Solute dispersion in micropolar-Newtonian fluid flowing through porous layered tubes with absorbing walls

Abstract

The physical mechanism of heat and mass transfer in solute dispersion in a two-fluid model of the blood flow through porous layered tubes with absorbing walls has been studied in the present work. For a more realistic representation of the blood flow in microvessels, the two-fluid approach is employed by considering the fluid in which the blood particles like RBCs, WBCs, and platelets are suspended as a micropolar fluid in the core region and the cell-free layer of plasma as Newtonian fluid in the peripheral region. A thin Brinkman layer mathematically governed by the Brinkman equation replicates the mechanical aspects of the porous layer near the tube wall. Either no-spin or no-couple stress condition at the micropolar-Newtonian fluid interface has been taken in to account to compare our findings with previous studies and the stress-jump condition of Ochoa-Tapia and Whitaker (J.A. Ochoa-Tapia and S. Whitaker, Int. J. Heat Mass Transfer 38 (1995) 2635–2646) is employed at the fluid-porous interface. A uniform magnetic field has also been applied in the transverse direction of the flow pattern to understand some of the clinically relevant aspects of blood flow in the cardiovascular system. Analytical expressions for the velocity and temperature field are used to obtain the expressions for diffusion coefficients and mean concentration by following the method of Sankarasubramanian and Gill (R. Sankarasubramanian and W.N. Gill, Proc. R. Soc. London. Ser. A 333 (1973) 115–132), to analyze the solute dispersion process in fluid flowing through tubes with wall reactions. The effect of plasma layer thickness, radiation parameter, coupling number, micro-rotation, thermal conductivity, Hartmann number, and permeability on the diffusion coefficients and mean concentration of the miscible species are discussed and depicted graphically. The multi-motivational work with the combination of a porous layer near the wall and heat transfers may leave a significant impact on drug delivery through the blood vessels for the treatment of cardiovascular diseases.