A Dynamic Heat Transfer Analysis of a Three Sided Pyramidal Fin of Scalene Triangular Cross-Sectional Area

A dynamic analysis is performed on a three sided pyramidal fin of scalene triangular cross-sectional area (from here on referred to as a TSPSCA). Finite differences are used to solve the governing equation and produce a temperature profile throughout the TSPSCA as a function of time. Dimensionless variables are used. The characteristics of the temperature profile throughout the TSPSCA as a function of time are dependent upon a dimensionless parameter: the thermal conductance due to convection per the thermal conductance due to conduction. It is assumed that the temperature of the fin is homogenous and equal to the temperature of the convecting fluid at time equal zero. The results show that when the conductance ratio is high, the fin temperature profile reaches steady-state quickly; and that the temperatures through the fin deviate greatly from the fin base. Conversely, as this ratio falls in magnitude, the temperature throughout the fin at steady-state approaches the temperature of the fin base; and is slower to reach steady-state.