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13. FULLY DEVELOPED MHD NATURAL CONVECTION FLOW IN A VERTICAL ANNULAR MICROCHANNEL IN THE PRESENCE OF HEAT GENERATING AND ABSORBING FLUID - AN EXACT SOLUTION by BabatundeAina and Sani Isa Volume 52 (July & Sept., 2019 Issue)
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FULLY DEVELOPED MHD NATURAL CONVECTION FLOW IN A VERTICAL ANNULAR MICROCHANNEL IN THE PRESENCE OF HEAT GENERATING/ABSORBING FLUID:AN EXACT SOLUTION

Babatunde Aina and Sani Isa

Department of Mathematics, Federal University, Gashua, Yobe State, Nigeria.

Department of Mathematics, Yobe State University, Damaturu, Yobe State, Nigeria.

Abstract

An analytical solution for fully developed MHD natural convection flow of viscous, incompressible, electrically conducting fluid in a vertical annular micro-channel in the presence of heat generating/absorbing fluid is presented. The velocity slip and temperature jump at the annular micro-channel surfaces are taken into account. Exact solution of momentum equation is derived separately in terms of Bessel’s function of first and second kind for heat generating fluid and modified Bessel’s function of first and second kind for heat absorbing fluid. The solutions obtained are graphically represented and the effects of governing parameters on velocity, temperature, volume flow rate and rate of heat transfer are investigated in detail. Result reveals that, as Hartmann number increase, there is a decrease in the fluid velocity as well as skin friction and increase in slip velocity for both heat generation and absorption.

Keywords: Heat Generation/Absorption Fluid; Hartmann Number; Annular Microchannel; Velocity Slip; Temperature Jump

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