Minimum mass convective fins with variable heat transfer coefficients

Pontryagin's maximum principles are applied to obtain the solution of minimum mass convective fins with variable heat transfer coefficients. It is shown that the volume and the width of the fin are uniquely related to the specified heat transfer rate and the properties of the material. For a power law spatial variation of the heat transfer coefficient, the results are set forth in a dimensionless form and they are given in tables or graphs, in order to aid design procedures. Several properties relating to the optimum volume, base thickness and the width of the fins with the properties of the material are also discussed. The method can also be used to solve problems of minimum mass fins having restricted width, often encountered in practice.