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Computational Study of MHD Nanofluid Flow with Effects of Variable Viscosity and Non-uniform Heat Generation

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Abstract

The thermodynamic study of an unsteady two-dimensional nanofluid flow through a permeable stretched sheet is looked at. Water is used as the primary fluid, along with four different nanoparticles, including copper (Cu), titanium dioxide (TiO2), copper oxide (CuO), and aluminium oxide (Al2O3). The heat transfer phenomenon is explained by an outside source. Additionally considered are the impacts of heat generation and absorption. A similarity transformation is used to convert the considered set of mathematical equations into a system of ODEs. The BVP4C method is then mathematically applied, coupled with shooting fashion. The results are given for cases involving copper nanoparticles. The effects of various physical parameters on the profiles of the dimensionless flow field, temperature, average entropy generation function, skin friction, and the Nusselt number are examined with illustrations and thorough explanations. As exceptional circumstances of the current inquiry, there is a strong agreement between the current conclusion and the findings of the other researchers. The average entropy generation number, temperature, and velocity profiles are shown to be strongly influenced by regulating factors. The authors conclude that the average entropy production number decreased in the existence of a temperature- and space-dependent heat source/sink, but it increased with increasing the viscosity parameter.

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Data Availability

No data are associated with this manuscript, which was randomly fixed constant value for convergence.

Abbreviations

\(u,v\) :

Velocity component in x−y direction

x :

Cartesian coordinate in horizontal direction

y :

Cartesian coordinate in vertical direction

B 0 :

Uniform magnetic field coefficient

C f :

Skin friction factor

C p :

Specific heat at constant pressure

A :

Unsteadyness parameter

Nu :

Nusselt number

P :

Pressure

Po :

Porosity parameter

Pr :

Prandtl number

N1 :

Heat source factor

N2 :

Heat sink factor

T :

Fluid Temperature

\({T}_{\infty }\) :

Free stream temperature

\({T}_{w}\) :

Wall temperature

\({U}_{w}\) :

Wall velocity

References

  1. Sharma, P., Kumar, V., Sokhal, G.S., Dasaroju, G., Bulasara, V.K.: Numerical study on performance of flat tube with water based copper oxide nanofluids. Mater. Today Proc. 21, 1800–1808 (2020)

    Article  Google Scholar 

  2. Suresh, S., Venkitaraj, K.P., Selvakumar, P., Chandrasekar, M.: Effect of Al2O3 Cu/water hybrid nanofluid in heat transfer. Exp. Therm. Fluid Sci. 38, 54–60 (2012)

    Article  Google Scholar 

  3. Sandhya, A., Reddy, G.R., Deekshitulu, G.V.S.R.: Heat and mass transfer effects on MHD flow past an inclined porous plate in the presence of chemical reaction. Int. J. Appl. Mech. Eng. 25(3), 86–102 (2020)

    Article  Google Scholar 

  4. Sandhya, A., Reddy, G., Deekshitulu, G.V.S.R.: Radiation and chemical reaction effects on MHD Casson fluid flow past a semi-infinite vertical moving porous plate. Indian J. Pure Appl. Phys. (IJPAP) 58(7), 548–557 (2020)

    Google Scholar 

  5. Vijaya, K., Reddy, G.R., Krishna, Y.H.: Heat and mass transfer slip flow of MHD Casson liquid past a vertically rotating cone with convective conditions. Adv. Math. Sci. J. 9(10), 7999–8007 (2020)

    Article  Google Scholar 

  6. Seethamahalakshmi, V., Murthy, C.V.R., Reddy, G.V.R.: Influence of Radiation and chemical reaction on MHD Casson Nanofluid on a stretching sheet. In: Diffusion Foundations, vol 28, pp. 57–64. Trans Tech Publications Ltd. (2020)

  7. Reddy, K.V., Reddy, G.V.R., Krishna, Y.H.: Effects of Cattaneo-Christov heat flux analysis on heat and mass transport of Casson nanoliquid past an accelerating penetrable plate with thermal radiation and Soret–Dufour mechanism. Heat Transfer 50(4), 3458–3479 (2021)

    Article  Google Scholar 

  8. Ibrahim, S.M., Suneetha, K., Reddy, G.V.: A study on free convective heat and mass transfer flow through a highly porous medium with radiation, chemical reaction and Soret effects. J. Comput. Appl. Res. Mech. Eng. (JCARME) 8(2), 121–132 (2019)

    Google Scholar 

  9. Shah, Z., Bonyah, E., Islam, S., Gul, T.: Impact of thermal radiation on electrical MHD rotating flow of Carbon nanotubes over a stretching sheet. AIP Adv. 9, 15115 (2019)

    Article  Google Scholar 

  10. Kumar, T.S.: Hybrid nanofluid slip flow and heat transfer over a stretching surface. Partial. Differ. Equ. Appl. Math. 4, 100070 (2021)

    Article  Google Scholar 

  11. Emad Aly, H., Pop, I.: MHD flow and heat transfer over a permeable stretching/shrinking sheet in a hybrid nanofluid with a convective boundary condition. Int. J. Num. Methods Heat Fluid Flow 29, 3012–3038 (2019)

    Article  Google Scholar 

  12. Bejan, A.: Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-size Systems and Finite-time Processes. CRC Press, New York (1996)

    Google Scholar 

  13. Hassan, A., Hussain, A., Arshad, M., Awrejcewicz, J., Pawlowski, W., Alharbi, F.M., Karamti, H.: Heat and mass transport analysis of MHD rotating hybrid nanofluids conveying silver and molybdenum di-sulfide nano-particles under effect of linear and non-linear radiation. Energies 15(17), 6269 (2022)

    Article  Google Scholar 

  14. Arshad, M., Hassan, A., Haider, Q., Alharbi, F.M., Alsubaie, N., Alhushaybari, A., et al.: Rotating hybrid nanofluid flow with chemical reaction and thermal radiation between parallel plates. Nanomaterials 12(23), 4177 (2022)

    Article  Google Scholar 

  15. Arshad, M., Hassan, A.: A numerical study on the hybrid nanofluid flow between a permeable rotating system. Eur. Phys. J. Plus 137(10), 1126 (2022)

    Article  Google Scholar 

  16. Reddy, P.B., Salah, T., Jakeer, S., Mansour, M.A., Rashad, A.M.: Entropy generation due to magneto-natural convection in a square enclosure with heated corners saturated porous medium using Cu/water nanofluid. Chin. J. Phys. 77, 1863–1884 (2022)

    Article  MathSciNet  Google Scholar 

  17. Madhura, K.R., Babitha, Iyengar, S.S.: Impact of heat and mass transfer on mixed convective flow of nanofluid through porous medium. Int. J. Appl. Comput. Math. 3(1), 1361–1384 (2017)

    Article  MathSciNet  Google Scholar 

  18. Siddheshwar, P.G., Sakshath, T.N., Siddabasappa, C.: Effect of rotation on Brinkman–Bénard convection of a Newtonian nanoliquid using local thermal non-equilibrium model. Therm. Sci. Eng. Prog. 25, 100994 (2021)

    Article  Google Scholar 

  19. Veera Reddy, K., Vijaya, K., Ramana Reddy, G.V.: The Buongiorno model with Brownian and thermophoretic diffusion for MHD Casson nanofluid over an inclined porous surface. J. Naval Archit. Mar. Eng. 19(1), 31–45 (2022)

    Article  Google Scholar 

  20. Abolbashari, M.H., Freidoonimehr, N., Nazari, F., Rashidi, M.M.: Entropy analysis for an unsteady MHD flow past a stretching permeable surface in nano-fluid. Powder Technol. 267, 256–267 (2014)

    Article  Google Scholar 

  21. Rashad, A.M., Armaghani, T., Chamkha, A.J., Mansour, M.A.: Entropy generation and MHD natural convection of a nanofluid in an inclined square porous cavity: effects of a heat sink and source size and location. Chin. J. Phys.. J. Phys. 56(1), 193–211 (2018)

    Article  Google Scholar 

  22. Das, S., Chakraborty, S., Jana, R.N., Makinde, O.D.: Entropy analysis of unsteady magneto-nanofluid flow past accelerating stretching sheet with convective boundary condition. Appl. Math. Mech. 36, 1593–1610 (2015)

    Article  MathSciNet  Google Scholar 

  23. Freidoonimehr, N., Rashidi, M.M., Mahmud, S.: Unsteady MHD free convective flow past a permeable stretching vertical surface in a nano-fluid. Int. J. Therm. Sci. 87, 136–145 (2015)

    Article  Google Scholar 

  24. Waqas, H., Fida, M., Liu, D., Manzoor, U., Muhammad, T.: Numerical simulation of entropy generation for nanofluid with the consequences of thermal radiation and Cattaneo–Christov heat flux model. Int. Commun. Heat Mass TransferCommun. Heat Mass Transfer 137, 106293 (2022)

    Article  Google Scholar 

  25. Asad, S., Riaz, S.: Analysis of entropy generation and nonlinear convection on unsteady flow of MHD Prandtl fluid with Soret and Dufour effects. Arab. J. Math. 12(1), 49–69 (2023)

    Article  MathSciNet  Google Scholar 

  26. Hayat, T., Riaz, R., Aziz, A., Alsaedi, A.: Influence of Arrhenius activation energy in MHD flow of third grade nanofluid over a nonlinear stretching surface with convective heat and mass conditions. Physica A A 549, 124006 (2020)

    Article  MathSciNet  Google Scholar 

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A. Prepared the Introduction B. Mathematical formulation C. Writing code and drawing the Graphs D. Results and Discussion

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Correspondence to T. S. Rao.

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Seethamahalakshmi, V., Babitha, Rao, T.S. et al. Computational Study of MHD Nanofluid Flow with Effects of Variable Viscosity and Non-uniform Heat Generation. Int. J. Appl. Comput. Math 9, 124 (2023). https://doi.org/10.1007/s40819-023-01600-9

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