Heat transfer between two arbitrary shaped bodies in the jump regime with one body enclosed inside the other: A numerical study

A numerical technique is explored for calculation of steady state conductive heat transfer between two arbitrary shaped bodies one enclosed inside the other. The technique is based on an application of the Green's second identity that allows conversion of the 3-D and 2-D partial differential equations to a 2-D and a 1-D integral equation respectively. The integral equation is solved numerically for both the continuum and near continuum (jump) boundary conditions. Collocation with Gauss quadratures on the surface of the two bodies is used to obtain the solution.;The accuracy of the numerical technique is assessed through comparison of results with analytical solution for two concentric spheres and for a single cylindrical nuclear fuel pin geometry (two infinite cylinders) for a range of geometrical and physical parameters. Uniform temperatures were assumed at the inner and the outer curved surfaces for each of the two concentric bodies. Good agreements were obtained between the numerical and the analytical results for both jump and zero-jump boundary conditions.;Results of this study are presented in the normalized forms. The physical parameters are scaled with the parameters corresponding to the inner body. The geometric quantities are scaled with the radius of the inner body. It was found that for large dimensionless separation distances (range 0.2 to 104), and with 40 quadrature points, both local and total heat transfer rates agreed well (deviation <1.01%) with the corresponding analytical results for both jump and zero-jump boundary conditions. A slight rearrangement of the terms in the integral equations led to very good accuracy for small, dimensionless separation distances from 10-5 to 0.2. For the two concentric cylindrical system, good agreements between numerical results and the analytical values were also obtained (deviation < 0.08%).