Impacts of Thermal Conductivity and Variable Viscosity on the Dissipative Heat and Species Transport of MHD Flow in Porous Media
Asian Research Journal of Mathematics,
Page 1-10
DOI:
10.9734/arjom/2021/v17i930326
Abstract
The investigation of dissipative heat and species diffusion of a conducting liquid under the combined influence of buoyancy forces in a moving plate is examined in the existence of magnetic field. The flowing liquid heat conductivity and viscosity are taken to be linearly varied as a temperature function. The governing derivative equations of the problem are changed to anon-linear coupled ordinary derivative equations by applying similarity quantities. The dimensionless model is solved using shooting technique along with the Runge-Kutta method. The outcomes for the flow wall friction, heat gradient and species wall gradient are offered in table and qualitatively explained. The study revealed that the Newtonian fluid viscosity can be enhanced by increasing the fluid flow medium porosity and the magnetic field strength. Hence, the study will improve the industrial usage of Newtonian working fluid.
Keywords:
- Viscosity
- dissipation
- thermal conductivity
- porous medium
- buoyancy force
How to Cite
Mohammed, M. A., Baiyeri, J. F., Ogunbayo, T. O., & Esan, O. A. (2021). Impacts of Thermal Conductivity and Variable Viscosity on the Dissipative Heat and Species Transport of MHD Flow in Porous Media. Asian Research Journal of Mathematics, 17(9), 1-10. https://doi.org/10.9734/arjom/2021/v17i930326
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Reddy MG. Scaling transformation for heat and mass transfer effects on steady MHD free convection dissipative flow past an inclined porous surface. Int. J. of Appl. Math and Mech. 2013;9(10):1-18.
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Eshetu H, Shankar B. Heat and mass transfer through a porous media of MHD flow of nanofluid with thermal radiation, viscous dissipation and chemical reaction effects. American Chemical Science Journal. 2014;4(6):828-846.
Salawu SO, Dada MS, Adebimpe O. Analysis of pressure driven heat and mass transfer of hydromagnetic flow past Darcy-Forchheimer porous media using Lie group. Journal of Engineering and Applied Science. 2019;14(13):4405-4413.
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Erikson LE, Fan LT, Fox VG. Heat and mass transfer on a moving continuous plate with suction and injection. Ind. Eng. Chem. Fundamental. 1966;5:19-25.
Tsou FK, Sparrow FM, Golldstien RJ. Flow and heat transfer in the boundary layer in continuous moving surface. Int. J. Heat Mass transfer. 1967;10:219-235.
Salawu SO, Kareem RA. Analysis of heat absorption viscoelastic exothermic chemical reactive fluid with temperature dependent viscosity under bimolecular kinetic. Applications and Applied Mathematics: An International Journal. 2019;14(2):1232-1242.
Mureithi EW, Mwaonanji JJ, Makinde OD. On the boundary layer flow over a moving surface in a fluid with temperature-dependent viscosity. Open Journal of Fluid Dynamics. 2013;3:135-140.
Kareem RA, Salawu SO. Variable viscosity and thermal conductivity effect of soret and dufour on inclined magnetic field in non-Darcy permeable medium with dissipation. British Journal of Mathematics & Computer Science. 2017;22(3):1-12.
Gitima P. Effect of variable viscosity and thermal conductivity of micropolar fluid in a porous channel in presence of magnetic field. International Journal for Basic Sciences and Social Sciences. 2012;1(3): 69-77.
Krishnendu B, Layek GC, Rama SRG. Boundary layer slip flow and heat transfer past a stretching sheet with temperature dependent viscosity. Thermal Energy and Power Engineering. 2013;2(1):38-43.
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Salawu SO. On ignition slice-chain and heat distribution of MHD reactive Oldroyd 8-constant flow in a plane Couette. Int. Journal of Comput. Engin. and Comput. Sci. 2020;20:1-6.
Hazarika GC, Utpal SGC. Effects of variable viscosity and thermal conductivity on MHD flow past a vertical plate. Matematicas Ensenanza Universitaria. 2012;XX(2):45-54.
Hunegnaw D, Kishan N. Unsteady MHD heat and mass transfer flow over stretching sheet in porous medium with variable properties considering viscous dissipation and chemical reaction. American Chemical Science Journal. 2014;4(6):901-917.
Mukhopadhyay S, Layek GC, Samad SA. Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity. Int. J. Heat Mass Transfer. 2005;48:4460-4466.
Pantokratoras A. Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity: A numerical reinvestigation. Int. J. Heat Mass Transfer. 2008;51:104-110.
Saikrishnan P, Roy S. Non-uniform slot injection (suction) into steady laminar water boundary layers over (i) a cylinder and (ii) as phere. Int. J Eng. Sci. 2003;41:1351–65.
Bird RB, Stewart WE, Lightfoot EN. (). Transport phenomena. New York: Wiley; 1960.
Chiam TC. Heat transfer with variable conductivity in a stagnation-point flow towards a stretching sheet. International Communications in Heat and Mass Transfer. 1996;23(2):239-248.
Swati M, Iswar CM, Rama SRG. MHD flow and heat transfer past a porous stretchingnon-Iisothermal surface in porous medium with variable free stream temperature. Thermal Energy and Power Engineering. 2013;2(1):29-37.
Nalinakshi N, Dinesh PA, Chandrashekar DV. Effects of variable fluid properties and MHD onmixed convection heat transfer from a vertical heated plate embedded in a sparsely packed porous medium. IOSR Journal of Mathematics (IOSR-JM). 2013;7(1):20-31.
Alireza R, Mahmood F, Seyed RV. Analytical solution for MHD stagnation point flow and heat transfer over a permeable stretching sheet with chemical reaction. Journal of Theoretical and Applied Mechanics. 2013;51(3):675-686.
Okedoye AM. Analytical solution of MHD free convective heat and mass transfer flow in a porous medium. The Pacific Journal of Science and Technology. 2013;14(2):119-128.
Reddy MG. Scaling transformation for heat and mass transfer effects on steady MHD free convection dissipative flow past an inclined porous surface. Int. J. of Appl. Math and Mech. 2013;9(10):1-18.
Fenuga OJ, Aroloye SJ, Salawu SO. Mathematical model and solution for an unsteady MHD fourth grade fluid flow over a vertical plate in a porous medium with magnetic field and suction/injection effects. Journal Scientific Research. 2020;12(4):485-498.
Eshetu H, Shankar B. Heat and mass transfer through a porous media of MHD flow of nanofluid with thermal radiation, viscous dissipation and chemical reaction effects. American Chemical Science Journal. 2014;4(6):828-846.
Salawu SO, Dada MS, Adebimpe O. Analysis of pressure driven heat and mass transfer of hydromagnetic flow past Darcy-Forchheimer porous media using Lie group. Journal of Engineering and Applied Science. 2019;14(13):4405-4413.
Reddy GVR, Ibrahim SM, Bhagavan VS. Similarity transformations of heat and mass transfer effects on steady MHD free convection dissipation fluid flow past an inclined porous surface with chemical reaction. Journal of Naval Architecture and Marine Engineering. 2014;11:157-166.
Sakkiadis BC. Boundary layer behaviors on continuous surface. ALCHE. 1961;7(2):221-225.
Erikson LE, Fan LT, Fox VG. Heat and mass transfer on a moving continuous plate with suction and injection. Ind. Eng. Chem. Fundamental. 1966;5:19-25.
Tsou FK, Sparrow FM, Golldstien RJ. Flow and heat transfer in the boundary layer in continuous moving surface. Int. J. Heat Mass transfer. 1967;10:219-235.
Salawu SO, Kareem RA. Analysis of heat absorption viscoelastic exothermic chemical reactive fluid with temperature dependent viscosity under bimolecular kinetic. Applications and Applied Mathematics: An International Journal. 2019;14(2):1232-1242.
Mureithi EW, Mwaonanji JJ, Makinde OD. On the boundary layer flow over a moving surface in a fluid with temperature-dependent viscosity. Open Journal of Fluid Dynamics. 2013;3:135-140.
Kareem RA, Salawu SO. Variable viscosity and thermal conductivity effect of soret and dufour on inclined magnetic field in non-Darcy permeable medium with dissipation. British Journal of Mathematics & Computer Science. 2017;22(3):1-12.
Gitima P. Effect of variable viscosity and thermal conductivity of micropolar fluid in a porous channel in presence of magnetic field. International Journal for Basic Sciences and Social Sciences. 2012;1(3): 69-77.
Krishnendu B, Layek GC, Rama SRG. Boundary layer slip flow and heat transfer past a stretching sheet with temperature dependent viscosity. Thermal Energy and Power Engineering. 2013;2(1):38-43.
Dulal P, Hiranmoy M. Effects of temperature-dependent viscosity and variable thermal conductivity on MHD non-Darcy mixed convective diffusion of species over a stretching sheet. Journal of the Egyptian Mathematical Society. 2014;22:123-133.
Hunegnaw D, Naikoti K. MHD effects on heat transfer over stretching sheet embedded in porous medium with variable viscosity, viscous dissipation and heat source/sink. Ain Shams Engineering Journal. 2014;5:967-977.
Abel MS, Mahesha N. Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation. Applied Mathematical Modeling. 2008;32:1965-1983.
Salawu SO. On ignition slice-chain and heat distribution of MHD reactive Oldroyd 8-constant flow in a plane Couette. Int. Journal of Comput. Engin. and Comput. Sci. 2020;20:1-6.
Hazarika GC, Utpal SGC. Effects of variable viscosity and thermal conductivity on MHD flow past a vertical plate. Matematicas Ensenanza Universitaria. 2012;XX(2):45-54.
Hunegnaw D, Kishan N. Unsteady MHD heat and mass transfer flow over stretching sheet in porous medium with variable properties considering viscous dissipation and chemical reaction. American Chemical Science Journal. 2014;4(6):901-917.
Mukhopadhyay S, Layek GC, Samad SA. Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity. Int. J. Heat Mass Transfer. 2005;48:4460-4466.
Pantokratoras A. Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity: A numerical reinvestigation. Int. J. Heat Mass Transfer. 2008;51:104-110.
Saikrishnan P, Roy S. Non-uniform slot injection (suction) into steady laminar water boundary layers over (i) a cylinder and (ii) as phere. Int. J Eng. Sci. 2003;41:1351–65.
Bird RB, Stewart WE, Lightfoot EN. (). Transport phenomena. New York: Wiley; 1960.
Chiam TC. Heat transfer with variable conductivity in a stagnation-point flow towards a stretching sheet. International Communications in Heat and Mass Transfer. 1996;23(2):239-248.
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