Heat transfer and MHD flow of non-newtonian Maxwell fluid through a parallel plate channel: analytical and numerical solution

Alireza Rahbari,Mehdi Gholami,Bengt Sundén,Morteza Abbasi,Iman Rahimipetroudi,Davood Domiri Ganji

doi:10.5194/ms-9-61-2018

Abstract

Abstract. Analytical and numerical analyses have been performed to study the problem of magneto-hydrodynamic (MHD) flow and heat transfer of an upper-convected Maxwell fluid in a parallel plate channel. The governing equations of continuity, momentum and energy are reduced to two ordinary differential equation forms by introducing a similarity transformation. The Homotopy Analysis Method (HAM), Homotopy Perturbation Method (HPM) and fourth-order Runge-Kutta numerical method (NUM) are used to solve this problem. Also, velocity and temperature fields have been computed and shown graphically for various values of the physical parameters. The objectives of the present work are to investigate the effect of the Deborah numbers (De), Hartman electric number (Ha), Reynolds number (Rew) and Prandtl number (Pr) on the velocity and temperature fields. As an important outcome, it is observed that increasing the Hartman number leads to a reduction in the velocity values while increasing the Deborah number has negligible impact on the velocity increment.

Highlights

Non-Newtonian fluid flow is a fast-growing field of interest due to its various applications in different fields of engineering (Rivlin and Ericksen, 1955)
This number may be interpreted as the ratio of the relaxation time, and the characteristic time of an experiment or a computer simulation probing the response of the material (Reiner, 1964)
This is due to the fact that the applied transverse magnetic field produces damping in form of a Lorentz force thereby decreasing the magnitude of the velocity

Summary

Introduction

Non-Newtonian fluid flow is a fast-growing field of interest due to its various applications in different fields of engineering (Rivlin and Ericksen, 1955). The problem with this type of fluid is that there is not a single constitutive equation due to various rheological parameters appearing in such fluids. The dynamics of materials with the properties of elasticity and viscosity is a fundamental topic in fluid dynamics This kind of materials is referred to as Maxwell fluid (Mukhopadhyay, 2012; Adegbie et al, 2015). The Upper Convected Maxwell (UCM) model is the generalization of the Maxwell material for the case of large deformation using the upper convected time derivative

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