Consequences of variable wall permeability and magnetic field on non-isothermal flow in converging/diverging tubes

Abstract

The current article is devoted to the development of a theoretical model investigating heat transfer analysis of MHD blood flow through renal tubules. For this purpose, we consider the transport of Newtonian fluid inside a non-uniform tube whose lateral surface is kept at constant temperature. The walls of tube are considered to admit the variable permeation and the flow is actuated by an externally applied magnetic field. The solution of the problem is formulated analytically in terms of axial and radial velocities and temperature distribution under the presumption of lubrication approximation in the inertia free flow field. Implication of Darcy’s law for fluid seepage across the tubular membrane results in an ordinary differential equation having variable coefficients for the unknown pressure, which is successfully computed numerically using RK45 routine. Performance of velocity, pressure and temperature distributions has been investigated for various values of the physical parameters involving in the model. Moreover, flow rate behavior, fluid reabsorption and the leakage flux has been analyzed through graphs and tables. The characteristics of heat transfer in the flow field is also evaluated for various values of Brinkman number. A significant discovery reported in the results of present model reveals that the axial flow exhaustion and radial flow reversal are significantly influenced by the tube converging/diverging parameter and the Hartmann number as well. By employing a strong magnetic field, exhaustion and reversal phenomena in the flow field can be restrained up to a certain limit. Moreover, with an increasing wall permeability, there is a significant exhaustion of axial flow in a divergent tube and a prominent assistance takes place in the radial flow reversal for convergent tube. It is hoped that the present model will bear the potential to study flow in renal tubules and in hemodialyzer.