Abstract
A new kind of heat transfer fluid called hybrid nanofluid was introduced to enhance the performance of heat exchangers. The flow behavior may be investigated numerically to better comprehend the fluid features. This investigation aspires to unravel the boundary layer flow problem near the stagnation point of unsteady hybrid nanofluid. Such fluid is saturated in a porous medium on a vertical plate with the exertion of mixed convection. The governing model of the flow problem in the form of partial differential equations is simplified into ordinary differential equations by incorporating the appropriate similarity transformation. A built-in finite difference code in MATLAB known as boundary value problem of fourth-order code (bvp4c) is employed to solve the flow problem and execute the numerical solutions. The dual solutions generated by the solver necessitate the implementation of stability analysis, where this analysis indicates only the first solution is stable. As per stable solution, the heat transfer is augmented when the volume concentration of copper is increasingly added to the alumina–water nanofluid suspension. The conversion of the fluid state from laminar to turbulent also can be prevented with the inclusion of a suitable higher volume concentration of copper. The higher value of the first and second resistant parameters due to porous media is considered in this investigation which concludes that these parameters aid in improving the heat transfer and skin friction rates. This investigation has proven hybrid nanofluid's ability to reinforce the heat transfer with the embedment of a porous medium.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Brunton SL, Noack BR, Koumoutsakos P (2020) Machine learning for fluid mechanics. Annu Rev Fluid Mech 52:477–508. https://doi.org/10.1146/annurev-fluid-010719-060214
Kochkov D, Smith JA, Alieva A et al (2021) Machine learning–accelerated computational fluid dynamics. Proc Natl Acad Sci 118:e2101784118. https://doi.org/10.1073/pnas.2101784118
Li Y, Chang J, Kong C, Bao W (2021) Recent progress of machine learning in flow modeling and active flow control. Chin J Aeronaut. https://doi.org/10.1016/j.cja.2021.07.027
Sabir O, M. Y. S. Tuan Ya T (2014) A new artificial neural network approach for fluid flow simulations: In: Proceedings of the international conference on neural computation theory and applications. SCITEPRESS—science and technology publications, Rome, Italy, pp 334–338
Sodhro AH, Li Y, Shah MA (2016) Energy-efficient adaptive transmission power control for wireless body area networks. IET Commun 10:81–90. https://doi.org/10.1049/iet-com.2015.0368
Sodhro AH, S.Obaidat M, Pirbhulal S, et al (2019) A novel energy optimization approach for artificial intelligence-enabled massive internet of things. In: 2019 international symposium on performance evaluation of computer and telecommunication systems (SPECTS). IEEE, Berlin, Germany, pp 1–6
Ahmad I, Shahabuddin S, Malik H et al (2020) Machine learning meets communication networks: current trends and future challenges. IEEE Access 8:223418–223460. https://doi.org/10.1109/ACCESS.2020.3041765
Zhang T, Sodhro AH, Luo Z et al (2020) A joint deep learning and internet of medical things driven framework for elderly patients. IEEE Access 8:75822–75832. https://doi.org/10.1109/ACCESS.2020.2989143
Wang D, Zhao N, Song B et al (2021) Resource management for secure computation offloading in softwarized cyber-physical systems. IEEE Internet Things J 8:9294–9304. https://doi.org/10.1109/JIOT.2021.3057594
Song F, Ai Z, Zhang H et al (2021) Smart collaborative balancing for dependable network components in cyber-physical systems. IEEE Trans Ind Inform 17:6916–6924. https://doi.org/10.1109/TII.2020.3029766
Raisin SN, Jamaludin J, Mohd Rahalim F et al (2020) Cyber-physical system (CPS) application- a review. Reka Elkomika J Pengabdi Kpd Masy 1:52–65. https://doi.org/10.26760/rekaelkomika.v1i2.52-65
Mackowski AW, Williamson CHK (2011) Developing a cyber-physical fluid dynamics facility for fluid–structure interaction studies. J Fluids Struct 27:748–757. https://doi.org/10.1016/j.jfluidstructs.2011.03.020
Guo L, Yan Y, Sun W, Zhu J (2017) Numerical investigation of flow unsteadiness and heat transfer on suction surface of rotating airfoils within a gas turbine cascade. Propuls Power Res 6:91–100. https://doi.org/10.1016/j.jppr.2017.05.005
Shafiq A, Sindhu TN (2017) Statistical study of hydromagnetic boundary layer flow of Williamson fluid regarding a radiative surface. Results Phys 7:3059–3067. https://doi.org/10.1016/j.rinp.2017.07.077
Gowda RB, Anwar MI, Manar FH, et al (2017) A cyber-physical fluid dynamics investigation of the impact of fluid structure interaction on low-Reynolds number wings and leading edge vortex evolution. In: 35th AIAA Applied Aerodynamics Conference. American Institute of Aeronautics and Astronautics, Denver, Colorado
El Hasadi YMF, Padding JT (2019) Solving fluid flow problems using semi-supervised symbolic regression on sparse data. AIP Adv 9:115218. https://doi.org/10.1063/1.5116183
Malika M, Bhad R, Sonawane SS (2021) ANSYS simulation study of a low volume fraction CuO–ZnO/water hybrid nanofluid in a shell and tube heat exchanger. J Indian Chem Soc 98:100200. https://doi.org/10.1016/j.jics.2021.100200
Saadoon ZH, Ali FH, Sheikholeslami M (2021) Numerical investigation of heat transfer enhancement using (Fe3O4 and Ag-H2O) nanofluids in (converge-diverge) mini-channel heat sinks. Mater Today Proc. https://doi.org/10.1016/j.matpr.2021.07.091
Zohary AC, Asrar W, Aldheeb M (2021) Numerical investigation on the pressure drag of some low-speed airfoils for UAV application. CFD Lett 13:29–48. https://doi.org/10.37934/cfdl.13.2.2948
Hanif H (2022) A computational approach for boundary layer flow and heat transfer of fractional Maxwell fluid. Math Comput Simul 191:1–13. https://doi.org/10.1016/j.matcom.2021.07.024
Hiemenz K (1911) Die Grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder. Dinglers Polytech J 326:321–324
Homann F (1936) Der Einfluß großer Zähigkeit bei der Strömung um den Zylinder und um die Kugel. ZAMM J Appl Math Mech Z Für Angew Math Mech 16:153–164. https://doi.org/10.1002/zamm.19360160304
Choi SUS, Eastman JA (1995) Enhancing thermal conductivity of fluids with nanoparticles. ASME Fluids Eng Div 231:99–106
Sidik NAC, Adamu IM, Jamil MM et al (2016) Recent progress on hybrid nanofluids in heat transfer applications: a comprehensive review. Int Commun Heat Mass Transf 78:68–79. https://doi.org/10.1016/j.icheatmasstransfer.2016.08.019
Babu JR, Kumar KK, Rao SS (2017) State-of-art review on hybrid nanofluids. Renew Sustain Energy Rev 77:551–565. https://doi.org/10.1016/j.rser.2017.04.040
Huminic G, Huminic A (2018) Hybrid nanofluids for heat transfer applications—a state-of-the-art review. Int J Heat Mass Transf 125:82–103. https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.059
Kshirsagar DP, Venkatesh MA (2021) A review on hybrid nanofluids for engineering applications. Mater Today Proc 44:744–755. https://doi.org/10.1016/j.matpr.2020.10.637
Abdullah AA, Ibrahim FS, Abdel Gawad AF, Batyyb A (2015) Investigation of unsteady mixed convection flow near the stagnation point of a heated vertical plate embedded in a nanofluid-saturated porous medium by self-similar technique. Am J Energy Eng 3:42. https://doi.org/10.11648/j.ajee.s.2015030401.13
Buongiorno J (2006) Convective transport in nanofluids. J Heat Transf 128:240–250. https://doi.org/10.1115/1.2150834
Sarkar J, Ghosh P, Adil A (2015) A review on hybrid nanofluids: recent research, development and applications. Renew Sustain Energy Rev 43:164–177. https://doi.org/10.1016/j.rser.2014.11.023
Tiwari RK, Das MK (2007) Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transf 50:2002–2018. https://doi.org/10.1016/j.ijheatmasstransfer.2006.09.034
Takabi B, Salehi S (2015) Augmentation of the heat transfer performance of a sinusoidal corrugated enclosure by employing hybrid nanofluid. Adv Mech Eng 6:147059. https://doi.org/10.1155/2014/147059
Suresh S, Venkitaraj KP, Selvakumar P, Chandrasekar M (2011) Synthesis of Al2O3–Cu/water hybrid nanofluids using two step method and its thermo physical properties. Colloids Surf Physicochem Eng Asp 388:41–48. https://doi.org/10.1016/j.colsurfa.2011.08.005
Ghadikolaei SS, Yassari M, Sadeghi H et al (2017) Investigation on thermophysical properties of Tio2–Cu/H2O hybrid nanofluid transport dependent on shape factor in MHD stagnation point flow. Powder Technol 322:428–438. https://doi.org/10.1016/j.powtec.2017.09.006
Nadeem S, Abbas N, Khan AU (2018) Characteristics of three dimensional stagnation point flow of Hybrid nanofluid past a circular cylinder. Res Phys 8:829–835. https://doi.org/10.1016/j.rinp.2018.01.024
Aly EH, Pop I (2020) MHD flow and heat transfer near stagnation point over a stretching/shrinking surface with partial slip and viscous dissipation: hybrid nanofluid versus nanofluid. Powder Technol 367:192–205. https://doi.org/10.1016/j.powtec.2020.03.030
Abbasian Arani AA, Aberoumand H (2021) Stagnation-point flow of Ag-CuO/water hybrid nanofluids over a permeable stretching/shrinking sheet with temporal stability analysis. Powder Technol 380:152–163. https://doi.org/10.1016/j.powtec.2020.11.043
Zainal NA, Nazar R, Naganthran K, Pop I (2020) Unsteady stagnation point flow of hybrid nanofluid past a convectively heated stretching/shrinking sheet with velocity slip. Mathematics 8:1649. https://doi.org/10.3390/math8101649
Zainal NA, Nazar R, Naganthran K, Pop I (2020) Unsteady three-dimensional MHD non-axisymmetric Homann stagnation point flow of a hybrid nanofluid with stability analysis. Mathematics 8:784. https://doi.org/10.3390/math8050784
Zainal NA, Nazar R, Naganthran K, Pop I (2021) Unsteady EMHD stagnation point flow over a stretching/shrinking sheet in a hybrid Al2O3-Cu/H2O nanofluid. Int Commun Heat Mass Transf 123:105205. https://doi.org/10.1016/j.icheatmasstransfer.2021.105205
Zainal NA, Nazar R, Naganthran K, Pop I (2021) Unsteady MHD stagnation point flow induced by exponentially permeable stretching/shrinking sheet of hybrid nanofluid. Eng Sci Technol Int J 24:1201–1210. https://doi.org/10.1016/j.jestch.2021.01.018
Anuar NS, Bachok N (2021) Double solutions and stability analysis of micropolar hybrid nanofluid with thermal radiation impact on unsteady stagnation point flow. Mathematics 9:276. https://doi.org/10.3390/math9030276
Waini I, Ishak A, Pop I (2021) Unsteady hybrid nanofluid flow on a stagnation point of a permeable rigid surface. ZAMM J Appl Math Mech Z Für Angew Math Mech https://doi.org/10.1002/zamm.202000193
Rostami MN, Dinarvand S, Pop I (2018) Dual solutions for mixed convective stagnation-point flow of an aqueous silica–alumina hybrid nanofluid. Chin J Phys 56:2465–2478. https://doi.org/10.1016/j.cjph.2018.06.013
Khan MR, Pan K, Khan AU, Nadeem S (2020) Dual solutions for mixed convection flow of SiO2−Al2O3/water hybrid nanofluid near the stagnation point over a curved surface. Phys Stat Mech Its Appl 547:123959. https://doi.org/10.1016/j.physa.2019.123959
Zainal NA, Nazar R, Naganthran K, Pop I (2020) MHD mixed convection stagnation point flow of a hybrid nanofluid past a vertical flat plate with convective boundary condition. Chin J Phys 66:630–644. https://doi.org/10.1016/j.cjph.2020.03.022
Khashiie NS, Md Arifin N, Pop I (2020) Mixed convective stagnation point flow towards a vertical riga plate in hybrid Cu-Al2O3/water nanofluid. Mathematics 8:912. https://doi.org/10.3390/math8060912
Jamaludin A, Naganthran K, Nazar R, Pop I (2020) MHD mixed convection stagnation-point flow of Cu-Al2O3/water hybrid nanofluid over a permeable stretching/shrinking surface with heat source/sink. Eur J Mech B Fluids 84:71–80. https://doi.org/10.1016/j.euromechflu.2020.05.017
Khan U, Zaib A, Abu Bakar S, Ishak A (2021) Stagnation-point flow of a hybrid nanoliquid over a non-isothermal stretching/shrinking sheet with characteristics of inertial and microstructure. Case Stud Therm Eng 26:101150. https://doi.org/10.1016/j.csite.2021.101150
Khashi’ie NS, Arifin NM, Merkin JH, et al (2021) Mixed convective stagnation point flow of a hybrid nanofluid toward a vertical cylinder. Int J Numer Methods Heat Fluid Flow. https://doi.org/10.1108/HFF-11-2020-0725
Wahid NS, Arifin NM, Khashi’ie NS, Pop I, (2021) Mixed convection of a three-dimensional stagnation point flow on a vertical plate with surface slip in a hybrid nanofluid. Chin J Phys 74:129–143. https://doi.org/10.1016/j.cjph.2021.08.013
Ishak A, Merkin JH, Nazar R, Pop I (2008) Mixed convection boundary layer flow over a permeable vertical surface with prescribed wall heat flux. Z Für Angew Math Phys 59:100–123. https://doi.org/10.1007/s00033-006-6082-7
Bachok N, Ishak A, Pop I (2013) Mixed convection boundary layer flow over a moving vertical flat plate in an external fluid flow with viscous dissipation effect. PLoS ONE 8:e60766. https://doi.org/10.1371/journal.pone.0060766
Jamaludin A, Nazar R, Pop I (2017) Three-dimensional mixed convection stagnation-point flow over a permeable vertical stretching/shrinking surface with a velocity slip. Chin J Phys 55:1865–1882. https://doi.org/10.1016/j.cjph.2017.08.006
Khan U, Zaib A, Abu Bakar S et al (2021) Buoyancy effect on the stagnation point flow of a hybrid nanofluid toward a vertical plate in a saturated porous medium. Case Stud Therm Eng 27:101342. https://doi.org/10.1016/j.csite.2021.101342
Merkin JH (1980) Mixed convection boundary layer flow on a vertical surface in a saturated porous medium. J Eng Math 14:301–313. https://doi.org/10.1007/BF00052913
Ahmad K, Ishak A (2017) Magnetohydrodynamic (MHD) Jeffrey fluid over a stretching vertical surface in a porous medium. Propuls Power Res 6:269–276. https://doi.org/10.1016/j.jppr.2017.11.007
Waini I, Ishak A, Groşan T, Pop I (2020) Mixed convection of a hybrid nanofluid flow along a vertical surface embedded in a porous medium. Int Commun Heat Mass Transf 114:104565. https://doi.org/10.1016/j.icheatmasstransfer.2020.104565
Khashiie NS, Arifin NM, Pop I (2020) Non-Darcy mixed convection of hybrid nanofluid with thermal dispersion along a vertical plate embedded in a porous medium. Int Commun Heat Mass Transf 118:104866. https://doi.org/10.1016/j.icheatmasstransfer.2020.104866
Fatunmbi EO, Ogunseye HA, Sibanda P (2020) Magnetohydrodynamic micropolar fluid flow in a porous medium with multiple slip conditions. Int Commun Heat Mass Transf 115:104577. https://doi.org/10.1016/j.icheatmasstransfer.2020.104577
Mat Noor NA, Shafie S, Admon MA (2020) Effects of viscous dissipation and chemical reaction on MHD squeezing flow of Casson nanofluid between parallel plates in a porous medium with slip boundary condition. Eur Phys J Plus 135:855. https://doi.org/10.1140/epjp/s13360-020-00868-w
Haider F, Hayat T, Alsaedi A (2021) Flow of hybrid nanofluid through Darcy-Forchheimer porous space with variable characteristics. Alex Eng J 60:3047–3056. https://doi.org/10.1016/j.aej.2021.01.021
Jafar AB, Shafie S, Ullah I (2020) MHD radiative nanofluid flow induced by a nonlinear stretching sheet in a porous medium. Heliyon 6:e04201. https://doi.org/10.1016/j.heliyon.2020.e04201
Khanafer K, Vafai K (2019) Applications of nanofluids in porous medium: a critical review. J Therm Anal Calorim 135:1479–1492. https://doi.org/10.1007/s10973-018-7565-4
Khanafer K, Vafai K (2019) A critical review on the applications of fluid-structure interaction in porous media. Int J Numer Methods Heat Fluid Flow 30:308–327. https://doi.org/10.1108/HFF-07-2019-0592
Menni Y, Chamkha AJ, Azzi A (2019) Nanofluid transport in porous media: a review. Spec Top Rev Porous Media Int J 10:49–64. https://doi.org/10.1615/SpecialTopicsRevPorousMedia.2018027168
Kasaeian A, Daneshazarian R, Mahian O et al (2017) Nanofluid flow and heat transfer in porous media: a review of the latest developments. Int J Heat Mass Transf 107:778–791. https://doi.org/10.1016/j.ijheatmasstransfer.2016.11.074
Mahdi RA, Mohammed HA, Munisamy KM, Saeid NH (2015) Review of convection heat transfer and fluid flow in porous media with nanofluid. Renew Sustain Energy Rev 41:715–734. https://doi.org/10.1016/j.rser.2014.08.040
Devi SU, Devi SA (2017) Heat transfer enhancement of Cu-Al2O3/water hybrid nanofluid flow over a stretching sheet. J Niger Math Soc 36:419–433
Oztop HF, Abu-Nada E (2008) Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow 29:1326–1336. https://doi.org/10.1016/j.ijheatfluidflow.2008.04.009
Weidman PD, Kubitschek DG, Davis AMJ (2006) The effect of transpiration on self-similar boundary layer flow over moving surfaces. Int J Eng Sci 44:730–737. https://doi.org/10.1016/j.ijengsci.2006.04.005
Harris SD, Ingham DB, Pop I (2009) Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transp Porous Media 77:267–285. https://doi.org/10.1007/s11242-008-9309-6
Khashi’ie NS, Arifin NM, Pop I et al (2021) A new similarity solution with stability analysis for the three-dimensional boundary layer of hybrid nanofluids. Int J Numer Methods Heat Fluid Flow 31:809–828. https://doi.org/10.1108/HFF-04-2020-0200
Merkin JH (1986) On dual solutions occurring in mixed convection in a porous medium. J Eng Math 20:171–179. https://doi.org/10.1007/BF00042775
Shampine LF, Kierzenka J, Reichelt MW (2004) Solving boundary value problems for ordinary differential equations in Matlab with bvp4c. MATLAB File Exchange
Shampine LF, Gladwell I, Thompson S (2003) Solving ODEs with MATLAB, 1st edn. Cambridge University Press, Cambridge
Raza J, Farooq M, Mebarek-Oudina F, Mahanthesh B (2019) Multiple slip effects on MHD non-Newtonian nanofluid flow over a nonlinear permeable elongated sheet: numerical and statistical analysis. Multidiscip Model Mater Struct 15:913–931. https://doi.org/10.1108/MMMS-11-2018-0190
Kierzenka J, Shampine LF (2001) A BVP solver based on residual control and the Maltab PSE. ACM Trans Math Softw 27:299–316. https://doi.org/10.1145/502800.502801
Ishak A, Nazar R, Pop I (2006) Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet. Meccanica 41:509–518. https://doi.org/10.1007/s11012-006-0009-4
Khalili S, Dinarvand S, Hosseini R et al (2014) Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid. Chin Phys B 23:048203. https://doi.org/10.1088/1674-1056/23/4/048203
Bachok N, Ishak A, Pop I (2012) The boundary layers of an unsteady stagnation-point flow in a nanofluid. Int J Heat Mass Transf 55:6499–6505. https://doi.org/10.1016/j.ijheatmasstransfer.2012.06.050
Acknowledgements
The authors acknowledge Universiti Putra Malaysia, Universiti Teknikal Malaysia Melaka, and the support provided by the Ministry of Higher Education Malaysia (MOHE) in the form of Fundamental Research Grant Scheme (KPTFRGS/1/2019/STG06/IPM/02/3, Vot 5540309) and MyBrainSc.
Author information
Authors and Affiliations
Contributions
Nur Syahirah Wahid contributed to investigation, software, formal analysis, validation, writing—review and editing, and visualization. Norihan Md Arifin contributed to validation, supervision, and funding acquisition. Najiyah Safwa Khashi’ie contributed to conceptualization, methodology, formal analysis, and writing—review and editing. Ioan Pop contributed to conceptualization, methodology, and supervision. Norfifah Bachok and Mohd Ezad Hafidz Hafidzuddin contributed to supervision and writing—review and editing. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Code availability
MATLAB bvp4c codes are provided in Supplementary Information.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Wahid, N.S., Arifin, N.M., Khashi’ie, N.S. et al. Unsteady mixed convective stagnation point flow of hybrid nanofluid in porous medium. Neural Comput & Applic 34, 14699–14715 (2022). https://doi.org/10.1007/s00521-022-07323-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-022-07323-0