Stress-Work and Chemical Reaction Effects on MHD Forced Convection Heat and Mass Transfer Slip-Flow Towards A Convectively Heated Plate In A Non-Darcian Porous Medium With Surface Mass-Flux
Keywords:
Forced convection, higher order chemical reaction, heat and mass transfer, Magnetohydrodynamics (MHD), stress work, non-Darcy model, nonlinear Roseland radiation.
Abstract
Analysis is conducted numerically on forced-convective heat and reactive solute mass transfer of a steady incompressible, electrically conducting, chemically reacting and Joule dissipating viscous fluid streaming towards a stationary porous planar surface embedded in a saturated non-Darcian porous medium in the presence of surface mass flux, pressure stress-work and velocity slip. The governing coupled nonlinear boundary layer partial differential equations are transformed by existing similarity variables into a set of nonlinear, ordinary differential equations in conjunction with the accompanying boundary conditions and then solved using a shooting quadrature along with fourth order Runge-Kutta integration scheme. The features of the flow, heat and mass transfer characteristics as per the skin friction coefficient, heat and mass transfer rates subject to simulated values of the Darcian number, Forchheimer number, Prandtl number, Eckert number, Schmidt number, reaction rate and order, mass flux (transpiration) and Biot number are analysed and discussed by means of tables while the dimensionless temperature, velocity and concentration profiles are captured through graphs. All these basic flow parameters bear significant influences on the flow.
References
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[34] Olanrewaju, P. O. and Adeniyan, A. (2013): Dufour and Soret effects on MHD free convection with thermal radiation and mass transfer past a vertical plate embedded in a porous medium, Nonlinear Sci. Lett. A, vol. 4, no. 1, pp. 21-34.
[35] Hayat, T., Rashid, M., Imtiaz, M., Alsaedi, A. (2015): Magnetohydrodynamic (MHD) stretched flow of nanofluid with power-law velocity and chemical reaction, AIP Advances 5, 117121, pp.1-19, ; doi: 10.1063/1.4935649.
[36] Adeniyan, A. and Aroloye, S. J. (2015): Effects of thermal dissipation, heat generation/absorption on MHD mixed convection boundary layer flow over a permeable vertical plate embedded in an anisotropic porous medium, Gen. Math. Notes, vol. 30, no. 2, pp. 31-53.
[37] Adeniyan, A. (2015): Mixed convection of a viscous dissipation and chemically reacting stagnation-point flow near a vertical permeable plate in a porous medium with thermal radiation and heat source/sink, Asian J. Math. and Applications, ID ama 0264, 23 pages.
[38] Fatumbi, E. O and Fenuga, O. J. (2017): MHD Micropolar Fluid Flow Over a Permeable Stretching Sheet in the presence of Variable Viscosity and Thermal Conductivity with Soret and Dufour Effects, Int. J. of Math Analysis and Optimization, pp. 211 – 232.
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[41] Grubka, L. J. and Bobba, K. M. (1985): Heat transfer characteristics of a continuous, stretching surface with variable temperature, Transactions of ASME J. Heat Transfer, vol.107, pp. 248-250.
[2] Andersson, H. I., Hansen, O. R. and Holmedal, B. (1994): Diffusion of chemically reactive species from a stretching sheet, Int. J. Heat Mass Transfer, vol. 37, issue 4, pp. 659-664.
[3] Weidman, P. D., Kubitschek, D. G., Davis, A. M.(2006): The effect of transpiration on self-similar flow over moving surfaces, Int. J. Engineering Science, pp. 730-737.
[4] Kechil, S. A. and Hashim, I. (2008): Series solution of flow over nonlinearly stretching sheet with chemical reaction and magnetic field, Phy. Lett. A, vol. 372, pp. 2258-2263.
[5] Merkin, J. H. and Pop, I. (2011): The forced convection flow of a uniform stream over a flat surface with a convective surface boundary condition, Commun. Nonlinear Sci. Numer. Simlat., vol. 16, pp. 3602-3609.
[6] Uddin, M. J., Khan, W. A., Ismail, A. I. M. (2013): MHD forced convective laminar boundary layer flow from a convectively heated moving vertical plate with radiation and transpiration effect, PLoS ONE, vol. 8, issue 5, pp. 1-10.
[7] Gebhart, B. (1962): Effects of viscous dissipation in natural convection, J. Fluid Mech., vol. 14, pp.225-232.
[8] Gebhart, B. and Mollendorf, J. (1969): Viscous dissipation in external natural convection flows, J. Fluid Mech., vol. 38, pp. 97-107.
[9] Zakerullah, M. (1972): Viscous dissipation and pressure work effects in axisymmetric natural convection flows, Ganit J. Banglandesh Math. Soc., vol. 2, no. 1, pp. 43.
[10] Ackroyd, J. A. D. (1974): Stress work effects in laminar flat-plate natural convection, J. Fluid Mech., vol. 62, pp. 677-695.
[11] Joshi, Y. and Gebhart, B. (1981): Effect of pressure stress work and viscous dissipation in some natural convection flows, Int. J. Heat Mass Transfer, vol. 24, no. 10, pp. 1377-1388.
[12] Pantokratoras, A. (2003): Effect of viscous dissipation and pressure stress work in natural convection along a vertical isothermal plate. New results, Int. J. Heat and Mass Transfer, vol. 46., pp. 4979-4983.
[13] Pantokratoras, A. (2005): Effect of viscous dissipation in natural convection along a heated vertical plate, Appl. Math. Modelling, vol. 29, pp. 553-564.
[14] Alam, M. M., Alim, M. A., Chowdhury, M. K. (2006): Effect of pressure stress work and viscous dissipation in natural convection flow along a vertical flat plate with heat conduction, J. Naval Arch. and Marine Eng., vol. 3, pp. 67-76.
[15] Bhuiyan, A. S., Azim, N. H. M. A., Chowdhury, M. K. (2014): Joule heating effects on MHD natural convection flows in presence of pressure stress work and viscous dissipation from a horizontal circular cylinder, J. of Appl. Fluid Mech., vol. 7, no. 1, pp. 7-13.
[16] Eldabe, N. T. M., Elbashbeshy, E. M. A., Youssef, I. K., Sedki, A. M. (2014): The effects of temperature dependent viscosity and viscous dissipation on MHD convection flow from an isothermal horizontal circular cylinder in the presence of stress work and heat generation, Euro. Sci. Journal, vol. 10, no. 36, pp.81-103.
[17] Islam, M. M., Alam, M. M., Parvev, M. M., Karim, R. (2015), Conjugate effects of stress work and heat generation on MHD natural convection flow along a vertical flat plate with power law variation of surface temperature, J. of Comp. and Math. Sci., vol. 6, no. 9, pp. 460-472.
[18] Makinde, O. D. (2010): Similarity solution of hydromagnetic heat and mass transfer over a vertical plate with a convective surface boundary condition, Int. J. of the Phy. Sciences, vol. 5, issue 6, pp. 700-710.
[19] Babu, P. R., Rao, J. A., Sheri, S. (2014): Radiation effect on MHD heat and mass transfer flow over a shrinking sheet with mass suction, J. of Appl. Fluid Mech., vol. 7, no. 4, pp. 641-650.
[20] Ozinik, M. N. (1973): Thermal Radiation Transfer and Interactions with Conduction and Convection, John Wiley & Sons, New York.
[21] Cess, R. D. (1966): The Interaction of Thermal Radiation in Boundary Layer Heat Transfer, Proceedings of the 3rd International Heat Transfer Conference, vol. 5, pp. 154-163.
[22] Cess, R. D. (1966): The Interaction of Thermal Radiation in Boundary Layer Heat Transfer, Proceedings of the 3rd International Heat Transfer Conference, vol. 5, pp. 154-163.
[24] Makinde, O. D. and Ogulu, A. (2008): The effect of thermal radiation on heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field, Chem. Eng. Commun., vol. 195, issue 12, pp.1575-1584.
[25] Olanrewaju, P. O., Adeniyan, A. and Alao, S. F. (2013): Soret and Dufour effects on hydromagnetic free convection flow with heat generation and mass transfer past a porous plate in the presence of chemical reaction and thermal radiation, Far East J. of Appl. Math., vol. 20, no. 1, pp. 41-66.
[26] Makinde, O. D. (2009): On MHD boundary-layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux, Int. J. of Num. Methods for Heat & Fluid Flow, vol. 19, nos. 3/4 pp. 546-554.
[27] Rashidi, M. M., Rostami, B., Freidoonimehr, N., Abbasbandy, S. (2014): Free convective heat and mass transfer for MHD fluid flow over a permeable vertical stretching sheet in the presence of the radiation and buoyancy effects, Ain Shams Eng. Journal, issue 5, pp. 901-912.
[28] Omowaye, A. J. and Ajayi, A. O. (2014): Effects of some thermo-physical properties on force convective stagnation point on a stretching sheet with convective boundary conditions in the presence of thermal radiation and magnetic field, Math. Theory and Modelling, vol. 4, no. 9, pp. 24-30.
[29] Akinbobola, T. E. and Okoya, S. S. (2015): The flow of second grade fluid over a stretching sheet with variable thermal conductivity and viscosity in the presence of heat source/sink, J. of Nig. Math. Soc., vol. 34, pp. 331-342.
[30] Salem, A. M. (2006): Coupled heat and mass transfer in Darcy-Forchheimer mixed convection from a vertical flat plate embedded in a fluid-saturated porous medium under the effects of radiation and viscous dissipation, J. of Korean Phy. Soc., vol. 48, no. 3, pp. 409-413.
[31] Rashidi, M. M., Rahimzadeh, N., Ferdows, M., Uddin, M. J., Bég, O. A. (2012): Group theory and differential transform analysis of mixed convection and mass transfer from a horizontal surface with chemical reaction effects, Chem. Eng. Commun., vol. 199, no. 8, pp. 1012-1043.
[32] Makinde, D. O. (2005): Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate, Int. Comm. in Heat and Mass Transfer, vol. 32, pp. 1411-1419.
[33] Makinde, O. D., Zimba, K., Bég, A. O. (2012): Numerical study of chemically-reacting boundary layer flow with Soret/Dufour effects and a convective surface boundary condition, Int. J. of Thermal & Environmental Eng., vol. 4, no. 1, pp. 89-98.
[34] Olanrewaju, P. O. and Adeniyan, A. (2013): Dufour and Soret effects on MHD free convection with thermal radiation and mass transfer past a vertical plate embedded in a porous medium, Nonlinear Sci. Lett. A, vol. 4, no. 1, pp. 21-34.
[35] Hayat, T., Rashid, M., Imtiaz, M., Alsaedi, A. (2015): Magnetohydrodynamic (MHD) stretched flow of nanofluid with power-law velocity and chemical reaction, AIP Advances 5, 117121, pp.1-19, ; doi: 10.1063/1.4935649.
[36] Adeniyan, A. and Aroloye, S. J. (2015): Effects of thermal dissipation, heat generation/absorption on MHD mixed convection boundary layer flow over a permeable vertical plate embedded in an anisotropic porous medium, Gen. Math. Notes, vol. 30, no. 2, pp. 31-53.
[37] Adeniyan, A. (2015): Mixed convection of a viscous dissipation and chemically reacting stagnation-point flow near a vertical permeable plate in a porous medium with thermal radiation and heat source/sink, Asian J. Math. and Applications, ID ama 0264, 23 pages.
[38] Fatumbi, E. O and Fenuga, O. J. (2017): MHD Micropolar Fluid Flow Over a Permeable Stretching Sheet in the presence of Variable Viscosity and Thermal Conductivity with Soret and Dufour Effects, Int. J. of Math Analysis and Optimization, pp. 211 – 232.
[39] Hughes, W. F. and Gaylord, E. W. (1964), Basic equations of engineering science, Schaum’s outline series, McGraw-Hill Bk Coy, New York.
[40] Jaluria, Y. (1980), Natural convection heat and mass transfer, 1st Ed., Pergamon Press, Oxford, N.Y.
[41] Grubka, L. J. and Bobba, K. M. (1985): Heat transfer characteristics of a continuous, stretching surface with variable temperature, Transactions of ASME J. Heat Transfer, vol.107, pp. 248-250.
Published
2018-08-06
How to Cite
Adeniyan, A., & Adigun, J. A. (2018). Stress-Work and Chemical Reaction Effects on MHD Forced Convection Heat and Mass Transfer Slip-Flow Towards A Convectively Heated Plate In A Non-Darcian Porous Medium With Surface Mass-Flux. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2018, 338 - 355. Retrieved from http://ijmso.unilag.edu.ng/article/view/49
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