The method of temperature-correlated projiles is used to obtain the solution oj optimum convective fin when the thermal conductivity and heat transfer co@icient are functions of temperature. The prqfile is shown to be convenient to obtain an analytical solution of the resulting nonlinear heat transfer equation. It is sholvn that the projile correctly predicts the optimization problems with spatial variation of the heat transfer co@icients reported in the literature. The effect qf temperature dependence on heat tran@ coeficients is,ftiund to he important in the design qfoptimum,fins.
Using the projile, an approximate solution.for the optimum jin, including the @tict of temperature dependence on convection heat trunsfer coejicient (use@ for parametric study and desi~gn analysis), is obtained. The exact solution, using numerical integration of the resulting equations, is compared with the approximate solutions. The results are reported in terms qf dimensionless yuuntities convenient in design analysis. The method is shown to be very use@ for parametric study where the optimization problem is given in terms of two parameters : the tip temperature and a prqfile parameter.