Mixed convective flow of immiscible viscous fluids confined between a long vertical wavy wall and a parallel flat wall

Abstract

In this work, the flow and heat transfer in a long channel composed of a smooth and a corrugated wall filled with two immiscible viscous fluids is studied under laminar flow conditions. Non-linear equations governing the motion have been solved by linearization technique, wherein the flow is assumed to be in two parts; a mean part and a perturbed part. Exact solutions are obtained for the mean part and a perturbed part using long wave approximation. Separate solutions are matched at the interface using suitable matching conditions. The results are presented graphically for various governing parameters such as Grashof number, viscosity ratio, width ratio and conductivity ratio. The effect of these parameters on the physical characteristics such as Nusselt number and skin friction at the walls is studied. It is found that Grashof number, viscosity ratio and width ratio enhance the flow whereas, conductivity ratio reduces the flow. Rate of heat transfer and skin friction for varying parameters is also shown graphically.

International Journal of Engineering, Science and Technology, Vol. 2, No. 6, 2010, pp. 256-277