Abstract
In this paper, we have obtained an analytical solution to the problem of unsteady free convection and mass transfer flow of an incompressible fluid through a vertical channel in the presence of Dufour effect (or diffusion thermo). The bounding plates are assumed to have ramped wall temperature as well as specie concentration. The mathematical model responsible for the physical situation is presented in dimensionless form and solved analytically using the powerful Laplace Transform Technique (LTT) under relevant initial and boundary conditions. In order to cross check the accuracy of the analytical results, numerical solutions are obtained using PDEPE solver in MATLAB. The expressions for temperature, concentration, and velocity are obtained. The effects of Dufour parameter, Prandtl number ( P r ) , Schmidt number ( S c ) , and dimensionless time are described during the course of these discussions. The temperature, concentration, and velocity profiles are graphically presented for some realistic values of P r = 0.025 , 0.71 , 7.0 , 11.62 , 100.0 and S c = 0.22 , 0.60 , 1.00 , 2.62 , while the values of all other parameters are arbitrarily taken.
Highlights
Fluid flow, and the combined heat and mass transfer through a channel, have received less attention than the case of a single plate
The objective of the present work is to provide an analytical solution for the unsteady free investigated the Dufour effect on free convective flow with heat absorption, thermal radiation, chemical convection and mass transfer flow, in a vertical channel, with ramped wall temperature and ramped reaction, and magnetic field with ramped wall temperature over a single vertical plate contained in a wallpermeable specie concentration, in the presence of Dufour effect
The results presented here are compared with existing literature present work
Summary
The combined heat and mass transfer through a channel, have received less attention than the case of a single plate. Authors in [28] presented a numerical solution to the general problem of MHD flow, heat, and mass transfer of viscous incompressible nano-fluid past a uniformly stretching sheet through a porous media with heat generation/absorption, thermal radiation, chemical reaction, Dufour effect, and Soret effect. The objective of the present work is to provide an analytical solution for the unsteady free investigated the Dufour effect on free convective flow with heat absorption, thermal radiation, chemical convection and mass transfer flow, in a vertical channel, with ramped wall temperature and ramped reaction, and magnetic field with ramped wall temperature over a single vertical plate contained in a wallpermeable specie concentration, in the presence of Dufour effect. The present results will have specific applications in the design of solar energy collectors, geothermal systems, cooling of electronic equipment, and in the design of chemical processing equipment
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