The Effect of Inside and Outside Fluids on the Optimization of a Reversed Trapezoidal Fin

A reversed trapezoidal fin with variable lateral surface slope is optimized using a two-dimensional analytic method. For a fin base boundary condition, convection from the inside fluid to the inside wall and conduction from the inside wall to the fin base are considered. Heat loss from the fin tip surface is not ignored. The maximum heat loss at the practical fin length, the corresponding optimum fin efficiency, fin length and fin base height are presented as a function of the fin inside and outside convection characteristic numbers. One of the results shows that the optimum fin shape becomes 'fatter and shorter' as the ratio of fin tip height to base height increases.