Natural convection flow of Rivlin–Ericksen fluid and heat transfer through non-Darcy medium with radiation

Abstract

The natural convection of non-Newtonian fluids between parallel plates has many engineering applications such as heat exchangers, cooling of electronic equipments, nuclear reactors, solar devices, polymer processing industries, food industries, and petroleum reservoirs. Numerical solution is introduced to solve the governing equations of natural convection of non-Newtonian (Rivlin–Ericksen) fluid flow and heat transfer under the influences of non-Darcy resistance force, constant pressure gradient, dissipation, and radiation. The novelty of this article is to solve this problem between parallel plates channel instead of one plate. The fluid flows between two heated parallel plates that are kept at constant temperatures. Second-order accurate finite difference schemes transform the coupled non-linear differential (momentum and energy) equations to linearized system of algebraic equations. Some comparisons are made to study the convergence and stability of the present results. Effects of parameters of fluid and heat on the velocity field, temperature, skin friction factor, and Nusselt number are illustrated and discussed. The present results and their comparisons with available results are listed and shown in tables and figures. The present results show that the numerical solution is of good agreement with previous analytical and numerical solutions.

Study effects of non-Darcy and heat source on MHD Rivlin-Ericksen Fluid of third-grade flow in a porous medium

“…At x = +b and x = b, the walls are kept at constant temperatures T 1 and T 2 , respectively, with T 1 > T 2 . The fluid near the wall is caused by the temperature difference, at x = −b to rise and the fluid near the wall at x = +b to fall [1][2][3][4][5][6][7][8][9][10].…”

“…Many researchers have described the natural convection of non-Newtonian fluids [1][2][3][4][5][6][7][8][9][10]. A specific class of Rivlin-Ericksen fluid was investigated [6][7].…”

“…A specific class of Rivlin-Ericksen fluid was investigated [6][7]. For the present nonlinear system of differential equations, there are various analytical and numerical methods that present different solutions [1][2][3][4][5][6][7][8]. Etbaeitabari et al [7] introduced the solution analytically with heat transfer assessment and modeling, they created a novel technique that is independent of tiny parameters and is based on the (VIM).…”

“…Because of its simplicity, (FDM) is commonly used to solve linear and non-linear differential equations. Rivlin-Ericksen fluid flow with the effect of non-Darcy medium and radiation investigated using (FDM) ( [1] and [3]). Using the software MAPLE, the identical problem is solved numerically (Runge-Kutta ) as well.…”

Numerical Study of Natural Convection for Generalized Second-Grade Fluids Confined in a Square Cavity Subjected to Horizontal Heat Flux

“…They have noted that the effect of elasticity on Nusselt number depends on the value of Weissenberg number. Also, a set of studies [7][8][9][10] have been done for viscoelastic second-grade fluids in different geometries. It has been noticed that the elasticity is considered as a resistance force, which trends to depreciate heat transfer within the flow and decelerate the fluid motion.…”