Journal of Applied and Computational Mechanics
Non-similar Solutions of MHD Mixed Convection over an Exponentially Stretching Surface: Influence of Non-uniform Heat Source or Sink
Document Type : Research Paper
Authors
1 Department of Mathematics, Karnatak University, Pavate Nagar, Dharwad – 580003, India
2 Faculty of Engineering, Kuwait College of Science and Technology, Doha, Kuwait
Abstract
In this paper, an analysis of magnetohydrodynamic (MHD) mixed convection over an exponentially stretching surface in the presence of a non-uniform heat source/sink and suction/injection is presented. The governing boundary layer equations are transformed into a set of non-dimensional equations by using a group of non-similar transformations. The resulting highly non-linear coupled partial differential equations are solved by using the implicit finite difference method in combination with the quasilinearization technique. Numerical results for the velocity, temperature and concentration profiles, as well as the skin friction coefficient, wall heat transfer and mass transfer rates are computed and presented graphically for various parameters. The results indicate that the velocity profile reduces, while the temperature profile increases in presence of the effects of magnetic field and suction at the wall. The velocity ratio parameter increases the skin-friction coefficient and the Schmidt number decreases the wall mass transfer rate. The temperature profile increases for the positive values of Eckert number and space as well as temperature dependent heat source/sink parameters, while the opposite behavior is observed for negative values of same parameters.
Keywords
Main Subjects
[1] Alfven, H., Existence of electromagnetic-hydrodynamic waves, Nature,150 (1942) 405.
[2] Ahmed, S., Zueco, J., Luis, M., Gonzalez, L., Effects of chemical reaction, heat and mass transfer and viscous dissipation over a MHD flow in a vertical porous wall using perturbation method, International Journal of Heat Mass transfer, 104 (2017) 409-418.
[3] Rauf, A., Siddiq, M. K., Abbasi, F. M., Meraj, M. A., Asharaf, M., Shehzad, S. A., Influence of convective conditions on three dimensional mixed convection hydromagnetic boundary layer flow of Casson nanofluid, Journal of Magnetism and Magnetic Materials, 416 (2016) 200-207.
[4] Hayat, T., Shafiq A., Alsaedi, A., Characteristics of magnetic field and melting heat transfer in stagnation point flow of Tangent- hyperbolic liquid, Journal of Magnetism and Magnetic Materials, 405 (2016) 97-106.
[5] Hayat, T., Ullah, I., Muhammad, T., Alsaedi, A., Magnetohydrodynamic (MHD) three-dimensional flow of second grade nanofluid by a convectively heated exponentially stretching surface, Journal of Molecular Liquids, 220 (2016) 1004–1012.
[6] Hayat, T., Ullah, I., Farooq, M., Alsaedi, A., Analysis of non-linear radiative stagnation point flow of Carreau fluid with homogeneous-heterogeneous reactions, Microsystem Technologies, (2018). https://doi.org/10.1007/s00542-018-4157-y.
[7] Hayat, T., Ullah, I., Ahmad, B., Alsaedi, A., Radiative flow of Carreau liquid in presence of Newtonian heating and chemical reaction, Results in Physics, 7 (2017) 715-722.
[8] Hayat T., Ullah, I., Alsaedi, A., Asghar S., Magnetohydrodynamics stagnation-point flow of sisko liquid with melting heat transfer and heat generation/absorption, Journal of Thermal Science and Engineering Applications, 10 (2018) 051015.
[9] Hayat, T., Ullah, I., Waqas, M., Alsaedi, A., Flow of chemically reactive magneto Cross nanoliquid with temperature-dependent conductivity, Applied Nanoscience, 8 (2018) 1453-1460.
[10] Hayat, T., Ullah, I., Muhammad, T., Alsaedi, A., Radiative three-dimensional flow with Soret and Dufour effects, International Journal of Mechanical Sciences, 113 (2017) 829-837.
[11] Hayat, T., Ullah, I., Ahmad, B., Alsaedi, A., MHD mixed convection flow of third grade liquid subject to non-linear thermal radiation and convective condition, Results in Physics, 7 (2017) 2804-2811.
[12] Khan, M. I., Waqas, M., Hayat, T., Alsaedi, A., A comparative study of Casson fluid with homogeneous-heterogeneous reactions, Journal of Colloidal and Interface Science, 498 (2017) 85-90.
[13] Khan, M. I., Hayat, T., Khan, M. I., Alsaedi, A., Activation energy impact in nonlinear radiative stagnation point flow of Cross nanofluid, International Communications in Heat and Mass Transfer, 91 (2018) 216-224.
[14] Hayat, T., Khan, M. I., Qayyum, S., Alsaedi, A., Entropy generation in flow with silver and copper nanoparticles, Colloids and Surfaces A, 539 (2018) 335-346.
[15] Hayat, T., Qayyum, S., Khan, M. I., Alsaedi, A., Entropy generation in magnetohydrodynamic radiative flow due to rotating disk in presence of viscous dissipation and Joule heating, Physics of Fluids, 30 (2018) 017101.
[16] Hayat, T., Khan, M. I., Qayyum, S., Alsaedi, A., Modern developments about statistical declaration and probable error for skin friction and Nusselt number with copper and silver nanoparticles, Chinese Journal of Physics, 55 (2017) 2501-2513.
[17] Hayat, T., Khan, M.I., Qayyum, S., Alsaedi, A., Khan, M. I., New thermodynamics of entropy generation minimization with nonlinear thermal radiation and nanomaterials, Physics Letters A, 382 (2018) 749-760.
[18] Hayat, T., Khan, M., Khan, M. I., Alsaedi, A., Ayub, M., Electromagneto squeezing rotational flow of Carbon (Cu)-Water (H2O) kerosene oil nanofluid past a Riga plate: A numerical study, PLoS ONE, 12 (8) (2017) e0180976.
[19] Khan, M. I., Ullah, S., Hayat, T., Khan, M. I., Alsaedi, A., Entropy generation minimization (EGM) for convection nanomaterial flow with nonlinear radiative heat flux, Journal of Molecular Liquids, 260 (2018) 279-291.
[20] Khan, M. I., Qayyum, S., Hayat, T., Khan, M. I., Alsaedi, A., Khan, T. A., Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection, Physics Letters A, 382 (2018) 2017-2026.
[21] Hossam, S., Hassan, Symmetry Analysis for MHD Viscous Flow and Heat Transfer over a Stretching Sheet, Applied Mathematics, 6 (2015) 78-94.
[22] Magyari, E., Keller, B., Heat and mass transfer in the boundary layers on exponentially stretching continuous surface, Journal of Physics D: Applied Physics, 32 (1999) 577-585.
[23] Bidin, B., Nazar, R., Numerical solution of the boundary layer flow over an exponentially stretching with thermal radiation, European Journal of Scientific Research, 33 (2009) 710-717.
[24] Mukhopadhyay S., Slip effects on MHD boundary layer flows over an exponentially stretching sheet with suction/blowing and thermal radiation, Ain Shams Engineering Journal, 4 (2013) 485-491.
[25] Jusoh, R., Nazar, R., Pop, I., Magnetohydrodynamics rotating flow and heat transfer of ferrofluid due to an exponentially permeable stretching/ shrinking sheet, Magnetism and Magnetic Materials, 465 (2018) 365-374.
[26] Pal, D., Chatterjee, S., Effects of radiation on Darcy-Forchheimer convective flow over a stretching sheet in a micropolar fluid with non- uniform heat source/sink, Journal of Applied Fluid Mechanics, 8(2) (2015) 207-212.
[27] Pal, D., Chatterjee, S., Heat and mass transfer in MHD non-Darcian flow of a micropolar fluid over a stretching sheet embedded in a porous media with non-uniform heat source and thermal radiation, Communications Nonlinear Science Numerical Simulation, 15(7) (2010) 1843-1857.
[28] Rahman, M. M., Uddin, M. J., Aziz, A., Effects of variable electric conductivity and non-uniform heat source (or sink) on convective micropolar fluid flow along an inclined flat plate with surface heat flux, International Journal of Thermal Sciences, 48(12) (2009) 2331-2340.
[29] Bhukta, D., Dash, G. C., Mishra, S. R., Baag, S., Dissipation effect on MHD mixed convection flow over a stretching sheet through porous medium with non-uniform heat source/sink, Ain Shams Engineering Journal, 8 (2017) 353–361.
[30] Mabood, F., Ibrahim, S. M., Effects of Soret and non-uniform heat source on MHD non-Darcian convective flow over a stretching sheet in a dissipative micropolar fluid with radiation, Journal of Applied Fluid Mechanics, 9(5) (2016) 2503-2513.
[31] Mabood, F., Ibrahim, S. M., Rashidi, M. M., Shadloo, M. S., Lorenzini, G., Non-uniform heat source/sink and Soret effects on MHD non-Darcian convective flow past a stretching sheet in a micropolar fluid with radiation, International Journal Heat and Mass Transfer, 93 (2016) 674–682.
[32] Mahantesh, M., Nandeppanavar, K., Vajravelu, M., Abel, S., Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink, Communications Nonlinear Science Numerical Simulation, 16 (2011) 3578–3590.
[33] Ramesh, G. K., Chamkha, A. J., Gireesha, B. J., MHD mixed convection flow of a viscoelastic fluid over an inclined surface with a non-uniform heat source/sink, Canadian Journal of Physics, 91(12) (2015) 1074-1080.
[34] Ramesh, G. K., Gireesha, B. J., Bagewadi, C. S., MHD flow of a dusty fluid near the stagnation point over a permeable stretching sheet with non-uniform source/sink, International Journal Heat and Mass Transfer, 55 (2012) 4900–4907.
[35] Sandeep, N., Sulochana, C., Dual solutions for unsteady mixed convection flow of MHD micropolar fluid over a stretching/shrinking sheet with non-uniform heat source/sink, Engineering Science and Technology, doi.org/10.1016/j.jestch.2015.05.006.
[36] Chamkha, A.J., MHD flow of a uniformly stretched vertical permeable surface in the presence of heat generation/absorption and a chemical reaction, International Communications in Heat and Mass Transfer, 30(3) (2003) 413–422.
[37] Patil, P. M., Pop, I., Effects of surface mass transfer on unsteady mixed convection flow over a vertical cone with chemical reaction, Heat and Mass Transfer, 47 (2011) 1453-1464.
[38] Patil, P. M., Shashikant, A., Roy, S., Momoniat E., Unsteady mixed convection over an exponentially decreasing external flow velocity, International Journal of Heat and Mass Transfer, 111 (2017) 643-650.
[39] Patil, P. M., Chamkha, A. J., Roy, S., Effects of chemical reaction on mixed convection flow of a polar fluid through a porous medium in the presence of internal heat generation, Meccanica, 47 (2012) 483-499.
[40] Patil, P. M., Roy, S., Pop, I., Chemical reaction effects on unsteady mixed convection boundary layer flow past a permeable slender vertical cylinder due to a nonlinearly stretching velocity, Chemical Engineering Communications, 200 (2013) 398-417.
[41] Schlichting, H., Gersten, K., Boundary Layer Theory, Springer, New York, 2000.
[42] Patil, P. M., Ramane, H. S., Roy, S., Hindasageri, V., Momoniat, E., Influence of mixed convection in an exponentially decreasing external flow velocity, International Journal of Heat and Mass Transfer, 104 (2017) 392-399.
[43] Patil, P. M., Latha, D. N., Roy, S., Momoniat, E., Double diffusive mixed convection flow from a vertical exponentially stretching surface in presence of the viscous dissipation, International Journal of Heat and Mass Transfer, 112 (2017) 758-766.
[44] Varga, R.S., Matrix Iterative Analysis, Prentice-Hall, USA, 2000.
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