Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions

Mohammed Al-Khawaja,Mohamed Selmi

doi:10.1016/j.ijft.2020.100046

Abstract

Abstract A laminar electrically-conducting flow inside an electrically-insulated rectangular duct in a uniform transverse magnetic field with both uniform surface temperature and uniform heat flux boundary conditions are considered numerically. The problem with aspect ratios of the range from 1:10 to 10:1 and Hartmann number M up to 1000 is solved using a highly accurate technique which is spectral method. The flow variables are expanded in terms of linear combinations of Chebyshev polynomials chosen to satisfy the boundary conditions implicitly. The resulting equations are collocated using the Gauss points to produce a system of nonlinear algebraic equations which is solved iteratively using Gauss elimination. Convergence properties of the numerical method reveals that for aspect ratio of less than 4 to 1, the flow is well resolved with as small as 29 by 29 Chebyshev polynomials; however, as the aspect ratio increases to more than 4 to 1, the number of polynomials required for an adequate resolution can be as high as 49 by 49 polynomials. It is found when the magnetic field is turned on, the pressure drop, in general, increases with the field for different aspect ratios. However, the pressure drop increase will be slower near the aspect ratio of 10. Also, the heat transfer increases with the field for most of the cases, but for some cases the field will have adverse effect on the heat transfer, particularly, for constant surface temperature boundary condition at aspect ratio > 4 and M 4 and M

Highlights

IntroductionSayed-Ahmed [1] has solved numerically the problem of MHD flow and heat transfer in a rectangular duct with constant wall heat flux axially and constant wall temperature peripherally
Due to its importance and vast applications, the magneto-hydrodynamics has become the primary interests for many researchers since last century.Sayed-Ahmed [1] has solved numerically the problem of MHD flow and heat transfer in a rectangular duct with constant wall heat flux axially and constant wall temperature peripherally
The heat transfer increases with the field for most of the cases, but for some cases the field will have adverse effect on the heat transfer, for constant surface temperature boundary condition at aspect ratio > 4 and M < 100

Summary

Introduction

Sayed-Ahmed [1] has solved numerically the problem of MHD flow and heat transfer in a rectangular duct with constant wall heat flux axially and constant wall temperature peripherally. He examined the effect of the Hall term and the variable viscosity on the velocity and temperature fields. Smolentsev [2,3] studied experimentally laminar heat transfer in MHD-flow in a rectangular duct with large aspect ratio, 10:1, for the case of one-sided heating with the heat flux applied to one of the side walls He has found experimentally and numerically that the correlation of the fully-developed temperature distribution in the channel cross-. As the Hartmann number increases within that range the temperature at the channel centerline decreases

Methods

Results

Conclusion