Flow and heat transfer of couple stress and viscous fluids in a vertical channel

The problem of steady, laminar, fully developed flow and heat transfer of viscous and couple stress fluids in a vertical channel is investigated. The transport properties of the fluids in both the regions are assumed to be constant. The walls of the channel are considered to be isothermaI. The goveming momentum and energy equations are coupled and nonlinear due to the buoyancy effects. The basic equations are solved analytically using the regular perturbation method and numerically using the Runge-Kutta-GiII method. The results are represented graphically for different vaIues of the couple stress parameter, viscosity ratio, width ratio, coefficient of thermaI expansion ratio, density ratio, conductivity ratio, ratio of the Grashof number and Reynolds number and Eckert number on velocity and temperature distributions. In addition, results for the Nusselt number are computed for different values of the physical parameters and presented in a tabular form. It is found that the effect of the couple stress parameter is to promote the motion of the fluid.