Temperature distribution in Couette flow past a permeable bed

The temperature distribution in a steady plane Couette flow having one permeable bounding wall is investigated in the presence of buoyancy forceN ₀ whenN ₀>0, it is shown that heat is transported both by convection and diffusion. The effect of convection is to increase the magnitude of the temperature distribution both in the free and Darcy flows. In particular, it is shown that the wall shear has no significant effect on the temperature distribution. The rate of heat transfer between the fluid and the surface is also calculated and it is shown that, it increases with the porous parameterσ. Although the viscous dissipation has very little effect on the temperature distribution yet its effect is significant on heat transfer.