Effect of internal heat source on magneto-stationary convection of couple stress fluid under magnetic field modulation

Abstract

The present article provides an analytical solution of nonlinear heat transfer of an electrically conducting Couple stress liquid under a magnetic field modulation with an internal heat source. A weakly nonlinear theory is used to obtain the rate of heat transfer concerning the Nusselt number. A cubic Landau equation is derived in terms of amplitude of convection and solved by using Mathematica 8 software. The effect of various system parameters are obtained on nonlinear heat transfer which is discussed in detail by graphically. The Prandtl number, internal Rayleigh number, Couple stress parameter and magnetic Prandtl number destabilize the system while Chandrasekhar number has stabilizing effect. Hence, Couple stress parameter and internal Rayleigh number increase the rate of heat transfer.