Abstract

The effects of variable viscosity and thermal conductivity on the MHD flow of micropolar fluid on a continuous moving surface in the presence of a transverse magnetic field are studied considering the viscosity and thermal conductivity as the inverse linear functions of temperature where the microinertia density is assumed to be variable and not constant, as many other earlier published papers. Also, the viscous dissipation effect is taken into account. The partial differential equations governing the flow and heat transfer of the problem are transformed into dimensionless form of ordinary differential equations by using similarity substitutions. The governing boundary value problems so obtained are then solved numerically using Runge-Kutta method. The effects of various parameters viz. viscosity parameter, thermal conductivity parameter, magnetic parameter, coupling constant parameter, Eckert number and Prandtl number on velocity, micro-rotation, temperature field and micro-inertia density are studied and results are presented graphically. The co-efficient of skin-friction and Nusselt number are also computed and presented in tabular form.

References

• Abd El-hakiem M., Modather M., Abdou M, The effect of variable viscosity on MHD natural convection in micropolar fluids, Int. J. Appl. Mech. Engg., 11, 2( 2006), pp. 301-320.
• Eringen A.C., Simple micro fluids, Int. J. Eng. Sci., 2 (1964) pp. 205-217
• Eringen A.C., Theory of micropolar fluids, J. Math. Mech., 16, (1966), pp.1-18
• Eringen A.C., Theory of micropolar fluids, J. Math. Anal. Appl., 38(1972), pp.480- 496
• Gorla R.S., Heat transfer in micropolar boundary layer flow over a flat plate, Int. J. Eng. Sci., 21 (1983), pp. 791-796
• Gorla R.S.R., Combined forced and free convection in micropolar boundary layer flow on a vertical flat plate, Int. J. Engng. Sci., 26, 385-391, 1988.
• Gorla R.S.R., Takhar H.S., Slaouti A., Magneto hydrodynamic free convection boundary layer flow of a thermo micropolar fluid over a vertical plate, Int. J. Eng. Sci., 36(1998) pp. 315-327
• Guram G.S., Smith A.C., Stagnation flow of micropolar fluids with strong and weak interactions, Comp. Math. With Appl., 6, 213-233, 1980
• Hoyt J.W., Fabula A.G., The effect of additives on fluid friction, U S Naval Ordinance Test Station Report, 1964
• Ishak A., Nazar R., Pop I., Flow of a micropolar fluid on a continuous moving surface, Arch. Mech., 58,6,(2006), pp.529-541
• Khound P.K., Hazarika G.C., The effect of variable viscosity and thermal conductivity on liquid film on an unsteady stretching surface, Proc. of 46th Annual Tech. Session, Ass Sc. Soc. 2000, pp. 47-56
• Lai, F.C. and Kulacki, F.A., The effect of variable viscosity on convective heat and mass transfer along a vertical surface in saturated porous medium, Int. J.Heat and Mass Transfer 33, 1028-1031
• Muthucumaraswami R., Sundar M., Subramonium V.S.A., Magnetic field effects on flow past an accelerated isothermal vertical plate with heat and mass diffusion, Annals of faculty Engineering, Hunedoara- Int. J. of Eng., 2012,pp.177-180
• Modather M., Abdou M., Roshdy El-Zahar E., Variable viscosity effect on heat transfer over a continuous moving surface with variable internal heat generation in micropolar fluids, Appl.Math. Sci, 6,128, 2012, pp. 6365-6379
• Peddieson J., Mecnitt R. P., Boundary layer theory for a micropolar fluid, Recent Adv. Engng. Sci., 5 (1997) pp.405-425
• Rajesh V., MHD free convection flow past an accelerated vertical porous plate with variable temperature through a porous medium, Acta Technica Corviniensis, Bulletin and Engineering, pp.91-96
• 17. Salem A. M., Odda S. N., Influence of variable viscosity and thermal conductivity on flow of micropolar fluid past a continuously moving plate with suction or injection, The Korean society for Ind. Appl. Math., 2005
• Sarma U., Hazarika G. C., Effects of variable viscosity and thermal conductivity on heat and mass transfer flow along a vertical plate in the presence magnetic field, Int. J. Phy. Education,
• Sarma U., Hazarika G. C. Effects of variable viscosity and thermal conductivity on combined free-forced convection and mass transfer flow passed a vertical porous plate, Antarctica J. Math., 7(4), 2010, pp.461-472
• Soundalgekar V.M., Takhar H.S., Flow of micropolar fluid past a continuously moving plate with vriable spin gradient viscosity, Acta Mech., 131, 139-151, 1998
• Vogel W.M., Patterson A.M., An experimental investigation of additives injected into the boundary layer of an underwater body, Pacific Naval Lab. of the Defence Res. Board of Canada, Report 64-2, 1964.