Abstract
This paper investigates the influence of temperature-dependent viscosity on peristaltic flow of a Newtonian fluid past a vertical asymmetric channel through a porous medium in the presence of heat and mass transfer. A mathematical model is analyzed under assumptions of long wavelength and small Reynolds number. The resulting system of coupled nonlinear differential equations with corresponding boundary conditions is computed in two different cases. In the first case (labeled as system I), all non-dimensional parameters, which are functions of viscosity, have been considered as constants within the flow (as treated in previous peristaltic flow problems). In the second case (labeled as system II), these mentioned parameters are then assumed to vary with temperature. Solutions in each case have been obtained using an easy and highly accurate series-based method called the multi-step differential transform method (MsDTM). The effects of the pertinent physical parameters on the longitudinal velocity, temperature, concentration, longitudinal pressure gradient, and pressure rise per wavelength are analyzed graphically and through tables for both systems I and II. The results reveal that the longitudinal pressure gradient and the pressure rise per wavelength in the case of system II are of lower magnitude than the equivalent values of system I. Another interesting observation is that the temperature field in the case of system II, increases with a decrease in the fluid viscosity, which is in accordance with physical observations, whereas the opposite behavior appears in the case of system I. A detailed comparison between system I and system II demonstrates that in modelling fluid problems with variable viscosity, treating the viscosity-dependent parameters as constants leads to unrealistic results. Such a model is applicable for the transportation of physiological flows (blood flow models) in the arteries with heat and mass transfer.