Exact solution to the conjugate problem of nonuniform cooling of fuel rods

In this article, the analytical solution to a conjugate heat transfer problem is presented.The temperature distribution of the cladding of a fuel rod is determined, assuming, that the internal heat generation rate is constant, while the local heat transfer coefficient isvariable along the cladding perimeter, because of contact between adjacent rods. The contact occurs in one point (four-cusp channel) or along a line of the wetted perimeter.Due to asymmetric geometry, the heat transfer coefficient depends on the blocking percentage of the channel and vanishes at the points of contact between adjacent rods.The energy balance equation is solved in two regions (h=0 in the former, and h given by a quadratic form in the latter) of the rod perimeter. This quadratic form was deduced by Turner et al. in 1982, solving numerically the fluid-flow problem. The solution of the thermal problem is obtained resorting to the use of Green's function; the results are given in terms of parabolic-cylinder functions.Some graphs are obtained and discussed; the results show satisfactory agreement with other data available in the literature. Numerical work was performed by personal computer.