection equations are interconnected with the imperative partial differential equations (PDEs). Similarity transformations are implemented to translate pertinent complicated partial differential equations into ordinary differential equations (ODEs). The BVP4C approach from the MATLAB assemblage computational methods scheme is extensively impacted by the results of these ODEs. The impact of several physical parameters, including Williamson fluid We(0.2We1.2), the magnetic field parameter M(0.0M2.5), Brownian motion Nb(0.0Nb1.0), thermophoresis diffusion Nt(0.1Nt0.9). In addition, various physical quantities of the skin friction (RexCfx), Nusselt number (Nux), Sherwood number (Shx), and motile microorganisms (Nnx) are occupied and demonstrate the visualization of graphs and tabular values. These outcomes are validated with earlier obtained results, displaying excellent synchronicity in the physical parameters. Furthermore, the physical quantities concerning the non-dimensional parameters are anticipated by employing Multiple Linear Regression (MLR) in Machine Learning (ML) as successfully executed a novelty of this study. These innovative techniques can help to advance development and technologies for future researchers. The real-world implications of this research are that bio-remediation, microbial movements in mixed fluids, and cancer prevention therapy are crucial. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Computational Fluid Dynamics)
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<p>Geometrical interpretation of the problem.</p>
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<p>Flow chart of the proposed approach.</p>
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<p>Impact of <span class="html-italic">M</span> values on <math display="inline"><semantics><mrow><msup><mi>f</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>η</mi><mo>)</mo></mrow></mrow></semantics></math> of velocity distribution.</p>
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<p>Impact of <math display="inline"><semantics><mrow><mi>W</mi><mi>e</mi></mrow></semantics></math> values on <math display="inline"><semantics><mrow><msup><mi>f</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>η</mi><mo>)</mo></mrow></mrow></semantics></math> of velocity distribution.</p>
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<p>Impact of <span class="html-italic">K</span> values on <math display="inline"><semantics><mrow><mi>θ</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math> of temperature distribution.</p>
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<p>Impact of <math display="inline"><semantics><mrow><mi>N</mi><mi>b</mi></mrow></semantics></math> values on <math display="inline"><semantics><mrow><mi>θ</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math> of temperature distribution.</p>
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<p>Impact of <math display="inline"><semantics><mrow><mi>N</mi><mi>t</mi></mrow></semantics></math> values on <math display="inline"><semantics><mrow><mi>θ</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math> of temperature distribution.</p>
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<p>Impact of <math display="inline"><semantics><mrow><mi>S</mi><mi>c</mi></mrow></semantics></math> values on <math display="inline"><semantics><mrow><mi>ϕ</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math> of concentration distribution.</p>
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<p>Impact of <math display="inline"><semantics><msub><mi>σ</mi><mi>m</mi></msub></semantics></math> values on <math display="inline"><semantics><mrow><mi>ϕ</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math> of concentration distribution.</p>
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<p>Impact of <span class="html-italic">E</span> values on <math display="inline"><semantics><mrow><mi>ϕ</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math> of concentration distribution.</p>
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<p>Impact of <math display="inline"><semantics><mrow><mi>L</mi><mi>b</mi></mrow></semantics></math> values on <math display="inline"><semantics><mrow><mi>χ</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math> of microorganism distribution.</p>
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<p>Impact of <math display="inline"><semantics><mrow><mi>P</mi><mi>e</mi></mrow></semantics></math> values on <math display="inline"><semantics><mrow><mi>χ</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math> of microorganism distribution.</p>
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<p>Impact of the skin friction coefficient on the magnetic field parameter and Williamson fluid parameter.</p>
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<p>Impact of the Nusselt number on the Prandtl number and thermophoresis diffusion.</p>
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<p>Impact of the Sherwood number on the Schmidt number and Brownian motion factor.</p>
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<p>Impact of the number of motile microorganisms on the bio-convection Lewis number and Peclet number.</p>
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21 pages, 7035 KiB  
Article
Melting Heat Transfer Rheology in Bioconvection Cross Nanofluid Flow Confined by a Symmetrical Cylindrical Channel with Thermal Conductivity and Swimming Microbes
by Fuad A. Awwad, Emad A. A. Ismail, Taza Gul, Waris Khan and Ishtiaq Ali
Symmetry 2023, 15(9), 1647; https://doi.org/10.3390/sym15091647 - 25 Aug 2023
Cited by 4 | Viewed by 1075
Abstract
Nonlinear thermal transport of non-Newtonian polymer flows is an increasingly important area in materials engineering. Motivated by new developments in this area which entail more refined and more mathematical frameworks, the present analysis investigates the boundary-layer approximation and heat transfer persuaded by a [...] Read more.
Nonlinear thermal transport of non-Newtonian polymer flows is an increasingly important area in materials engineering. Motivated by new developments in this area which entail more refined and more mathematical frameworks, the present analysis investigates the boundary-layer approximation and heat transfer persuaded by a symmetrical cylindrical surface positioned horizontally. To simulate thermal relaxation impacts, the bioconvection Cross nanofluid flow Buongiorno model is deployed. The study examines the magnetic field effect applied to the nanofluid using the heat generated, as well as the melting phenomenon. The nonlinear effect of thermosolutal buoyant forces is incorporated into the proposed model. The novel mathematical equations include thermophoresis and Brownian diffusion effects. Via robust transformation techniques, the primitive resulting partial equations for momentum, energy, concentration, and motile living microorganisms are rendered into nonlinear ordinary equations with convective boundary postulates. An explicit and efficient numerical solver procedure in the Mathematica 11.0 programming platform is developed to engage the nonlinear equations. The effects of multiple governing parameters on dimensionless fluid profiles is examined using plotted visuals and tables. Finally, outcomes related to the surface drag force, heat, and mass transfer coefficients for different influential parameters are presented using 3D visuals. Full article
(This article belongs to the Special Issue Symmetry in System Theory, Control and Computing)
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Figure 1
<p>(<b>a</b>) Physical configuration and coordinates; (<b>b</b>) computational flow chart.</p>
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<p>(<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>u</mi> <mn>0</mn> <mo>′</mo> </msubsup> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>Re</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <mi>α</mi> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>u</mi> <mn>0</mn> <mo>′</mo> </msubsup> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>a</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <mi>λ</mi> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>u</mi> <mn>0</mn> <mo>′</mo> </msubsup> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>M</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <mi>N</mi> <mi>c</mi> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>u</mi> <mn>0</mn> <mo>′</mo> </msubsup> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <mi>N</mi> <mi>r</mi> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>ς</mi> </mfenced> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>N</mi> <mi>t</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <msub> <mi>θ</mi> <mi>w</mi> </msub> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>ς</mi> </mfenced> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>i</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <mi>ε</mi> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>ς</mi> </mfenced> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>a</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <mi>α</mi> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced> <mi>ς</mi> </mfenced> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>Pr</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <mi>λ</mi> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <mi>h</mi> <mfenced> <mi>ς</mi> </mfenced> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>N</mi> <mi>t</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <mi>L</mi> <mi>e</mi> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <mi>h</mi> <mfenced> <mi>ς</mi> </mfenced> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>N</mi> <mi>t</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <msub> <mo>∈</mo> <mn>1</mn> </msub> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <mi>h</mi> <mfenced> <mi>ς</mi> </mfenced> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>a</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <mi>α</mi> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) Υ<math display="inline"><semantics> <mrow> <mfenced> <mi>ς</mi> </mfenced> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>L</mi> <mi>b</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo> </mo> <mi mathvariant="normal">P</mi> </mrow> <mi>e</mi> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) Υ<math display="inline"><semantics> <mrow> <mfenced> <mi>ς</mi> </mfenced> </mrow> </semantics></math> impacts for various <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>a</mi> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <mi>α</mi> </mrow> </semantics></math>.</p>
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<p>Skin friction estimation via <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mi>N</mi> <mi>r</mi> <mo>,</mo> <mi>N</mi> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> parameters.</p>
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<p>Skin friction estimation via <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>a</mi> <mo>,</mo> <mi>M</mi> <mi>a</mi> <mo>,</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> parameters.</p>
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<p>Heat transfer estimation via <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>M</mi> <mi>a</mi> <mo>,</mo> <mi>P</mi> <mi>r</mi> <mo>,</mo> <mi>N</mi> <mi>b</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> parameters.</p>
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<p>Heat transfer estimation via different physical parameters <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>N</mi> <mi>t</mi> <mo>,</mo> <mi>R</mi> <mi>d</mi> <mo>,</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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<p>Mass flow rate estimation via different physical parameters <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>L</mi> <mi>e</mi> <mo>,</mo> <mi>Pr</mi> <mo>,</mo> <mi>N</mi> <mi>b</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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<p>Mass flow rate estimation via different physical parameters <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>α</mi> <mo>,</mo> <mi>N</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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<p>Microorganism estimation via different physical parameters <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>M</mi> <mi>a</mi> <mo>,</mo> <mi>L</mi> <mi>b</mi> <mo>,</mo> <mi>P</mi> <mi>e</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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19 pages, 7189 KiB  
Review
Second-Generation Bio-Fuels: Strategies for Employing Degraded Land for Climate Change Mitigation Meeting United Nation-Sustainable Development Goals
by Atreyi Pramanik, Aashna Sinha, Kundan Kumar Chaubey, Sujata Hariharan, Deen Dayal, Rakesh Kumar Bachheti, Archana Bachheti and Anuj K. Chandel
Sustainability 2023, 15(9), 7578; https://doi.org/10.3390/su15097578 - 5 May 2023
Cited by 8 | Viewed by 3531
Abstract
Increased Greenhouse Gas (GHG) emissions from both natural and man-made systems contribute to climate change. In addition to reducing the use of crude petroleum’s derived fuels, and increasing tree-planting efforts and sustainable practices, air pollution can be minimized through phytoremediation. Bio-fuel from crops [...] Read more.
Increased Greenhouse Gas (GHG) emissions from both natural and man-made systems contribute to climate change. In addition to reducing the use of crude petroleum’s derived fuels, and increasing tree-planting efforts and sustainable practices, air pollution can be minimized through phytoremediation. Bio-fuel from crops grown on marginal land can sustainably address climate change, global warming, and geopolitical issues. There are numerous methods for producing renewable energy from both organic and inorganic environmental resources (sunlight, air, water, tides, waves, and convective energy), and numerous technologies for doing the same with biomass with different properties and derived from different sources (food industry, agriculture, forestry). However, the production of bio-fuels is challenging and contentious in many parts of the world since it competes for soil with the growth of crops and may be harmful to the environment. Therefore, it is necessary to use wildlife management techniques to provide sustainable bio-energy while maintaining or even improving essential ecosystem processes. The second generation of bio-fuels is viewed as a solution to the serious issue. Agricultural lignocellulosic waste is the primary source of second-generation bio-fuel, possibly the bio-fuel of the future. Sustainable practices to grow biomass, followed by their holistic conversion into ethanol with desired yield and productivity, are the key concerns for employing renewable energy mix successfully. In this paper, we analyze the various types of bio-fuels, their sources, and their production and impact on sustainability. Full article
(This article belongs to the Special Issue Prospects and Challenges of Bioeconomy Sustainability Assessment)
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<p>17 UN-SDG goals.</p>
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<p>Flow diagram showing the selection criteria and procedure of second-generation bio-fuels production.</p>
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<p>Waste energy inverse pyramid.</p>
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<p>Methods and turning MSW into energy.</p>
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<p>Bio-fuel products from lignocellulosic biomass.</p>
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<p>An overview of biodiesel production from algal feedstock.</p>
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<p>Figure shows that a transition to green fuels will result in a green environment resulting in clean energy.</p>
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25 pages, 7382 KiB  
Article
Evolutionary Padé Approximation for Heat and Mass Transfer Analysis of Falkner–Skan Flow of a Bio-Convective Casson Fluid
by Ghada Ali Basendwah, Nauman Raza and Javaid Ali
Mathematics 2023, 11(7), 1688; https://doi.org/10.3390/math11071688 - 31 Mar 2023
Cited by 2 | Viewed by 1106
Abstract
This study presents numerical work to investigate the Falkner–Skan flow of a bio-convective Casson fluid over a wedge using an Evolutionary Padé Approximation (EPA) scheme. The governing partial differential equations and boundary conditions of a Falkner–Skan flow model are transformed to a system [...] Read more.
This study presents numerical work to investigate the Falkner–Skan flow of a bio-convective Casson fluid over a wedge using an Evolutionary Padé Approximation (EPA) scheme. The governing partial differential equations and boundary conditions of a Falkner–Skan flow model are transformed to a system of ordinary differential equations involving ten dimensionless parameters by using similarity transformations. In the proposed EPA framework, an equivalent constrained optimization problem is formed. The solution of the resulting optimization problem is analogous to the solution of the dimensionless system of ordinary differential equations. The solutions produced in this work, with respect to various combinations of the physical parameters, are found to be in good agreement with those reported in the previously published literature. The effects of a non-dimensional physical-parameter wedge, Casson fluid, fluid phase effective heat capacity, Brownian motion, thermophoresis, radiation, and magnetic field on velocity profile, temperature profile, fluid concentration profile, and the density of motile microorganisms are discussed and presented graphically. It is observed that the fluid velocity rises with a rise in the Casson fluid viscosity force parameter, and an increase in the Prandtl number causes a decrease in the heat transfer rate. Another significant observation is that the temperature and fluid concentration fields are greatly increased by an increase in the thermophoresis parameter. An increase in the Péclet number suppresses the microorganism density. Moreover, the increased values of the Prandtl number increase the local Nusslet number, whereas the skin friction is increased when an increase in the Prandtl number occurs. Full article
(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)
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<p>Physical configuration of Falkner–Skan flow model.</p>
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<p>(<b>a</b>) DE based exploration in <math display="inline"><semantics> <mrow> <msup> <mi mathvariant="double-struck">R</mi> <mn>2</mn> </msup> </mrow> </semantics></math> (<b>b</b>) Schematic diagram of NMS method.</p>
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<p>Schematic diagram of EPA scheme.</p>
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<p>Convergence curves of optimization process for velocity profiles with respect to variations in (<b>a</b>) Casson fluid viscosity force parameter (<b>b</b>) Magnetic field parameter (<b>c</b>) Hartree pressure gradient parameter.</p>
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<p>Impact of Casson fluid viscosity force parameter on velocity profile.</p>
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<p>Impact of magnetic field parameter on velocity profile.</p>
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<p>Impact of fluid flow parameter on velocity profile.</p>
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<p>Convergence curves of optimization process for temperature field with respect to variations in (<b>a</b>) Radiation parameter (<b>b</b>) Prandtl number (<b>c</b>) Thermophoresis parameter.</p>
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<p>Impact of radiation parameter on temperature field.</p>
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<p>Impact of Prandtl number on temperature field.</p>
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<p>Impact of thermophoresis parameter on temperature field.</p>
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<p>Impact of magnetic field parameter on fluid’s concentration.</p>
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<p>Impact of thermophoresis parameter on fluid’s concentration field.</p>
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<p>Impact of Casson fluid viscosity force parameter on fluid’s concentration field.</p>
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<p>Convergence curves of optimization process for (<b>a</b>) concentration and (<b>b</b>) density fields.</p>
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<p>Impact of radiation parameter on density profile of microorganism.</p>
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<p>Impact of Péclet number on microorganism density field.</p>
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<p>Impact of fluid parameter on microorganism density field.</p>
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14 pages, 1880 KiB  
Article
Significance of Weissenberg Number, Soret Effect and Multiple Slips on the Dynamic of Biconvective Magnetohydrodynamic Carreau Nanofuid Flow
by Pardeep Kumar, Hemant Poonia, Liaqat Ali, Nehad Ali Shah and Jae Dong Chung
Mathematics 2023, 11(7), 1685; https://doi.org/10.3390/math11071685 - 31 Mar 2023
Cited by 16 | Viewed by 2397
Abstract
This study focused on the analysis of two-dimensional incompressible magnetohydrodynamic Carreau nanofluid flow across a stretching cylinder containing microorganisms with the impacts of chemical reactions and multiple slip boundary conditions. Moreover, the main objective is concerned with the enhancement of thermal transportation with [...] Read more.
This study focused on the analysis of two-dimensional incompressible magnetohydrodynamic Carreau nanofluid flow across a stretching cylinder containing microorganisms with the impacts of chemical reactions and multiple slip boundary conditions. Moreover, the main objective is concerned with the enhancement of thermal transportation with the effect of heat source and bioconvection. By assigning pertinent similarity transitions to the governing partial differential equations, a series of equations (ODES) is generated. An optimum computational solver, namely the bvp5c software package, is utilized for numerical estimations. The impact of distinct parameters on thermal expansion, thermophoresis, and the Nusselt number has been emphasized, employing tables, diagrams, and surface maps for both shear thinning (n < 1) and shear thickening (n > 1) instances. Motile concentration profiles decrease with Lb and the motile microorganism density slip parameter. It is observed that with increasing values of Pr, both the boundary layer thickness and temperature declined in both cases. The Weissenberg number demonstrates a different nature depending on the type of fluid; skin friction, the velocity profile and Nusselt number drop when n < 1 and increase when n > 1. The two- and three-dimensional graphs show the simultaneous effect of involving parameters with physical quantities. The accuracy of the existing observations is evidenced by the impressive resemblance between the contemporary and preceding remedies. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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<p>Graphical representation of the model.</p>
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<p>Variation in velocity profile with simultaneous effect of M and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>1</mn> </msub> </semantics></math> in (<b>a</b>,<b>b</b>).</p>
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<p>Simultaneous effect of <math display="inline"><semantics> <msub> <mi>W</mi> <mi>e</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>1</mn> </msub> </semantics></math> for both <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>&lt;</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>&gt;</mo> <mn>1</mn> </mrow> </semantics></math> on velocity profile in (<b>a</b>,<b>b</b>).</p>
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<p>Temperature distribution fluctuation with simultaneous effect of M and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>2</mn> </msub> </semantics></math> for both cases in (<b>a</b>,<b>b</b>).</p>
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<p>Temperature distribution variation with simultaneous effect of <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>r</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>2</mn> </msub> </semantics></math> for both cases in (<b>a</b>,<b>b</b>).</p>
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<p>Concentration profile fluctuation against simultaneous effect of <math display="inline"><semantics> <msub> <mi>C</mi> <mi>h</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>3</mn> </msub> </semantics></math> for both cases in (<b>a</b>,<b>b</b>).</p>
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<p>Motile concentration profile fluctuation with simultaneous effect of <math display="inline"><semantics> <msub> <mi>L</mi> <mi>b</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>4</mn> </msub> </semantics></math> for both the shearing thinning and shear thickening situations in (<b>a</b>,<b>b</b>).</p>
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<p>Variation in <math display="inline"><semantics> <mrow> <mo>{</mo> <mi>C</mi> <msub> <mi>f</mi> <mi>x</mi> </msub> <mi>R</mi> <msubsup> <mi>e</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <mo>}</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mo stretchy="false">{</mo> <mi>N</mi> <msub> <mi>u</mi> <mi>x</mi> </msub> <mi>R</mi> <msubsup> <mi>e</mi> <mi>x</mi> <mrow> <mo>−</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">}</mo> </mrow> </semantics></math>, for different values of <math display="inline"><semantics> <msub> <mi>W</mi> <mi>e</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>2</mn> </msub> </semantics></math> for both dilatant and pseudoplastic fluids.</p>
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<p>Variation in <math display="inline"><semantics> <mrow> <mo stretchy="false">{</mo> <mi>N</mi> <msub> <mi>n</mi> <mi>x</mi> </msub> <mi>R</mi> <msubsup> <mi>e</mi> <mi>x</mi> <mrow> <mo>−</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">}</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mo stretchy="false">{</mo> <mi>S</mi> <msub> <mi>h</mi> <mi>x</mi> </msub> <mi>R</mi> <msubsup> <mi>e</mi> <mi>x</mi> <mrow> <mo>−</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">}</mo> </mrow> </semantics></math>, for different values of <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>e</mi> </mrow> </semantics></math>, <span class="html-italic">M</span> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>3</mn> </msub> </semantics></math> for dilatant fluid and pseudoplastic fluid.</p>
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14 pages, 5901 KiB  
Article
Enhancement of Molecular Transport into Film Stacked Structures for Micro-Immunoassay by Unsteady Rotation
by Hinata Maeno, Satoshi Ogata, Tetsuhide Shimizu and Ming Yang
Micromachines 2023, 14(4), 744; https://doi.org/10.3390/mi14040744 - 28 Mar 2023
Cited by 1 | Viewed by 1710
Abstract
A film-stacked structure consisting of polyethylene terephthalate (PET) films stacked in a gap of 20 µm that can be combined with 96-well microplates used in biochemical analysis has been developed by the authors. When this structure is inserted into a well and rotated, [...] Read more.
A film-stacked structure consisting of polyethylene terephthalate (PET) films stacked in a gap of 20 µm that can be combined with 96-well microplates used in biochemical analysis has been developed by the authors. When this structure is inserted into a well and rotated, convection flow is generated in the narrow gaps between the films to enhance the chemical/bio reaction between the molecules. However, since the main component of the flow is a swirling flow, only a part of the solution circulates into the gaps, and reaction efficiency is not achieved as designed. In this study, an unsteady rotation is applied to promote the analyte transport into the gaps using the secondary flow generated on the surface of the rotating disk. Finite element analysis is used to evaluate the changes in flow and concentration distribution for each rotation operation and to optimize the rotation conditions. In addition, the molecular binding ratio for each rotation condition is evaluated. It is shown that the unsteady rotation accelerates the binding reaction of proteins in an ELISA (Enzyme Linked Immunosorbent Assay), a type of immunoassay. Full article
(This article belongs to the Special Issue μ-TAS: A Themed Issue in Honor of Professor Andreas Manz)
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<p>Schematic image for fabrication of 3D-Stack and utilization within a well.</p>
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<p>Specification of 3D-Stack in a well and the simulation model.</p>
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<p>An imaging process for calculation of high concentration area.</p>
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<p>Scheme of sandwich ELISA using a conventional 96-well plate and 3D-Stack methods. Black Y is goat anti-human IgA antibody; Green Y with orrange dots is detection antibody with HRP; gray dots are BSA for blocking; red dot are human IgA, Orange squares in last step are AMB substrate.</p>
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<p>Process for evaluation of binding rate in a sandwich ELISA.</p>
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<p>Calculated changes in concentration distribution of analytes in steady rotation conditions.</p>
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<p>Calculated increase in binding rate during steady rotation.</p>
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<p>Calculated image of variation in concentration distributions after stopping the flow.</p>
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<p>Calculated variation in concentration distributions after stopping the flow in 0.1 s and re-rotation.</p>
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<p>Calculated increase in the binding rate for stop and re-rotation compared to steady rotation conditions.</p>
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<p>Calculated variation in interfacial area between high and low concentration.</p>
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<p>Calculated variation in binding rate after repeating the stopping and re-rotating for 30 s by stopping time in 0.1 s and changing rotation time from 0.1 s to 10 s.</p>
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<p>Calculated variation in volume of reacted solution responding to rotation time.</p>
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<p>Experimental results on binding rate for various reaction times.</p>
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<p>Calibration curve for ELISA of IgA using 96 well and 96 well with 3D-Stack.</p>
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<p>Coefficient of variation in the result of absorbance for each condition of ELISA.</p>
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