Optimization of circular fins with variable thermal parameters

The optimization of rectangular profile circular fins with variable thermal conductivity and convective heat transfer coefficients is discussed. The l inear variation of the thermal conductivity is considered to be of the form k = k(a)(1 + beta(T- T-a)), and the heat transfer coefficient is assumed t o vary according to an exponential function with the distance from the bore of the form h = h(b) exp (gamma(r - r(b))/(r(e)-r(b))). The nonlinear cond ucting-convecting-radiating heat transfer equation is solved by the differe ntial transformation method. The effective of convective-radiative heat tra nsfer at the fin tip is considered. It is shown that, considering the therm al conductivity and heat transfer coefficient are both constant, for a give n fin volume, the optimum fin length is almost independent of the fin base temperature for pure convection. However, for both convection-radiation and purl radiation, the length of the optimum fins for higher temperatures is shorter than the length of the fins with lower temperatures. (C) 1998 The F ranklin Institute. Published by Elsevier Science Ltd.