Wall reabsorption effects on heat and mass transfer of viscous fluid in a narrow leaky tube

Abstract

AbstractThe steady heat and mass transfer problem of flow of an incompressible Newtonian fluid is investigated in this study. The axisymmetric flow of a non-isothermal and highly viscous fluid is considered through a narrow leaky tube of uniform cross-section with linear reabsorption across the wall. The Navier–Stokes equations are solved for axially symmetric and slow flow in the tube. The effects of linear reabsorption parameter on the dimensionless radial and axial velocities, temperature, concentration, shear stress, leakage flux, fractional reabsorption, pressure drop across the tube as well as the Nusselt and Sherwood numbers have been investigated analytically. For 50% fractional reabsorption, inlet radial velocity is half of the reabsorption velocity along the tube. It has been shown that increase in the strength of linear reabsorption parameter considerably reduces the radial velocity, while, axial velocity shows opposite behaviour. At the exit region ($$z=0.9$$ z = 0.9 ), reverse flow phenomenon is observed for higher values of reabsorption parameter. The pressure, flow rate and wall shear stress decreases after entrance region ($$z=0.1$$ z = 0.1 ) of the tube. Nusselt number and Sherwood number show opposite behaviour inside the tube. At $$z=0.1$$ z = 0.1 the magnitude of Nusselt number is maximum, while the Sherwood number is minimum at the exit region with higher value of reabsorption parameter.