Exact,analytical heat transfer from longitudinal radiating fins of rectangular profile in a tube/fin ensemble

In this technical note, the problem concerning the quantification of heat transfer rates from an array of longitudinal radiating fins of rectangular profile in a tube/fin ensemble to a nonzero temperature sink is investigated. Radiating fins constitute essential elements in the thermal control of spacecrafts and satellites. We consider quasi one-dimensional heat conduction in the longitudinal radiating fins and neglect radiative exchange between the fins and the tubes carrying a hot fluid. It is demonstrated that the governing nonlinear differential equation of second order with constant coefficients and nonhomogeneous can be solved in exact, analytical implicit form. The pertinent temperature distributions eventually provide the magnitudes of heat transfer rates and fin efficiencies influenced by the radiation–conduction parameter and the sink temperature.