Transient Analysis of Two-Dimensional Pin Fins with Non-Constant Base Temperature(Heat Exchanger)

The transient response of a 2D pin fin with a time- and space-variation base temperature, is analyzed using the Laplace transformation method and the Duhamel's method. The temperature distributions of the pin fin are identical with published analytical solution for the case using the method of separation of variables, while the latter method can not treat 2D problem presented in this paper. The heat flux at fin base and the actual heat flux transferred from the lateral surface and the tip surface of the pin fin to the surroundings are also obtained. For all cases analyzed in this paper, the temperature distributions and the heat flux of the fin reach a steady periodic response after t=2 of dimensionless time. The results show that the effects of 2D conduction are large, particular at large time. Furthermore, as Bi_a value is small, the effect of the tip convection on heat transfer is quite significant for short pin fins.