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

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.
PAPER REVISED: 2016-05-22
PAPER ACCEPTED: 2016-05-23
  1. Özisik, M.N., Heat Conduction, Wiley, New York, USA, 1980, pp. 96.
  2. Alassar, R.S., Alminshawy, B.J., Heat Conduction from Two Spheres, AIChE J., 56 (2010), 9, pp. 2248-2256.
  3. Alassar, R.S., Conduction in Eccentric Spherical Annuli, International Journal of Heat and Mass Transfer, 54 (2011), pp. 3796-3800.
  4. Moon, P., Spencer, D.E., Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions, second ed., Springer-Verlag, New York, USA, 1988.
  5. Yılmazer, A., Kocar, C., Exact Solution of the Heat Conduction Equation in Eccentric Spherical Annuli, International Journal of Thermal Sciences, 68 (2013), pp.158-172.
  6. Yılmazer, A., Kocar, C., A Novel Analytical Method for Heat Conduction in Convectively Cooled Eccentric Cylindrical Annuli, International Journal of Thermal Sciences, 63 (2014), pp. 1-15.
  7. Fluent 6 User's Guide, Fluent Inc., 2003.
  8. Arfken, G., Mathematical Methods for Physicists, second ed., Academic Press, Orlando, FL, USA, 1970.
  9. Morse, P.M., Feshbach, H., Methods of Theoretical Physics, McGraw-Hill Book Company Inc, USA, 1953, pp. 1298-1301.
  10. Gongora-T, A., Ley-Koo, E., On the Evaluation of the Capacitance of Bispherical Capacitors, Revista Mexicana de Física 42 (1996), pp. 663-674.