MHD Micropolar Fluid Near a Vertical Plate with Newtonian Heating and Thermal Radiation in the Presence of Mass Diffusion
Pure and Applied Mathematics Journal
Volume 4, Issue 3, June 2015, Pages: 80-89
Received: Apr. 19, 2015; Accepted: Apr. 22, 2015; Published: May 13, 2015
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Authors
Ahmed A. Bakr, Department of Mathematics, Faculty of Science for Girls, King Khaled University, Abha, Saudi Arabia; Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt
Z. A. S. Raizah, Department of Mathematics, Faculty of Science for Girls, King Khaled University, Abha, Saudi Arabia
Ahmed M. Elaiw, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt
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Abstract
The effects of chemical reaction and thermal radiation on unsteady free convection flow of a micropolar fluid past a semi-infinite vertical plate embedded in a porous medium in the presence of heat absorption with Newtonian heating have been investigated. Both physically important boundary conditions of uniform wall concentration (UWC) and uniform mass flux (UMF) are considered. Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. Numerical results of velocity profiles of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid in UWC and UMF cases. Graphical results for velocity, temperature and concentration profiles of both phases based on the analytical solutions are presented and discussed. 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.
Keywords
Thermal Radiation, Chemical Reaction, Mass Diffusion, Newtonian Heating
To cite this article
Ahmed A. Bakr, Z. A. S. Raizah, Ahmed M. Elaiw, MHD Micropolar Fluid Near a Vertical Plate with Newtonian Heating and Thermal Radiation in the Presence of Mass Diffusion, Pure and Applied Mathematics Journal. Vol. 4, No. 3, 2015, pp. 80-89. doi: 10.11648/j.pamj.20150403.14
References
[1]
Eringen A C. Theory of micropolar fluids. J Math Mech, 1966, 16:1–18.
[2]
Ariman T, Turk M A, Sylvester N D. Microcontinuum fluid mechanics-a review. Int J Engng. Sci, 1973, 11:905–930.
[3]
Gorla R S R. Mixed convection in a micropolar fluid from a vertical surface with uniform heat flux. Int J Engng Sci, 1992, 30:349–358.
[4]
Rees D. A. S., Pop I. Free convection boundary layer flow of a micropolar fluid from a vertical flat plate. IMAJ Appl Math, 1998, 61:179–197.
[5]
Singh Ajay Kumar. Numerical solution of unsteady free convection flow of an incompressible micropolar fluid past an infinite vertical plate with temperature gradient dependent heat source. J Energy Heat and Mass Transfer, 2002, 24:185–194.
[6]
Hiremath P S, Patil P M. Free convection effects on oscillatory flow of couple stress field through a porous medium. Acta Mech, 1993, 98:143–158.
[7]
Kim Y J. Unsteady convection flow of micropolar fluids past a vertical plate embedded in a porous medium. Acta Mech, 2001, 148:105–116.
[8]
Bakr A A and Raizah Z A S: Unsteady MHD mixed convection flow of a viscous dissipating micropolar fluids in a boundary layer slip flow regime with Joule heating, International Journal of Scientific & Engineering Research, Volume 3, (8), 2012
[9]
Khandelwal K, Anil Gupta, Poonam, Jain N C. Effects of couple stresses on the flow through a porous medium with variable permeability in slip flow regime. Ganita, 2003, 54(2):203–212.
[10]
Sharma P K, Chaudhary R C. Effect of variable suction on transient free convective viscous incompressible flow past a vertical plate with periodic temperature variations in slip flow regime. Emirates Journal of Engineering Research, 2003, 8(2):33–38.
[11]
Hayat T., Javed T., Abbas Z., Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space, Int. J. Heat Mass Transfer 51 (2008) 4528–4534.
[12]
Asghar S., Gulzar M.M., Ayub M., Effects of partial slip on flow of a third grade fluid, Acta Mech. Sinica. 22 (2006) 393–396.
[13]
Khan M., Partial slip effects on the oscillatory flows of a fractional Jeffrey fluid in a porous medium, J. Porous Media 10 (2007) 473–488.
[14]
Asghar S., Khalique C.M., Ellahi R., Influence of a partial slip on flows of a second grade fluid in a porous medium, J. Porous Media 10 (2007) 797–805.
[15]
Cussler E L. Diffusion mass transfer in fluid systems[M]. 2nd Ed. Cambridge: Cambridge University Press. 1998.
[16]
Muthucumarswamy R, Ganesan P. First order chemical reaction on flow past an impulsively started vertical plate with uniform heat and mass flux. Acta Mech, 2001, 147:45–57.
[17]
Kandasamy R, Periasamy K, Prashu Sivagnana K K. Effects of chemical reaction, heat and mass transfer along wedge with heat source and concentration in the presence of suction or injection. Int J Heat Mass transfer, 2005, 48:1388–1394.
[18]
Bakr A.A., 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. Simul. 16 (2011) 698–710.
[19]
Ibrahim F.S., Elaiw A.M., Bakr A.A., Effect of the chemical reaction and radiation absorption on unsteady MHD mixed convection flow past a semi-infinite vertical permeable moving plate with heat source and suction, Commun. Nonlinear Sci. Numer. Simul. 13 (2008) 1056–1066.
[20]
Chaudhary RC, Jain P (2007) An exact solution to the unsteady free convection boundary-layer flow past an impulsively started vertical surface with Newtonian heating. J Eng Phys Thermophys 80:954–960
[21]
Merkin JH (1994) Natural convection boundary-layer flow on a vertical surface with Newtonian heating. Int J Heat Fluid Flow 15:392–398
[22]
Lesnic D, Ingham DB, Pop I (1999) Free convection boundary layer flow along a vertical surface in a porous medium with Newtonian heating. Int J Heat Mass Transf 42:2621–2627
[23]
Siegel, R., and Howell, J.R., Thermal Radiation heat transfer, 4th Edition, Taylor and Francis, New York, 2002.
[24]
Bakr A.A., Chemically Reacting Unsteady Magnetohydrodynamic Oscillatory Slip Flow of a Micropolar Fluid in a Planer Channel with Varying Concentration, American Journal of Applied Mathematics 2 (2014 ) 141-148.
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