Optimum geometry design of a longitudinal fin with volumetric heat generation under the influences of natural convection and radiation

In the present work, the geometry optimization of a longitudinal fin with volumetric heat generation is investigated. Heat is transferred by conduction along the fin and dissipated from the surface via natural convection to the ambient and radiation to the surrounding. The aim of the design problem is to maximize the fin heat loss for a given volume of fin. The design problem is reduced to an optimization problem for finding the positions of control points which represent the B-spline curves. The modified genetic algorithm is used to maximize an objective function that its maximum corresponds to the optimum fin profile. The effects of the base temperature, the variable convective heat transfer coefficient, the surface emissivity, and the volumetric heat generation on the fin profile, temperature distribution along the fin length, and the fin efficiency are investigated numerically.