Unsteady Hydromagnetic Flow of Eyring-Powell Nanofluid over an Inclined Permeable Stretching Sheet with Joule Heating and Thermal Radiation

Document Type: Research Paper

Authors

Department of Mathematics, School of Sciences and Languages, VIT-AP University, Amaravati, Andhra Pradesh, 522 237, India

Abstract

The present analysis deals with an unsteady magnetohydrodynamic flow of Eyring-Powell nanofluid over an inclined permeable stretching sheet. Effects of thermal radiation, Joule heating, and chemical reaction are considered. The effects of Brownian motion and thermophoresis on the flow over the permeable stretching sheet are discussed. Using Runge-Kutta fourth-order along with shooting technique, numerical and graphical results were obtained for the governing flow equations. The influence of various parameters on flow variables have been examined in detail. The results reveal that the temperature of the fluid enhanced with increasing Brownian and thermophoresis parameters. The increase of fluid velocity with the local Grashof number, the solutal Grashof number has been noticed. Further, the nanoparticles concentration decreased for a given increase in Brownian motion and chemical reaction parameters, while it increased with an increase in the thermophoresis parameter.

Keywords

Main Subjects

[1] Abu-Nada, E., Oztop, H. F., Effects of variable viscosity and thermal conductivity of  water nanofluid on heat transfer enhancement in natural convection, International Journal of Heat and Fluid Flow, 30(4), 2009, 669-690.

[2] Agbaje, T. M., Mondl, S., Motsa, S., Sibana, P., A numerical study of unsteady non-Newtonian Powell-Eyring nanofluid flow over a shrinking sheet with heat generation and thermal radiation, Alexandria Engineering Journal, 56, 2017, 81-91.

[3] Ashraf, M. B., Hayat, T., Alsaedi, A., Three-dimensional flow of Eyring-Powell nanofluid by convectively heated exponentially stretching sheet, The European Physical Journal Plus, 130, 2015, doi.org/10.1140/epjp/i2015-15005-9.

[4] Athira, P. R., Mahanthesh, B., Gireesha, B. J., Makinde, O. D., Non-linear convection in chemically reacting fluid with an induced magnetic field across a vertical porous plate in the presence of heat source/sink, Defect and Diffusion Forum, 387, 2018, 428-441.

[5] Azim, M. A., Mamun, A. A., Rahman, M. M., Viscous Joule heating MHD-conjugate heat transfer for a vertical flat plate in the presence of heat generation, International Communications in Heat and Mass Transfer, 37, 2010, 666-674.

[6] Bejan, A., Convection Heat Transfer, John Wiley & SonsInc., 2004.

[7] Buongiorno, J., Convective transport in nanofluid, Journal of Heat Transfer, 128(3), 2005, 240-250.

[8] Chamkha, A. J., Aly, A. M., Mansour, M. A., Similarity solution for unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and chemical reaction effects, Chemical Engineering Communications, 197(6), 2010, 846-858.

[9] Chen, C.-H., Combined effects of Joule heating and viscous dissipation on magnetohydrodynamic flow past a permeable, stretching surface with free convection and radiative heat transfer, Journal of Heat Transfer, 132, 2010, 1-5.

[10] Choi, S. U. S., Enhancing thermal conductivity of fluids with nanoparticles, American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED, 231, 1995, 99-105.

[11] Choi, S. U. S., Nanofluids: A new field of scientific research and innovative applications, Heat Transfer Engineering, 29, 2008, 429-431.

[12] Daniel, Y. S. Aziz, Z. A., Ismail, Z., Salah, F., Effects of thermal radiation, viscous and Joule heating on electrical MHD nanofluid with double stratification, Chinese Journal of Physics, 55, 2017, 630-651.

[13] Eegunjobi, A. S., Makinde, O. D., Srinivas, J., Unsteady MHD chemically reacting and radiating mixed convection slip flow past a stretching surface in a porous medium, Defect and Diffusion Forum, 377, 2017, 200-210.

[14] Gangadhar, K., Kumar, D. V., Ibrahim, S. M., Makinde, O. D., On spectral relaxation approach to radiating Powell-Eyring fluid flow over a stretching disk with Newtonian heating, Defect and Diffusion Forum, 387, 2018, 461-473.

[15] Gangadhar, K., Sobhana Babu, P. R., Makinde, O. D., Spectral relaxation method for Powell-Eyring fluid flow past a radially stretching heated disk surface in a porous medium, Defect and Diffusion Forum, 387, 2018, 575-586.

[16] Hayat, T., Ashraf, B., Shehzad, S. A., Abouelmagd, E., Three-dimensional flow of Eyring-Powell nanofluid over an exponentially stretching sheet, International Journal of Numerical Methods for Heat & Fluid Flow, 25(3), 2015, 593-616.

[17] Hayat, T., Gull, N., Farooq, M., Ahmad, B., Thermal radiation effect in MHD flow of Powell-Eyring nanofluid induced by a stretching cylinder, Journal of Aerospace Engineering, 29(1), 2016, 1-10.

[18] Hayat, T., Iqbal, Z., Qasim, M., Alsaedi, A., Flow of an Eyring-Powell fluid with convection boundary conditions, Journal of Mechanics, 29 (2), 2013, 217-224.

[19] Hayat, T., Khan, M. I., Alsaedi, A., Khan, M. I., Joule heating and viscous dissipation in flow of nanomaterial by a rotating disk, International Communications in Heat and Mass Transfer, 89, 2017, 190-197.

[20] Hayat, T., Khan, S. A., Khan, M. I., Alsaedi, A., Optimizing the theoretical analysis of entropy generation in the flow of second grade nanofluid, Physica Scripta, 94, 2019,085001.

[21] Hayat, T., Qasim, M., Mesloub, S., MHD flow and heat transfer over permeable stretching sheet with slip conditions, International Journal for Numerical Methods in Fluids, 66, 2011, 963-975.

[22] Hayat, T., Qayyum, S., Alsaedi, A., Ahmad, B., Modern aspects of nonlinear convection and magnetic field in flow of thixotropic nanofluid over a nonlinear stretching sheet with variable thickness, Physica B: Condensed Matter, 537, 2018, 267-276.

[23] Ibrahim, W., Shankar, B., MHD boundary layer flow and heat transfer of a nanofluid past a permeable stretching sheet with velocity, thermal and solutal slip boundary conditions, Computers & Fluids, 75, 2013, 1-10.

[24] Ishak, T., Nazar, R., Pop, I., Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature, Nonlinear Analysis: Real World Applications, 10, 2009, 2909-2913.

[25] Javed, T., Ali, N., Abbas, Z., Sajid, M., Flow of an Eyring-Powell non-Newtonian fluid over a stretching sheet, Chemical Engineering Communications, 200, 2013, 327-336.

[26] Kanzawa, A., Pfender, E., Numerical analysis of the Joule heating effect on plasma heat transfer, IEEE Transactions on Plasma Science, 6(1), 1978, 33-42.

[27] Khan, M., Shahid, A., Malik, M. Y., Salahuddin, T., Thermal and concentration diffusion in Jeffery nanofluid flow over an inclined stretching sheet: A generalized Fourier’s and Fick’s perspective, Journal of Molecular Liquids, 251, 2018, 7-14.

[28] Khan, W. A., Pop, I., Boundary-layer flow of a nanofluid past a stretching sheet, International Journal of Heat and Mass Transfer, 53, 2010, 2477-2483.

[29] Khanafer, K., Vafai, K., A critical synthesis of thermophysical characteristics of nanofluids, International Journal of Heat and Mass Transfer, 54, 2011, 4410-4428.

[30] Kuznetsov, A. V., Nield, D. A., Natural convective boundary layer flow of a nanofluid past a vertical plate, International Journal of Thermal Sciences, 49, 2010, 243-247.

[31] Makinde, O. D., Aziz, A., Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, International Journal of Thermal Sciences, 50, 2011, 1326-1332.

[32] Makinde, O.D., Osalusi, E., MHD steady flow in a channel with slip at permeable boundaries, Roman Journal of Physics, 51, 2006, 319-328.

[33] Malik, M. Y., Khan, I., Hussain, A., Salahuddin, T., Mixed convection flow of MHD Eyring-Powell nanofluid over a stretching sheet: A numerical study, AIP Advances 5, 2015, 1-13.

[34] Mehmood, R., Rana, S., Akbar, N. S., Nadeem, S., Non-aligned stagnation point flow of radiating casson fluid over a stretching surface, Alexandria Engineering Journal, 57(2), 2018, 939-946.

[35] Misra, J. C., Sinha, A., Effect of thermal radiation on MHD flow of blood and heat transfer in a permeable capillary in stretching motion, Heat Mass Transfer, 49, 2013, 617-628.

[36] Musa, A. M., Verdiana, G. M., Eunice, W. M., Makungu, N. J., Unsteady MHD flow of nanofluid with variable properties over a stretching sheet in the presence of thermal radiation and chemical reaction, International Journal of Mathematics and Mathematical Sciences, 2019, doi.org/10.1155/2019/7392459.

[37] Nadeem, S., Mehmood, R., Akbar, N. S., Non-orthogonal stagnation point flow of a nano non-Newtonian fluid towards a stretching surface with heat transfer, International Journal of Heat and Mass Transfer, 57, 2013, 679-689.

[38] Nayak, M. K., Hakeem, A. K., Makinde, O. D., Time varying chemical reactive magnetohydrodynamic non-linear Falkner-Skan flow over a permeable stretching/shrinking wedge: Buongiorno model, Journal of Nanofluids, 8(3), 2019, 467-476.

[39] Pal, D., Combined effects of non-uniform heat source/sink and thermal radiation on heat transfer over an unsteady stretching permeable surface, Communications in Nonlinear Science and Numerical Simulation, 16, 2011, 1890-1904.

[40] Pal, D., Mandal, G., Mixed convection-radiation on stagnation-point flow of nanofluids over a stretching/shrinking sheet in a porous medium with heat generation and viscous dissipation, Journal of Petroleum Science and Engineering, 126, 2015, 16-25.

[41] Pal, D., Talukdar, B., Combined effects of Joule heating and chemical reaction on unsteady magnetohydrodynamic mixed convection of a viscous dissipating fluid over a vertical plate in porous media with thermal radiation, Mathematical and Computer Modelling, 54, 2011, 3016-3036.

[42] Pantokratoras, A., Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity: A numerical reinvestigation, International Journal of Heat and Mass Transfer, 51, 2008, 104-110.

[43] Pantokratoras, A., Mixed convection flow along a vertical stretching permeable sheet in a Darcy− Brinkman isotropic porous medium, Journal of Porous Media, 17(11), 2014, 999-1006.

[44] Prasad, K. V., Vajravelu, K., Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet, International Journal of Heat and Mass Transfer, 52, 2009, 4956-4965.

[45] Prasad, K. V., Vajravelu, K., Vaidya, H., Gorder, R. A. V., MHD flow and heat transfer in a nanofluid over a slender elastic sheet with variable thickness, Results in Physics, 7, 2017, 1462-1474.

[46] Rahimi, J., Ganji, D. D., Khaki, M., Hosseinzadeh, Kh., Solution of the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linear stretching sheet by collocation method, Alexandria Engineering Journal, 56, 2017, 621-627.

[47] Ramzan, M. Bilal, M., Chung, J. D., Radiative flow of Powell-Eyring magneto-nanofluid over a stretching cylinder with chemical reaction and double stratification near a stagnation point, PLoS ONE, 12 (1), 2017, e0170790.

[48] Rehman, K. U., Malik, M. Y., Salahuddin, T., Naseer, M., Dual stratified mixed convection flow of Eyring-Powell fluid over an inclined stretching cylinder with heat generation/absorption effect, AIP Advances, 6, 2016, 075112.

[49] Rosca, A. V., Pop, I., Flow and heat transfer of Powell-Eyring fluid over a shrinking surface in a parallel free stream, International Journal of Heat and Mass Transfer, 71, 2014, 321-327.

[50] Sahoo, B., Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet, Applied Mathematics and Mechanics(English Edition), 31(2), 2010, 159-173.

[51] Sharidan, S., Mahmood, T., Pop, I., Similarity solutions for the unsteady boundary layer flow and heat transfer due to a stretching sheet, International Journal of Applied Mechanics and Engineering, 11(3), 2006, 647-654.

[52] Sharma, P. R., Sinha, S., Combined effects of viscous dissipation and Joule heating on unsteady MHD flow and heat transfer over a stretching sheet saturated in porous medium, Annals of Pure and Applied Mathematics, 14(3), 2017, 387-399.

[53] Shawky, H. M., Pulsatile flow with heat transfer of dusty magnetohydrodynamic Ree-Eyring fluid through a channel, Heat and Mass Transfer, 45, 2009, 1261–1269.

[54] Srinivas, S., Kumar, C. K., Reddy, A. S., Pulsating flow of Casson fluid in a porous channel with thermal radiation, chemical reaction and applied magnetic field, Nonlinear Analysis: Modelling and Control, 23 (2), 2018, 213-233.

[55] Srinivas, S., Reddy, P. B. A., Prasad, B. S. R. V., Effects of chemical reaction and thermal radiation on MHD flow over an inclined permeable stretching surface with non-uniform heat source/sink: An application to the dynamics of blood flow, Journal of Mechanics in Medicine and Biology, 14(5), 2014, 1450067.

[56] Su, X., Zheng, L., Hall effect on MHD flow and heat transfer of nanofluids over a stretching wedge in the presence of velocity slip and Joule heating, Central European Journal of Physics, 11(12), 2013, 1694-1703.

[57] Wang, X.-Q., Mujumdar, A. S., A review on nanofluids, part I: Theoretical and numerical investigations, Brazilian Journal of Chemical Engineering, 25, 2008, 613-630.

[58] Wang, X.-Q., Mujumdar, A. S., A review on nanofluids, part II: Theoretical and numerical investigations, Brazilian Journal of Chemical Engineering, 25, 2008, 631-648.

[59] Waqas, M., Jabeen, S., Hayat, T., Ijaz Khan, M., Alsaedi, A., Modeling and analysis for magnetic dipole impact in nonlinear thermally radiating Carreau nanofluid flow subject to heat generation, Journal of Magnetism and Magnetic Materials, 485, 2019, 197–204.

[60] Waqas, M., Shehzad, S. A., Hayat, T., Ijaz Khan, M., Alsaedi, A., Simulation of magnetohydrodynamics and radiative heat transport in convectively heated stratified flow of Jeffrey nanofluid, Journal of Physics and Chemistry of Solids, 133, 2019, 45–51.

[61] Zhu, J., Yang, D., Zheng, L., Zhang, X., Effects of second order velocity slip and nanoparticles migration on flow of buongiorno nanofluid, Applied Mathematics Letters, 52, 2016, 183-191.