An Engineering Technique to Optimize a Constant Thickness Fin with Arbitrarily Distributed Heat Sources 690198

An approximate physical model is postulated in order to simplify the boundary conditions associated with a fin of uniform thickness and arbitrarily distributed heat sources. Each heat source and adjacent portion of the fin is considered independently and a closed form solution of the field equation is derived. The solution is expressed in terms of the modified Bessel functions of the first and second kind. Use of the solution to the approximate model, along with thermal engineering design criteria, permits a linear combination of the independent portions of the fin in order to select the optimum over-all fin geometry. The validity of the approximate model is verified by comparisons with test data. Comparisons are also made with standard lumped-node finite difference analysis.