Dufour Effect with Ramped Wall Temperature and Specie Concentration on Natural Convection Flow through a Channel

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 (Pr), Schmidt number (Sc), 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 Pr = 0.025, 0.71, 7.0, 11.62, 100.0 and Sc = 0.22, 0.60, 1.00, 2.62, while the values of all other parameters are arbitrarily taken.Physics 2019, 1 112 unsteady magnetohydrodynamics natural convection flow through a porous medium, with ramped boundary conditions, over an infinite inclined wall in the presence of thermal radiation. Authors in [20] showed how heat and mass transfer were affected, by introducing a perfectly thin conducting baffle in a vertical channel, filled with electrically conducting and chemically reacting fluid. After inserting the baffle, the fluid is concentrated in each stream with different chemically reacting agents. The basic governing equations were solved by perturbation method and also by Differential Transformation Method (DTM). The effects of Joule-heating, chemical reactions, and thermal radiation on unsteady magnetohydrodynamic (MHD) natural convection, from a heated vertical porous plate in a micropolar fluid, were analyzed by [21]. The partial differential equations, governing the flow and heat and mass transfer, were solved numerically using an implicit finite-difference scheme. The case corresponding to vanishing of the anti-symmetric part of the stress tensor, that represents weak concentrations, was considered. Authors in [22] studied the steady laminar magneto-hydrodynamic thermosolutal Marangoni convection, in the presence of a uniform applied magnetic field, in the boundary layer approximation. They assumed that the surface tension varies linearly with both the temperature and concentration, and that the interface temperature and concentration are quadratic functions of the interface arc length x. Exact analytical solutions for the velocity, temperature, and concentration boundary layers were obtained.Two important phenomena in heat and mass transfer processes are Dufour and Soret effects. Dufour effect (also diffusion-thermo) is the transfer of heat, generated by a concentration gradient, while Soret effect (also thermal diffusion) is the mass transfer generated by temperature ...

Soret and Dufour effects on transient free convention heat and mass transfer flow in a vertical channel with ramped wall temperature and specie concentration: an analytical approach

“…It is important to note that in the absence of Soret effect (i.e. when S r ¼ 0), the analytical solutions for temperature, concentration and velocity given by Equations ( 44)-( 46) correspond with the solutions obtained in Jha and Gambo (2019). In other words, the result obtained in Jha and Gamb ( 2019) is a particular case of the results presented in this article.…”

“…Although the magnitudes of the two effects are small, however, they have been seen to have direct relevance in systems where density differences in the flow region exist such as in petrology, isotopes separation, hydrology, chemical processing, geoscience among others (Ashyralyev & Gambo, 2016;Isah, Jha, & Jeng-Eng, 2016;Jha & Gambo, 2019;Omowaye, Fagbade, & Ajayi, 2015;Tippa, Narahari, & Rajashekhar, 2014;Uwanta & Usman, 2014). Several studies reveal that free convection heat and mass transfer flow can be affected by Soret effect, Dufour effect or the combination of the two (Bourich, Hasnaoui, Mamou, & Amahmid, 2004;Isah et al, 2016;Jha & Gambo, 2019;Kafoussias & Williams, 1995;Lagra, Bourich, Hasnaoui, Amahmid, & Er-Raki, 2018;Mortimer & Eyring, 1980;Omowaye et al, 2015;Raju, Narahari, & Rajashekhar, 2014;Reddy, 2016;Soret, 1979;Tippa et al, 2014;Uwanta & Usman, 2014). However, when the two effects are combined, the resulting system of governing equations becomes highly complicated and its analytical solution has been an outstanding challenge in heat and mass transfer process.…”

An exact analysis of radiative heat transfer and unsteady MHD convective flow of a second‐grade fluid with ramped wall motion and temperature

“…By eliminating the thermal radiation from our considered model, Equation (37) and (38), respectively, become identical to the Equations (22) and (26) of Samiulhaq et al 57…”

“…Maiti and Mandal 21 addressed the wall slip condition, buoyancy effect, and ramped surface condition for time‐dependent motion over an infinite wall. Jha and Gambo 22 examined a naturally convective channel flow under the impression of Dufour effect with specie concentration and ramped boundary surface. Seth et al 23‐26 extensively contributed to the literature by investigating the various physical aspects of mass and heat transfer phenomenons dealing with Hall current, Darcy's law, thermal radiation, chemical reaction, and nonuniform temperature conditions.…”

Influence of ramped pressure gradient on transient flow formation in a horizontal porous channel

“…It was noticed that all the transport phenomena involved in the flow formations are lowered when a ramped wall temperature boundary condition is considered by Jha and Gambo. 17 Lei et al 18 presented a transient stage comparison of Couette flow of an incompressible Newtonian fluid under step shear stress and step velocity boundary conditions. An analysis of the effect of ramped wall temperature and radiation on MHD natural convection flow near a vertical plate was presented.…”