Mixed convective flow of two immiscible viscous fluids in a vertical wavy channel with traveling thermal waves

Abstract

The problem of fully developed laminar mixed convection flow in a vertical wavy channel filled with two immiscible viscous fluids is studied analytically. 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 is solved using long wave approximation. Separate solutions are matched at the interface using suitable matching conditions. Numerical results are presented graphically for the distribution of velocity and temperature fields for varying physical 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, width ratio, and conductivity ratio enhance the velocity parallel to the flow direction. Reversal effect is observed on the velocity which is perpendicular to the flow direction. The Nusselt number remains invariant on Grashof number. As the width ratio decreases, the Nusselt number decreases at the right wall and increases at the left wall and reversal effect is observed for variations of conductivity ratio. The skin friction increases at the left wavy wall and decreases at the right wavy wall as the Grashof number increases. © 2011 Wiley Periodicals, Inc.