OPTIMIZATION OF CONVECTIVE FIN WITH TEMPERATURE-DEPENDENT THERMAL PARAMETERS

The method of temperature-correlated profiles is used to obtain the solution of optimum convective fin when the thermal conductivity and heat transfer coefficient are functions of temperature. The profile is shown to be convenient to obtain an analytical solution of the resulting nonlinear heat transfer equation. It is shown that the profile correctly predicts the optimization problems with spatial variation of the heat transfer coefficients reported in the literature. The effect of temperature dependence on heat transfer coefficients is found to be important in the design of optimum fins. Using the profile, an approximate optimum fin, including the effect of temperature dependence on convection heat transfer coefficient (useful for parametric study and design 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 of dimensionless quantities convenient in design analysis. The method is shown to be very useful for parametric study where the optimization problem is given in terms of two parameters: the tip temperature and a profile parameter.