Chemically Reacting Unsteady Magnetohydrodynamic Oscillatory Slip Flow of a Micropolar Fluid in a Planer Channel with Varying Concentration
American Journal of Applied Mathematics
Volume 2, Issue 4, August 2014, Pages: 141-148
Received: Aug. 12, 2014; Accepted: Aug. 21, 2014; Published: Aug. 30, 2014
Views 3442      Downloads 174
A. A. Bakr, Department of Mathematics, Faculty of Science for Girls, Abha, King Khaled University, Saudi Arabia; Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt
Article Tools
Follow on us
The study examines the problem of unsteady MHD mixed convection in a micropolar fluid with oscillatory flow of an electrically conducting optically thin fluid through a planer channel filled with saturated porous medium. The effect of buoyancy, heat source, thermal radiation and chemical reaction are taken into account embedded with slip boundary condition, varying temperature and concentration. The closed-form analytical solutions are obtained for the momentum, angular momentum, energy and concentration equations. The influence of the various parameters entering into the problem in the velocity, temperature and concentration fields are discussed with the help of graphs. Finally the effects of the pertinent parameters on the skin friction, couple stress and the rate of heat transfer coefficient at the plate are discussed.
Micropolar Fluid, Oscillatory Flow, Thermal Radiation, Chemical Reaction, Heat and Mass Transfer, Planer Channel
To cite this article
A. A. Bakr, Chemically Reacting Unsteady Magnetohydrodynamic Oscillatory Slip Flow of a Micropolar Fluid in a Planer Channel with Varying Concentration, American Journal of Applied Mathematics. Vol. 2, No. 4, 2014, pp. 141-148. doi: 10.11648/j.ajam.20140204.15
Cooper WL, Nee VW and Yang KT. Fluid mechanics of oscillatory and modulated flows and associated applications in heat and mass transfer - a review. J Energy, Heat and Mass Transfer 1993; 15: 1–19.
Fusegi T. Numerical study of convective heat transfer from periodic open cavities in a channel with oscillatory through flow. Int J Heat and Fluid flow 1997; 18: 376-383.
Cheng CH, Huag HS, Huang WH. Flow reversal and heat transfer of fully developed mixed convection in vertical channels. J Thermo Phys, Heat Transfer 1990;4:375–83.
Hamadah TT, Wirtz RA. Analysis of laminar fully developed mixed convection in a vertical channel with opposing buoyancy. ASME J Heat Transfer 1991;113:507–10.
Barletta A. Heat transfer by fully developed flow and viscous heating in a vertical channel with prescribed wall heat fluxes. Int J Heat Mass transfer 1999;42:3501–13.
Umavathi JC, Prathap kumar J, Chamha AJ, Pop I. Mixed convection in a porous channel. Trans Porous Med 2005;61:315–35.
Prathap kumar J, Umavathi JC, Pop I, Biradar BM. Fully developed mixed convection flow in a vertical channel containing porous and fluid layer with isothermal or iso flux boundaries, Trans Porous Med. Doi 10.1007/s11242-009-9347- 8.
Pop I, Grosan T, Cornelia R. Effect of heat generated by an exothermic reaction on the fully developed mixed convection flow in a vertical channel. Commun Non linear Sci Numer Simul. 15 (2010) 471–474
Gomaa H, and Al Taweel AM. Effect of oscillatory motion on heat transfer at vertical flat surfaces. Int J Heat and Mass Transfer 2005; 48: 1494–1504.
Abdelkader K and Lounes O. Heat transfer enhancement in oscillatory flow in channel with periodically upper and lower walls mounted obstacles. Int J of Heat and Fluid Flow 2007; 28: 1003–1012.
El-Hakiem MA. MHD oscillatory flow on free convection-radiation through a porous medium with constant suction velocity,” J Magnetism and Magnetic Materials 2000; 220: 271-276.
Makinde OD and Mhone PY. Heat transfer to MHD oscillatory flow in a channel filled with porous medium,” Rom. J Phys 2005; 50: 931–938.
Mehmood1 A and Ali A. The effect of slip condition on unsteady MHD oscillatory flow of a viscous fluid in a planer channel. Rom. J Phys 2007; 52: 85–91.
Gholizadeh A. MHD oscillatory flow past a vertical porous plate through porous medium in the presence of thermal and mass diffusion with constant heat source. Astrophys. Space Sci 1990; 174: 303-310.
Makinde OD. Unsteady incompressible flow in a porous channel. Proc. Rom. Appl. Indust. Math. Oradea 1994; 47–58.
Makinde OD, and Aziz A. MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition. Int J of Thermal Sciences 2010; 49: 1813-1820.
Abdul Hakeem AK, and Sathiyanathan K. An analytic solution of an oscillatory flow through a porous medium with radiation effect. Nonlinear Analysis: Hybrid Systems 2009; 3: 288-295.
Srinivas S and Muthuraj R. Effects of thermal radiation and space porosity on MHD mixed convection flow in a vertical channel using homotopy analysis method. Commun. Nonlinear Sci. Numer. Simulat 2010; 15: 2098–2108.
Pal D, and Talukdar B. Perturbation analysis of unsteady magnetohydrodynamic convective heat and mass transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction. Commun Nonlinear Sci Numer Simulat 2010; 15: 1813–1830.
Ibrahim FS, Elaiw AM and Bakr AA. Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi-infinite vertical permeable moving plate with heat source and suction. Comm. Nonlinear Sci. Numer. Simulat 2008; 13:1056–1066
Bakr AA. Effects of chemical reaction on MHD free convection and mass transfer flow of a micropolar fluid with oscillatory plate velocity and constant heat source in a rotating frame of reference. Commun Nonlinear Sci Numer Simulat 2011; 16: 698–710.
Bakr AA and Raizah ZAS. Unsteady MHD mixed convection flow of a viscous dissipating micropolar fluids in a boundary layer slip flow regime with Joule heating, Int J Scientific & Engineering Research 2012; 3:, (8).
Prakash J, Sivaraj R and Rushi Kumar B. Influence of chemical reaction on unsteady MHD mixed convective flow over a moving vertical porous plate. In J of Fluid Dynamics, in press.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186