Effect of Thermal Radiation and Viscous Dissipation on Steady MHD Free Convection and Mass Transfer Flow of a Micro Polar Fluid with Constant Heat and Mass Fluxes

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-52 Number-4
Year of Publication : 2017
Authors : Dr.R. Siva Gopal, Prof.R.Siva prasad
  10.14445/22315373/IJMTT-V52P535

MLA

Dr.R. Siva Gopal, Prof.R.Siva prasad "Effect of Thermal Radiation and Viscous Dissipation on Steady MHD Free Convection and Mass Transfer Flow of a Micro Polar Fluid with Constant Heat and Mass Fluxes", International Journal of Mathematics Trends and Technology (IJMTT). V52(4):234-248 December 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
We study, the effect of thermal radiation and viscous dissipation on steady MHD free convection and mass transfer flow of a micropolar fluid with constant heat and mass fluxes. The diffusion thermo, thermal diffusion, viscous dissipation and Joule heating have been considered for high speed fluid. The governing equations of the problem contain the partial differential equations which are transformed by similarity technique into dimensionless ordinary coupled non-linear differential equations. The dimensionless governing equations are solved numerically by using fourth order Runge–Kutta shooting iteration technique. We investigate in detail the distributions of velocity, microrotation, temperature and concentration across the boundary layer and also evaluated the skin friction, couple stress, the rate of heat and mass transfer at the plate.

Reference
[1] Altan, T., Oh, S., Gegel, H: Metal Forming Fundamentals and Applications. American Society of Metals, Metals Park, OH (1979).
[2] Ariman, T., Turk, M.A., Sylvester, N.D: Microcontinuum fluid mechanics–a review. Int. J. Eng. Sci. 12, pp. 273–293(1974).
[3] Char, M.I., Chang, C.L: Laminar free convection flow of micropolar fluids from a curved surface. J. Phys. D: Appl. Phys. 28, pp.1324–1331(1995).
[4] Chandrakala,P., Narayana, p : Radiation effects on MHD flow past an impulsively started infinite vertical plate with mass diffusion International Journal of Applied Mechanics and Engineering,Vol.19 (1),pp.17-26 (201
4) [5] Desseaux, A., Kelson, N.A: Flow of a micropolar fluid bounded by a stretching sheet. ANZIAM J. 42, pp. C536–C560 (2000).
[6] Ebert, F: A similarity solution for the boundary layer flow of a polar fluid. J.Chem. Eng. 5, pp. 85–92 (1973). [7] El-Amin, M.F: Magnetohydrodynamic free convection and mass transfer flow in micropolar fluid with constant suction. J. Magn. Magn. Mater. 234, p.567 (2001).
[8] El-Arabawy, H.A.M: Effect of suction/injection on the flow of a micropolar fluid past a continuously moving plate in the presence of radiation. Int. J. Heat Mass Transfer 46, pp. 1471–1477 (2003
). [9] El-Haikem, M.A., Mohammadein, A.A., El-Kabeir, S.M.M: Joule heating effects on magnetohydrodynamic free convection flow of a micropolar fluid. Int. J. Commun. Heat Mass Transfer 2, p. 219 (1999).
[10] Eringen, A.C: Theory of micropolar fluids. J. Math. Mech. 16, pp.1–18 (1966).
[11] Eringen, A.C: Theory of thermo micro fluids. J. Math. Anal. Appl. 38, pp. 480–496 (1972).
[12] Fisher, E.G: Extrusion of Plastics. Wiley, New York (1976).
[13] Gorla, R.S.R: Mixed convection in a micropolar fluid from a vertical surface with uniform heat flux. Int. J. Eng. Sci. 30, pp.349–358 (1992).[14] Gnaneswara Reddy, Machireddy : Thermal Radiation and Chemical Reaction Effects on Steady Convective Slip Flow with Uniform Heat and Mass Flux in the Presence of Ohmic Heating and a Heat Source, Tech Science Press FDMP, vol.10, no.4, pp.417-442( 2014).
[15] Hadimoto, B., Tokioka, T: Two-dimensional shear flows of linear micropolar fluids. Int. J. Eng. Sci. 7, pp.515–522 (1969).
[16] Harish Babu,D., Satya Narayana,P.V: Joule heating effects on MHD mixed convection of a Jeffrey fluid over a stretching sheet with power law heat flux: A numerical study, Journal of Magnetism and Magnetic Materials, Vol.412 , pp.185-193 (2016).
[17] Hitesh Kumar: Mixed convective–magnetohydrodynamic flow of a micropolar fluid with ohmic heating, radiation and viscous dissipation over a chemically reacting porous plate subjected to a constant heat flux and concentration gradient, Serb. Chem. Soc. 79 (4), pp.469–480 (2014).
[18] Hossain, M.A., Chowdhury, M.K., Takhar, H.S: Mixed convection flow of micropolar fluids with variable spin gradient viscosity along a vertical plate. J. Theor. Appl. Fluid Mech.1, pp. 64–77
(1995). [19] Karwe, M.V., Jaluria, Y: A Fluid flow and mixed convection transport from a moving plate in rolling and extrusion processes. J. Heat Transfer 110, pp. 655–661 (1988).
[20] Karwe, M.V., Jaluria, Y: Numerical simulation of thermal transport from a moving plate in rolling and extrusion processes. J. Heat Transfer 113, pp. 655–661 (1988).
[21] Kesavaiah,Ch., Satyanarayana,PV., Venkataramana, S : Radiation absorption, chemical reaction and magnetic filed effects on the free convection and mass transfer flow through porous medium with constant suction and constant heat flux, International Journal of Scientific Engineering and Technology,Vol.1(6), pp. 274-284 (2012).
[22] Khonsari, M.M., Brew, D: On the performance of finite journal bearing lubricated with micropolar fluids. ASLE Tribology Trans. 32, pp.155–160 (1989).
[23] Khonsari, M.M: On the self-excited whirl orbits of a journal in a sleeve bearing lubricated with micropolar fluids. Acta Mech. 81, pp.235–244 (1990).
[24] Kim, Y.J: Unsteady MHD convection flow of polar fluid past a vertical moving porous plate in a porous medium, Int. J. Heat Mass Transfer 44, p. 2791 (2001).
[25] Lee, J.D., Egigen, A.C: Boundary effects of orientation of nematic liquid crystals. J. Chem. Phys. 55, pp. 4509–4512 (1971).
[26] Lockwood, F., Benchaitra, M., Friberg, S: Study of polyotropic liquid crystals in viscometric flow and clastohydrodynamic contact. ASLE Tribology Trans. 30, pp.539–548 (1987).
[27] Mohammed Ibrahim, S., Sankar Reddy,T., Roja,P: Radiation Effects on Unsteady MHD Free Convective Heat and Mass Transfer Flow Of Past a Vertical Porous Plate Embedded In a Porous Medium with Viscous Dissipation ,IJIRSE,Vol.3,Issue11 (2014).
[28] Nachtsheim, P.R., Swigert, P: Satisfaction of the asymptotic boundary conditions in numerical solution of the system of non- linear equations of boundary layer type. NASA, TND-3004 (1965).
[29] Olajuwon,B.I., Oahimire, J.I: unsteady free convection heat and mass transfer in an mhd micropolar fluid in the presence of thermo diffusion and thermal radiatio, International Journal of Pure and Applied Mathematics Vol. 84 No. 2, pp. 15-37 (2013).
[30] Peddison, J., McNitt, R.P: Boundary layer theory for micro- polar fluid. Recent Adv. Eng. Sci. 5, pp.405–426 (1970).
[31] Rahman, M.M., Sattar, M.A: Magnetohydrodynamic convective flow of a micropolar fluid past a continuously moving porous plate in the presence of heat generation/absorption. ASME J. Heat Trans. 128, pp.142–152 (2006).
[32] Raju,K.V.S., Sudhakar Reddy, T., Raju, MC., Satya Narayana, PV., Venkataramana, S: MHD convective flow through porous medium in a horizontal channel with insulated and impermeable bottom wall in the presence of viscous dissipation and Joule heating, Ain Shams Engineering Journal, Vol .5(2), pp.543-551 (2014).
[33] Sakiadis, B.C: Boundary layer behavior on continuous solid surface; the boundary layer on a continuous flat surface. Am. ICHE J. 7, p. 221(1961).
[34] Seth,G.S., R. Sharma and B. Kumbhakar: Heat and Mass Transfer Effects on Unsteady MHD Natural Convection Flow of a Chemically Reactive and Radiating Fluid through a Porous Medium Past a Moving Vertical Plate with Arbitrary Ramped Temperature , Journal of Applied Fluid Mechanics, Vol. 9, No. 1, pp. 103-117( 2016).
[35] Tadmor, Z., Klein, I: Engineering Principles of Plasticating Extrusion, Polymer Science and Van nostrand Reinhold. Van nostrand Reinhold, New York(1970).
[36] Usha,P., Satya Narayana, PV: Thermal diffusion and radiation effects on mhd mixed convection flow in a channel with porous medium, International Journal of Mathematical Archive (IJMA), Vol.6,issue.7(2015).
[37] Venkateswarlu,B., Satya Narayana PV : Effects of Thermal Radiation on Unsteady MHD Micropolar Fluid past a Vertical Porous Plate in the Presence of Radiation Absorption, International Journal of Engineering Science,Vol.2259 (2016). [38] Yucel, A: Mixed convection micropolar fluid flow over horizontal plate with surface mass transfer. Intl. J. Eng. Sci. 27, pp.1593–1608 (1989).
[39] Ziaul Haque. Md and Mahmud Alam. Md : Micropolar fluid behaviors on steady MHD free convection and mass transfer flow with constant heat and Mass fluxes, joule heating and Viscous dissipation. Journal of king saud university-Engineering sciences 24 , pp.71-84 (2012).

Keywords
Micropolar fluids, Heat and Mass transfer, Soret effect, Dofur effect, Similarity.