A Theoretical Study on Mixed Convection in a Horizontal Annulus
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Abstract
A theoretical study has been conducted on mixed convection heat transfer of the flow through a horizontal annulus the outer surface heated with an axial uniform heat flux while the inner surface cooled at constant surface temperature. Theoretically the governing equations for a flow were reduced to four equations, which are continuity equation, radial and tangential momentum equation, axial momentum equation and vorticity equation in which the variables were the temperature, vorticity, stream function and axial velocity. These equations were reduced to dimensionless equations in which Reynolds, Prandtl and Rayleigh numbers were presented. These equations were solved numerically by using the marching process explicit finite difference method and Gauss elimination technique after changing the elliptic type energy and momentum equations to parabolic form by adding the change with time for each variable to the left hand side of these equations. Numerical results for the annuli heated by a uniform heat flux in the fully developed region were obtained and represented by stream function contours and isotherms for different values of Rayleigh and circumferential distribution of local Nussult number. The results were based on the fact that the secondary flow created by natural convection has significant effects on the heat transfer process, and reveal an increase in the Nussult number values as the heat flux increases in the horizontal position.
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References
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