Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption

Yusuf Samuel Taiwo

doi:10.11648/j.ijfmts.20170305.12

Abstract

This paper presents an exact solution of a fully developed natural convection flow in a vertical concentric annulus in the presence of transverse magnetic field and heat absorption. The non-dimensional form of the equation governing the flow is first obtained and then the unified analytical solutions for the temperature field, velocity field, and skin-frictions as well as rate of heat transfer are obtained for both isothermal and constant heat flux case on the outer surface of the inner cylinder. The effect of various identified governing parameters on the flow was illustrated with the aid of line graphs. It is found that the magnitude of maximum fluid velocity is greater in the case of isothermal heating compared with the constant heat flux case when the gap between the cylinders is less or equal to radius of the inner cylinder. More also, the various values of the non-dimensional heat absorption parameter (H) and the corresponding values of annular gap where these fields are almost the same are presented in table 1.

Highlights

Interest in buoyancy-driven flows and the related heat transfer has been on increase over the past few decades because of the importance of these flows in many different areas
In other to have a good knowledge of the effects of the governing parameters on the fluid temperature profiles, velocity profiles, skin-friction and rate of heat transfer at both surfaces as well as mass flow rate in the annular gap, we have employed a mathematical tool- MATLAB to generate the numerical values and line graph of the temperature 4, velocity, skin-friction Y at the outer surface of the inner cylinder, skin-friction Y[ at the inner surface of the outer cylinder, Nusselt number ef at the outer surface of the inner cylinder, Nusselt number ef[ at the inner surface of the outer cylinder and mass flow rate (Q) for some carefully selected flow parameters so as to comment on their effects on the flow formation
We observed in these Figures that increase in Hartmann number decreases the fluid velocity it is clear from Figures 4 and 5 that the magnitude of maximum value of the velocity profile is higher in the case of isothermal condition than the case of constant heat flux when the radius of outer cylinder is less than 3.5

Summary

Introduction

Interest in buoyancy-driven flows and the related heat transfer has been on increase over the past few decades because of the importance of these flows in many different areas (such as cooling of electronic equipment, pollution, materials processing, energy systems and safety in thermal processes). It is a known fact that in a physical application such as crystal growing the heat generation or absorption effect in the fluid is greatly dependent on temperature. Miyatake and Fujii [9] have discussed the free convection flow between vertical plates - one plate isothermally heated and other thermally insulated. Jha and Ajibade [11] have studied the unsteady free convective Couette flow of heat generating/absorbing fluid. They have examined the effect of periodic heat input in fluid flowing in a vertical porous plate [12]. Das et al [13] studied the radiation effects on free convection MHD Couette flow started exponentially with variable wall temperature in presence of heat generation.

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Conclusion