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

Karem Mahmoud Ewis

doi:10.1177/1687814019866033

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.

Highlights

The effects of parallel plate channel, non-Darcy medium, on natural convection of non-Newtonian fluids and heat transfer are studied because of their importance in engineering applications
Another validation of present solution is made by error analysis
Experimental results of present solution are not available, but some comparisons with available analytical and numerical results are made for special cases to show the validation of the present solution

Summary

Introduction

The effects of parallel plate channel, non-Darcy medium, on natural convection of non-Newtonian fluids and heat transfer are studied because of their importance in engineering applications. A homotopy analysis solution is presented for the natural convective heat transfer of a third-grade, non-Newtonian fluid flowing past an infinite porous plate through Darcy–Forchheimer porous medium.[4] The governing equations are transformed to a one-dimensional form. Their results indicate that a rise in third-grade viscoelasticity, suction, thermal conductivity, and permeability boosts velocities and temperatures, but increasing the Forchheimer parameter decreases velocities and temperatures because of resistance. The governing (momentum and energy) equations are written, respectively, as[2,4,12]

B V0 m kp h2

Conclusion