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Heat conduction in convectively cooled eccentric spherical annuli: A boundary integral moment method

ABSTRACT
In this paper heat conduction equation for an eccentric spherical annulus with the inner surface kept at a constant temperature and the outer surface subjected to convection is solved analytically. Eccentric problem domain is first transformed into a concentric domain via formulating the problem in Bispherical coordinates system. Since an analytical Green’s function for the heat conduction equation in Bispherical coordinates for an eccentric sphere subject to boundary condition of third type cannot be found, an analytical Green's function obtained for Dirichlet boundary condition is employed in the solution. Utilizing this Green's function yields a boundary integral equation (BIE) for the unknown normal derivative of the surface temperature distribution. The resulting BIE is solved analytically using method of moments. The method has been applied to heat generating eccentric spherical annuli and results are compared to the simulation results of Fluent CFD code. A very good agreement was observed in temperature distribution computations for various geometrical configurations and a wide range of Biot number. Variation of heat dissipation with radii and eccentricity ratios are studied and a very good agreement with FLUENT has been observed.
KEYWORDS
PAPER SUBMITTED: 1970-01-01
PAPER REVISED: 2016-05-22
PAPER ACCEPTED: 2016-05-23
PUBLISHED ONLINE: 2016-05-30
DOI REFERENCE: https://doi.org/10.2298/TSCI151231128Y
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