Heat conduction in axisymmetric body-duct configuration

A slender body placed axisymmetrically in a duct filled with fluid is considered, and a solution is obtained for the temperature field in the duct and for the steady heat flux through its wall under the assumption of small Peclet number and isothermal surfaces. The heat flux from the slender body is determined as a function of the blockage ratio (ratio of maximum body radius to duct radius) and the temperature difference between body and wall. The method of Green's functions is used, and the resulting Fredholm integral of the first kind is solved by the collocation method. When the body is a prolate spheroid, it is shown that an exact solution can be obtained. Numerical solutions were obtained for a spheroidal shape and for a sharp-edge body.