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MHD stagnation-point flow of hybrid nanofluid with convective heated shrinking disk, viscous dissipation and Joule heating effects

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Abstract

This paper describes the MHD stagnation-point flow of Cu-Al2O3/H2O hybrid nanofluid toward a convectively heated shrinking disk with convective boundary condition, suction, Joule heating and viscous dissipation effects. Similarity transformation reduces the PDEs into a system of ODEs, which then numerically solved using the bvp4c solver. The comparison between present and previous results in certain cases shows an excellent agreement with approximately 0% relative error. Two solutions exist in which the second solution appears near to the separation value of the velocity ratio parameter. The stability analysis shows that the first solution is physically stable (realizable in practice). An increase of suction and magnetic parameters extends the critical value and aids the performance of heat transfer operation. Further, the heat transfer rate boosts while the critical values unchanged with the rise of Eckert number (implies the operating Joule heating and viscous dissipation) and Biot number (implies the operating convective boundary condition). The temperature profile reduces with the increment of velocity ratio parameter, Eckert and Biot numbers while the velocity increases with the addition of velocity ratio and magnetic parameters. This study is important in the estimation of the flow and thermal behavior for Cu-Al2O3/H2O when the physical parameters are embedded.

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Abbreviations

\(a,b\) :

constant

\(B_{0}\) :

Strength of the magnetic field (constant)

\({\rm{Bi}}\) :

Biot number

\(C_{f}\) :

Skin friction coefficient along the r-direction

\(C_{p}\) :

Specific heat at constant pressure (\({\text{Jkg}}^{{ - 1}} {\text{K}}^{{ - 1}}\))

\({\rm{Ec}}\) :

Eckert number

\(f\left( \eta \right)\) :

Dimensionless stream function

\(k\) :

Thermal conductivity of the fluid (\({\text{Wm}}^{{ - 1}} {\text{K}}^{{ - 1}}\))

\(M\) :

Magnetic parameter

\({\rm{Nu}}_{r}\) :

Local Nusselt number

\(\Pr\) :

Prandtl number

\(\text{Re} _{r}\) :

Local Reynolds number

\(S\) :

Suction/injection parameter

\(T\) :

Fluid temperature (\({\text{K}}\))

\(T_{f}\) :

Temperature of the hot fluid (\({\text{K}}\))

\(T_{\infty }\) :

Ambient temperature (\({\text{K}}\))

\(u\) \(u,v\) :

velocity component in the r- and z-directions (\({\text{ms}}^{{ - 1}}\) )

\(u_{w}\) :

Velocity of the stretching/shrinking disk (\({\text{ms}}^{{ - 1}}\))

\(u_{e}\) :

Free stream velocity (\(\text{ms}^ {- 1}\))

\(w_{w}\) :

Mass velocity for the permeable disk (\({\text{ms}}^{{ - 1}}\))

\(\eta\) :

Similarity variable

\(\tau\) :

Dimensionless time variable

\(\theta\) :

Dimensionless temperature

\(\lambda\) :

Velocity ratio parameter

\(\mu\) :

Dynamic viscosity of the fluid (\({\text{kgm}}^{{ - 1}} {\text{s}}^{{ - 1}}\))

\(\nu\) :

Kinematic viscosity of the fluid (\({\text{m}}^{2} {\text{s}}^{{ - 1}}\))

\(\rho\) :

Fluid density (\({\text{kg\,m}}^{{ - 3}}\))

\(\phi _{1}\) :

Alumina concentration

\(\phi _{2}\) :

Copper concentration

\(f\) :

Base fluid

\(nf\) :

Nanofluid

\(hnf\) :

Hybrid nanofluid

\(s1\) :

Alumina’s solid component

\(s2\) :

Copper’s solid component

\(\prime\) :

Differentiation with respect to \(\eta\)

References

  1. Hiemenz K (1911) Die grenzschicht an einem in den gleichformingen flussigkeitsstrom eingetauchten graden kreiszylinder. Dinglers Polytech J 326:321–324

    Google Scholar 

  2. Wang CY (2008) Stagnation flow towards a shrinking sheet. Int J Non-Lin Mech 43:377–382

    Google Scholar 

  3. Shateyi S, Makinde OD (2013) Hydromagnetic stagnation-point flow towards a radially stretching convectively heated disk. Math Prob Eng 616947:8

    MathSciNet  MATH  Google Scholar 

  4. Tadmor Z, Klein I (1970) Engineering Principles of Plasticating Extrusion. Polymer Science Engineering Series New York, Van Norstrand Reinhold.

  5. Fisher EG (1976) Extrusion of Plastics. Wiley, New York

    Google Scholar 

  6. Goldstein S (1965) On backward boundary layers and flow in converging passages. J Fluid Mech 21:33–45

    MathSciNet  MATH  Google Scholar 

  7. Maxwell JC (1873) A treatise on electricity and magnetism. Clarendon Press, Oxford

    MATH  Google Scholar 

  8. Choi SUS, Eastman JA (1995) Enhancing thermal conductivity of fluids with nanoparticles. ASME Fluids Eng Div 231:99–106

    Google Scholar 

  9. Das SK, Choi SUS, Pradeep WY (2008) Nanofluids: Science and Technology. Wiley, New Jersey

    Google Scholar 

  10. Minkowycz WJ, Sparrow EM, Abraham JP (eds) (2017) Nanoparticle Heat Transfer and Fluid Flow. CRC Press, New York

    Google Scholar 

  11. Shenoy A, Sheremet M, Pop I (2016) Convective flow and heat transfer from wavy surfaces: Viscous fluids porous media and nanofluids. CRC Press, Boca Raton

    Google Scholar 

  12. Nield DA, Bejan A (2017) Convection in porous media, 5th edn. Springer, New York

    MATH  Google Scholar 

  13. Merkin JH, Pop I, Lok YY, Groşan T (2021) Similarity solutions for the boundary layer flow and heat transfer of viscous fluids, nanofluids, porous media, and micropolar fluids. Elsevier, Oxford, UK

    Google Scholar 

  14. Hatami M, Song D, Jing D (2016) Optimization of a circular-wavy cavity filled by nanofluid under the natural convection heat transfer condition. Int J Heat Mass Trans 98:758–767

    Google Scholar 

  15. Hatami M (2017) Nanoparticles migration around the heated cylinder during RSM optimization of a wavy-wall enclosure. Adv Powder Technol 28:890–899

    Google Scholar 

  16. Hatami M, Jing D (2017) Optimization of wavy direct absorber solar collector (WDASC) using Al2O3-water nanofluid and RSM analysis. Appl Therm Eng 121:1040–1050

    Google Scholar 

  17. Hatami M, Zhou J, Geng J, Song D, Jing D (2017) Optimization of a lid-driven T-shaped porous cavity to improve the nanofluids mixed convection heat transfer. J Mol Liq 231:620–631

    Google Scholar 

  18. Tang W, Hatami M, Zhou J, Jing D (2017) Natural convection heat transfer in a nanofluid filled cavity with double sinusoidal wavy walls of various phase deviations. Int J Heat Mass Trans 115:430–440

    Google Scholar 

  19. Pourmehran O, Rahimi-Gorji M, Hatami M, Sahebi SAR, Domairry G (2015) Numerical optimization of microchannel heat sink (MCHS) performance cooled by KKL based nanofluids in saturated porous medium. Taiwan Inst Chem Eng 55:49–68

    Google Scholar 

  20. Sheikholeslami M, Hatami M, Ganji DD (2015) Numerical investigation of nanofluid spraying on an inclined rotating disk for cooling process. J Mol Liq 21:577–583

    Google Scholar 

  21. Zhou J, Hatami M, Song D, Jing D (2016) Design of microchannel heat sink with wavy channel and its time-efficient optimization with combined RSM and FVM methods. Int J Heat Mass Trans 103:715–724

    Google Scholar 

  22. Bu W, Xu H, Khan I, Khan SIU, Zeb A (2022) Mixed convection squeezing flow of nanofluids in a rotating channel with thermal radiation. J Math 2022:3885463

    MathSciNet  Google Scholar 

  23. Khan SIU, Khan U, Ahmed N, Mohyud-Din ST, Khan I, Nisar KS (2021) Thermal transport investigation in AA7072 and AA7075 aluminum alloys nanomaterials based radiative nanofluids by considering the multiple physical flow conditions. Sci Rep 11:9837

    Google Scholar 

  24. Khan SIU, Alzahrani E, Khan U, Zeb N, Zeb A (2020) On mixed convection squeezing flow of nanofluids. Energies 13(12):3138

    Google Scholar 

  25. Babu JR, Kumar KK, Rao SS (2017) State-of-art review on hybrid nanofluids. Renew Sustain Energy Rev 77:551–565

    Google Scholar 

  26. 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

    MATH  Google Scholar 

  27. 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

    Google Scholar 

  28. Devi SPA, Devi SSU (2016) Numerical investigation of hydromagnetic hybrid Cu–Al2O3/water nanofluid flow over a permeable stretching sheet with suction. Int J Nonlin Sci Numer Simul 17(5):249–257

    Google Scholar 

  29. Tayebi T, Chamkha AJ (2019) Entropy generation analysis during MHD natural convection flow of hybrid nanofluid in a square cavity containing a corrugated conducting block. Int J Numer Methods Heat Fluid Flow 30(3):1115–1136

    Google Scholar 

  30. Ghalambaz M, Roşca NC, Roşca AV, Pop I (2020) Mixed convection and stability analysis of stagnation-point boundary layer flow and heat transfer of hybrid nanofluids over a vertical plate. Int J Numer Methods Heat Fluid Flow 30(7):3737–3754

    Google Scholar 

  31. Mehryan SA, Kashkooli FM, Ghalambaz M, Chamkha AJ (2017) Free convection of hybrid Al2O3-Cu water nanofluid in a differentially heated porous cavity. Adv Powder Technol 28(9):2295–2305

    Google Scholar 

  32. Mehryan SA, Izadpanahi E, Ghalambaz M, Chamkha AJ (2019) Mixed convection flow caused by an oscillating cylinder in a square cavity filled with Cu–Al2O3/water hybrid nanofluid. J Therm Anal Calorim 137(3):965–982

    Google Scholar 

  33. Mehryan SA, Ghalambaz M, Chamkha AJ, Izadi M (2020) Numerical study on natural convection of Ag–MgO hybrid/water nanofluid inside a porous enclosure: A local thermal non-equilibrium model. Powder Technol 367:443–455

    Google Scholar 

  34. Wahid NS, Arifin NM, Khashi’ie NS, Pop I (2021) Hybrid nanofluid slip flow over an exponentially stretching/shrinking permeable sheet with heat generation. Mathematics 9:30

    Google Scholar 

  35. Wahid NS, Arifin NM, Khashi’ie NS, Pop I, Bachok N, Hafidzuddin MEH (2021) Flow and heat transfer of hybrid nanofluid induced by an exponentially stretching/shrinking curved surface. Case Stud Therm Eng 25:100982

    Google Scholar 

  36. 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. Chinese J Phys 66:630–644

    MathSciNet  Google Scholar 

  37. 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(10):1649

    Google Scholar 

  38. Khan U, Zaib A, Mebarek-Oudina F (2020) Mixed convective magneto flow of SiO2–MoS2/C2H6O2 hybrid nanoliquids through a vertical stretching/shrinking wedge: stability analysis. Arabian J Sci Eng 45:9061–9073

    Google Scholar 

  39. Khan U, Shafiq A, Zaib A, Baleanu D (2020) Hybrid nanofluid on mixed convective radiative flow from an irregular variably thick moving surface with convex and concave effects. Case Stud Therm Eng 21:100660

    Google Scholar 

  40. Khan U, Waini I, Ishak A, Pop I (2021) Unsteady hybrid nanofluid flow over a radially permeable shrinking/stretching surface. J Mol Liq 331:115752

    Google Scholar 

  41. Khashiʼie NS, Arifin NM, Pop I, Wahid NS (2021) Effect of suction on the stagnation point flow of hybrid nanofluid toward a permeable and vertical Riga plate. Heat Transf 50:1895–1910

    Google Scholar 

  42. Khashiʼie NS, Arifin NM, Pop I, Wahid NS (2020) Flow and heat transfer of hybrid nanofluid over a permeable shrinking cylinder with Joule heating: a comparative analysis. Alexandria Eng J 59(3):1787–1798

    Google Scholar 

  43. Bakar SA, Arifin NM, Khashi’ie NS, Bachok N, (2021) Hybrid nanofluid flow over a permeable shrinking sheet embedded in a porous medium with radiation and slip impacts. Mathematics 9:878

    Google Scholar 

  44. Waini I, Ishak A, Pop I (2021) Agrawal flow of a hybrid nanofluid over a shrinking disk. Case Stud Therm Eng 25:100950

    Google Scholar 

  45. Suresh Kumar Raju S, Jayachandra Babu M, Raju CSK (2021) Irreversibility analysis in hybrid nanofluid flow between two rotating disks with activation energy and cross-diffusion effects. Chinese J Phys. https://doi.org/10.1016/j.cjph.2021.03.016

    Article  MathSciNet  Google Scholar 

  46. Waqas H, Farooq U, Naseem R, Hussain S, Alghamdi M (2021) Impact of MHD radiative flow of hybrid nanofluid over a rotating disk. Case Stud Therm Eng 26:101015

    Google Scholar 

  47. Shoaib M, Raja MAZ, Sabir MT, Awais M, Islam S, Shah Z, Kumam P (2021) Numerical analysis of 3-D MHD hybrid nanofluid over a rotational disk in presence of thermal radiation with Joule heating and viscous dissipation effects using Lobatto IIIA technique. Alexandria Eng J 60:3605–3619

    Google Scholar 

  48. Punith Gowda RJ, Naveen Kumar R, Aldalbahi A, Issakhov A, Prasannakumara BC, Rahimi-Gorji M, Rahaman M (2021) Thermophoretic particle deposition in time-dependent flow of hybrid nanofluid over rotating and vertically upward/ downward moving disk. Surf Interfaces 22:100864

    Google Scholar 

  49. Haider F, Hayat T, Alsaedi A (2021) Flow of hybrid nanofluid through Darcy-Forchheimer porous space with variable characteristics. Alexandria Eng J 60:3047–3056

    Google Scholar 

  50. Khan MI (2021) Transportation of hybrid nanoparticles in forced convective Darcy-Forchheimer flow by a rotating disk. Int Commun Heat Mass Transf 122:105177

    Google Scholar 

  51. Khashiʼie NS, Arifin NM, Nazar R, Hafidzuddin EH, Wahi N, Pop I (2020) Magnetohydrodynamics (MHD) axisymmetric flow and heat transfer of a hybrid nanofluid past a radially permeable stretching/shrinking sheet with Joule heating. Chinese J Phys 64:251–263

    MathSciNet  Google Scholar 

  52. Khashiʼie NS, Arifin NM, Pop I (2021) Unsteady axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable stretching/shrinking disc. Int J Numer Methods Heat Fluid Flow 31(6):2005–2021

    Google Scholar 

  53. Farooq U, Afridi MI, Qasim M, Lu DC (2018) Transpiration and viscous dissipation effects on entropy generation in hybrid nanofluid flow over a nonlinear radially stretching disk. Entropy 20(9):668

    Google Scholar 

  54. 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

    Google Scholar 

  55. Lund LA, Omar Z, Khan I, Seikh AH, Sherif ES, Nisar KS (2020) Stability analysis and multiple solution of Cu–Al2O3/H2O nanofluid contains hybrid nanomaterials over a shrinking surface in the presence of viscous dissipation. J Mater Res Technol 9(1):421–432

    Google Scholar 

  56. Zainal NA, Nazar R, Naganthran K, Pop I (2021) Viscous dissipation and MHD hybrid nanofluid flow towards an exponentially stretching/shrinking surface. Neural Comput Appl 33:11285–11295

    Google Scholar 

  57. 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

    Google Scholar 

  58. Schlichting H, Gerstern K (2000) Boundary-Layer Theory, 8th edn. Springer, Berlin

    Google Scholar 

  59. Pop I, Ingham DB (2001) Convective heat transfer: mathematical and computational viscous fluids and porous media. Pergamon, Oxford

    Google Scholar 

  60. Heydari M, Loghmani GB, Rashidi MM, Hosseini SM (2015) A numerical study for off-centered stagnation flow towards a rotating disc. Propuls Power Res 4:169–178

    Google Scholar 

  61. Merkin JH (1986) On dual solutions occurring in mixed convection in a porous medium. J Eng Math 20:171–179

    MATH  Google Scholar 

  62. 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

    MATH  Google Scholar 

  63. 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 Med 77:267–285

    Google Scholar 

  64. Hosseinzadeh S, Hosseinzadeh K, Rahai M, Ganji DD (2021) Analytical solution of nonlinear differential equations two oscillators mechanism using Akbari-Ganji method. Modern Phys Lett B 35(31):2150462

    Google Scholar 

  65. Fallah MN, Talebi HR, Hosseinzadeh K, Ganji DD (2021) Thermal analysis of a moving fin using the radial basis function approximation. Heat Transfer 50(8):7553–7567

    Google Scholar 

  66. Gulzar MM, Aslam A, Waqas M, Javed MA, Hosseinzadeh K (2020) A nonlinear mathematical analysis for magneto-hyperbolic-tangent liquid featuring simultaneous aspects of magnetic field, heat source and thermal stratification. Appl Nanosci 10(12):4513–4518

    Google Scholar 

  67. Hatami M, Ganji DD (2014) Motion of a spherical particle in a fluid forced vortex by DQM and DTM. J Particuology 16:206–212

    Google Scholar 

  68. Hatami M, Ganji DD (2014) Motion of a spherical particle on a rotating parabola using Lagrangian and high accuracy multi-step differential transformation method. Powder Technol 258:94–98

    Google Scholar 

  69. Hatami M, Sheikholeslami M, Domairi G (2014) High accuracy analysis for motion of a spherical particle in plane Couette fluid flow by multi-step differential transformation method. Powder Technol 260:59–67

    Google Scholar 

  70. Wang CY (2008) Off-centered stagnation flow towards a rotating disc. Int J Eng Sci 46:391–396

    MathSciNet  MATH  Google Scholar 

  71. Erfani E, Rashidi MM, Parsa AB (2010) The modified differential transform method for solving off-centered stagnation flow toward a rotating disc. Int J Comput Methods 07:655–670

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

We acknowledge the Ministry of Higher Education (MOHE) Malaysia and Universiti Teknikal Malaysia Melaka for the FRGS Scheme FRGS/1/2021/STG06/UTEM/03/1. We also appreciate the research support from Universiti Putra Malaysia and Babes-Bolyai University.

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Authors and Affiliations

  1. Fakulti Teknologi Kejuruteraan Mekanikal Dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal, 76100, Melaka, Malaysia

    Najiyah Safwa Khashi’ie

  2. Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400, Serdang, Selangor, Malaysia

    Nur Syahirah Wahid & Norihan Md Arifin

  3. Institute for Mathematical Research, Universiti Putra Malaysia, 43400, Serdang, Selangor, Malaysia

    Norihan Md Arifin

  4. Department of Mathematics, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    Ioan Pop

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  1. Najiyah Safwa Khashi’ie
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Khashi’ie, N.S., Wahid, N.S., Md Arifin, N. et al. MHD stagnation-point flow of hybrid nanofluid with convective heated shrinking disk, viscous dissipation and Joule heating effects. Neural Comput & Applic 34, 17601–17613 (2022). https://doi.org/10.1007/s00521-022-07371-6

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