Effect of Temperature Dependent Sink on Peristaltic Transport in a Differentially Heated Vertical Annulus Filled with a Porous Material

Abstract

In this article, we have presented a mathematical analysis to study the peristaltic flow through vertical annulus filled with a porous material bounded by two concentric uniform tubes. This analysis can serve as a model which may help in understanding the mechanism of physiological flows and heat transfer in a vertical annulus subject to differentially heating in the presence of a temperature dependent sink. The inner tube is uniform and rigid, while the outer tube has a sinusoidal wave traveling down its wall. It is analyzed in a wave frame of reference moving with velocity of the wave under a zero Reynolds number and long wavelength approximation in the presence of a temperature dependent sink. The analytical solutions are obtained for temperature, axial velocity, stream function and axial pressure-gradient. We also present numerical integration in order to analyze the pressure rise and frictional forces on the inner and outer tubes. In order to have an estimate of the quantitative effects of various emerging physical parameters on flow characteristics which are involved in the solutions of the considered analysis, we have used the MATLAB software for plotting the contour graphs and discussed in details. We have observed that the intensity of heat sink increases when amplitude ratio is increased. The trapped bolus appears when Darcy number is small but the important observation is that for the large values of Darcy number, the trapped bolus disappears and fluid moves like a block, which shows some sort of rigidity.