Flow and heat transfer of a couple-stress fluid sandwiched between viscous fluid layers

Abstract

The problem of steady laminar fully developed flow and heat transfer in a horizontal channel consisting of a couple-stress fluid sandwiched between two clear viscous fluids is analyzed analytically. The fluids in all regions are assumed to be incompressible, immiscible, and the transport properties of the fluids in all regions are assumed to be constant. Under these assumptions, the resulting governing equations constitute a set of coupled linear ordinary differential equations that is solved analytically. The closed form solutions obtained for the velocity and temperature fields in the channel are evaluated numerically for various parametric conditions. These results are illustrated graphically to illustrate the effects of the physical parameters governing the flow such as the viscosity ratio, conductivity ratio, couple-stress parameter, Eckert number, and the Prandtl number on the velocity and temperature profiles. In addition, results for the rate of heat transfer are computed for different values of the physical parameters and presented in tabular form. It is found that the effect of the couple stress parameter is to promote the motion of the fluid.PACS Nos.: 44.15.+a