Soret and Dufour effects between two rectangular plane walls with heat source/sink

Abstract

This study addresses the thermo-diffusion and the diffusion-thermo phenomena in a semi-infinite absorbent channel whose walls are contracting/expanding, with heat source/sink effects. The governing partial differential equations with suitable boundary conditions are transformed to a system of dimensionless ordinary differential equations. An analytic solution of the problem has been found using a technique called homotopy analysis method (HAM). HAM gives consistently valid answers to the problem over an extensive variety of parameters and also provides better accuracy. To validate the analytical results, a comparison has been presented with a numerical solution calculated by using the parallel shooting method. The effects of dimensionless parameters, that is, deformation parameter, Reynolds number, Soret and Dufour numbers, and heat source/sink parameter on the expressions of velocity, temperature, and concentration profiles are analyzed graphically to understand the physics of the deformable channel. It has been noted that the velocity across the channel is higher for the expanding channel, as compared to that for the contracting channel. Also the Soret and Dufour number increases the temperature of the fluid, and decreases the concentration. The temperature profile has an increasing behavior in the case of heat source, and a decreasing behavior in the case of heat sink. K E Y W O R D S deformable porous channel, heat and mass transfer, heat source/sink, incompressible fluid, Soret and Dufour effects | INTRODUCTIONThe study of laminar flow inside parallel porous walls is substantial because of its applications in engineering, biological sciences, and chemistry. The flow between parallel porous walls is an old question and the models for such flow for different physical situations improved with the passage of time. The simplest model for the flow in infinite parallel walls was described by Poiseuille 1 with the assumptions of steady, laminar, incompressible, and one dimensional flow. Hagen and Poiseuille had presented the theory of the flow through a straight pipe and considered rotational symmetry and constant pressure gradient. Similarly, flow in an infinite long channel with top suction and bottom injection, and unsteady flow in an infinite channel with oscillating pressure are also discussed in the literature. These initial models were expressed in one dimension and were consistent to certain approximations. Berman 2 was the first to consider laminar, two dimensional, incompressible, viscous flows that occurred due to the uniform suction between rectangular parallel and semi-infinite porous walls. He derived his solution using the perturbation technique assuming that Reynolds number is small. His work was later extended by various authors for numerous values of Reynolds number and varying flow conditions (see Sellars, 3 Proudman, 4 and Terill 5 ). Oscillatory flow in a channel has been studied by Ali and Asghar 6 for the case of small suction. Marwat and Asghar 7 investigated the flow between inclined plane w...

Numerical Treatment For MHD Axisymmetric Rotating Bodewadt Rheology Under Ohmic Heating And Viscous Dissipation Effects

“…Rafiq et al [31] formulated the impacts of heat transfer in fluid flow produced by a revolving permeable disk with variable characteristics of fluid. Several attempts in this regime has been made by investigators includes [32][33][34][35][36][37][38][39][40].…”

Multislip and Soret–Dufour influence on nonlinear convection flow of MHD dissipative Casson fluid over a slendering stretching sheet with generalized heat flux phenomenon

“…Layek et al 42 analyzed the Soret–Dufour influence on the expanding permeable sheet conveying Powell–Eyring fluid; therein, the solutal and thermal profiles are found to upsurge for higher magnitudes of Soret and Dufour parameters. Soret and Dufour parameters speedup the temperature and slow down the concentration profiles 43,44 . Recent literature on Soret–Dufour influence with different fluid properties and geometries includes Idowu and Falodun, 45–47 Kaladhar et al, 48 Khan et al, 49 and Faraz et al 50 to mention a few.…”

“…Soret and Dufour parameters speedup the temperature and slow down the concentration profiles. 43,44 Recent literature on Soret-Dufour influence with different fluid properties and geometries includes Idowu and Falodun, [45][46][47] Kaladhar et al, 48 Khan et al, 49 and Faraz et al 50 to mention a few.…”