An Investigation of Heat Flow in Hydromagnetic Eyring-Powell Fluid in the Presence of Cattaneo-Christov Heat Flux

Document Type : Research Article

Authors

Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria

Abstract

This paper examines the flow and heat transfer characteristics of an Eyring-Powell fluid passing over a stretched sheet surface that is being heated by hot fluid from beneath. The thermal mechanism of the model is analyzed on the considerations that the thermal conductivity is a linear function of temperature, the fluid viscosity obeys the Reynolds model, and that the Cattaneo–Christov heat flux model is incorporated into the energy equation. The governing nonlinear partial differential equations were transformed into a system of nonlinear ordinary differential equations using suitable similarity variables. The resulting self-similar problems were then solved using the spectral quasi-linearization method (SQLM). The effectiveness and accuracy of this method were demonstrated through error analysis and comparative studies with relevant existing results. Graphical outcomes illustrating the impact of pertinent fluid parameters in the model equations are presented as velocity and temperature profiles. It is noteworthy that both fluid temperature and velocity decline when the thermal relaxation parameter and slip velocity parameter  are increased. The results also reveal that the fluid variables, such as the thermal relaxation time parameter , Eyring-Powell parameter , slip velocity parameter , surface-convection parameter , or radiation parameter  boost the rate of heat transfer when any of these parameters is increased.

Keywords

Main Subjects


 [1]      R. Ellahi, E. Shivanian, S. Abbasbandy, and T. Hayat,Numerical study of magnetohydrodynamics generalized Couette flow of Eyring-Powell fluid with heat transfer and slip condition. Int J Numer Methods Heat Fluid Flow, 26 (2016), http:// dx.doi.org/10.1108/HFF-04-2015-0131.
 [2]      Krishna PM, Sandeep N, Reddy JVR, Sugunamma V., Dual solutions for unsteady flow of Powell-Eyring fluid past an inclined stretching sheet, J Nav Archit Mar Eng., 13 (2016), 89–99. http://dx.doi.org/10.3329/jname.v13i1.25338.
 [3]      Mishra S, Pal D, Mondal H, Sibanda P., On radiative-magnetoconvective heat and mass transfer of a nanofluid past a non-linear stretching surface with Ohmic heating and convective surface boundary condition, Propuls Power Res, 5 (2016), 326–37. http://dx.doi.org/10.1016/j.jppr.2016.11.007.
[4]       Rahimi J, Ganji DD, Khaki M, Hosseinzadeh K., Solution of the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linear stretching sheet by collocation method, Alex Eng J., (2016) 4–10. http://dx.doi.org/10.1016/ j.aej.2016.11.006.
[5]       Raju CSK, Sandeep N., Falkner-Skan flow of a magnetic-Carreau fluid past a wedge in the presence of cross diffusion effects, Eur Phys J Plus, 131 (2016). http:// dx.doi.org/10.1140/epjp/i2016-16267-3.
 [6]      M. Patel, M.G. Timol, Numerical treatment of Powell-Eyring fluid flow using method of satisfaction of asymptotic boundary conditions (MSABC), Appl. Numer. Math., 59 (2009),  2584– 2592.
[7]       T. Hayat, M. Awais, S. Asghar, Radiative effects in a three-dimensional fow of MHD Eyring-Powell fuid, J. Egypt. Math., Soc., 21 (2013), 379–384.
[8]       A.V. Rosca, I.M. Pop, Flow and heat transfer of Powell-Eyring fluid over a shrinking surface in a parallel free stream, Int. J. Heat Mass Transf., 71 (2014), 321–327.
[9]       S. Panigrahi, M. Reza, A. K. Mishra, Mixed convective fow of a Powell-Eyring fluid over a non-linear stretching surface with thermal diffusion and diffusion thermo. Procedia Eng., 127(2015), 645–651.
[10]     T. Hayat, Z. Iqbal, M. Qasim, S. Obidat, Steady flow of an Eyring Powell fluid over a moving surface with convective boundary conditions, Int. J. Heat Mass Transf., 55 (2012), 1817– 1822.
[11].     T. Hayat, S. Nadeem, Flow of 3D Eyring-Powell fluid by utilizing Cattaneo-Christov heat flux model and chemical processes over an exponentially stretching surface, Results Phys. 8 (2018), 397–403.
[12].    M. M. Khader, M. M. Babatin, Numerical study for improvement the cooling process through a model of Powell-Eyring fluid flow over a stratified stretching sheet with magnetic field. Case Stud. Term. Eng., (2022), 101786.
[13]     W. Abbas, Ahmed M. Megahed, M. S. Emam, Hassan M. H. Sadek., MHD dissipative Powell‑Eyring fluid flow due to a stretching sheet with convective boundary conditions and slip velocity. Scientific Reports, (2023) https://doi.org/10.1038/s41598-023-42609-w   13:15674
[14]     W. Abbas, M. M. Ahmed, Powell-Eyring fuid fow over a stratifed sheet through porous medium with thermal radiation and viscous dissipation. AIMS Math., 6(2021), 13464–13479.
[15]     L.J. Crane, Flow past a stretching plate. Z. Angew, Math. Phys., 21 (1970), 645–647.
[16]     M. Kumari,  G. Nath, Flow and heat transfer in a stagnation-point flow over a stretching sheet with a magnetic field, Mech. Res. Commun., 26 (1999), 469–478.
[17]     S. Mukhopadhyay, Slip effects on MHD boundary layer flow over an exponentially stretching sheet with suction/blowing and thermal radiation, Ain Shams Eng. J., 4 (2013), 485–491.
[18]     A. J. Chamkha, Aly, A. M. Mansour, Similarity solution for unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and chemical reaction efects. Chem. Eng. Commun. 197 (2010), 846–858.
[19]     M. Turkyilmazoglu, Exact solutions for two-dimensional laminar flow over a continuously stretching or shrinking sheet in an electrically conducting quiescent couple stress fluid. Int. J. Heat Mass Transf. 72 (2014), 1–8
[20]     J. V. Tawade, Efects of thermophoresis and Brownian motion for thermal and chemically reacting Casson nanofuid flow over a linearly stretching sheet, Results Eng. 100448 (2022).
[21]     W. Ibrahim, B. Shankar, M.M. Nandeppanavar, MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet, Int. J. Heat Mass Transf., 56 (2013),  1–9.
[22]      Fourier JBJ. Théorie Analytique De La Chaleur. Paris, (1822).
[23]     Cattaneo C. Sulla conduzione del calore. Atti Semin Mat Fis Univ Modena Reggio Emilia, 3 (1948), 83–101.
[24]     Christov CI., On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction, Mech Res Commun, 36 (2009), 481–6.
[25]     Hayat T, Aziz A, Muhammad T, Alsaedi A., Model and comparative study for flow of viscoelastic nanofluids with Cattaneo-Christov Double Diffusion, PLoS One 12(1) (2017). 0168824.
[26]     Liu L, Zheng L, Liu F, Zhang X., An improved heat conduction model with Riesz fractional Cattaneo-Christov flux, Int J Heat Mass Transfer, 103 (2016),1191–7.
[27]     Meraj MA, Shehzad SA, Hayat T, Abbasi FM, Alsaedi A. Darcy-Forchheimer flow of variable conductivity Jeffrey liquid with Cattaneo-Christov heat flux theory. Appl Math Mech 38(4) (2017), 557–66.
[28]     Reddy JVR, Sugunamma V, Sandeep N., Cross diffusion effects on MHD flow over three different geometries with Cattaneo-Christov heat flux, J Mol Liq, 223 (2016), 1234–41.
 [29]    Haddad SAM., Thermal instability in Brinkman porous media with CattaneoChristov heat flux, Int J Heat Mass Transfer, 68 (2014), 659–68.
[30]     Hayat T, Khan MI, Farooq M, Alsaedi A, Waqas M, Yasmeen T., Impact of Cattaneo-Christov heat flux model in flow of variable thermal conductivity fluid over a variable thicked surface, Int. J. Heat Mass Transfer, 99 (2016), 702–10.
[31]     Abbasi FM, Shehzad SA., Heat transfer analysis for three dimensional flow of Maxwell fluid with temperature dependent thermal condutivity: application of Cattaneo-Christov heat flux model, J. Mol Liq 220 (2016), 848–54.
[32]      L.O. Sogbetun, B.I. Olajuwon and O. Fagbemiro, heat transfer in an mhd flow of an erying-powell fluid over a convectively heated stretching sheet in the presence of heat source and thermal radiation, Mathematics in Applied Sciences and Engineering, 6(1) (2025), 20-35
[33]      Hayat, T., Ali, S., Farooq, M. A. & Alsaedi, A. On comparison of series and numerical solutions for flow of Eyring-Powell fluid with newtonian heating and internal heat generation/absorption. PLoS ONE 10 (2015) 1-13.