A decomposition analysis on convecting–radiating rectangular plate fins for variable thermal conductivity and heat transfer coefficient

The present study concentrates to make a complete thermal analysis on a rectangular fin with its primary surface by taking into consideration of radiation heat exchange with the surrounding along with the convective mode of heat transfer. The one side of the primary surface is heated by a fluid with high temperature which may be required to dissipate heat quickly by a fin array system. To analyze an actual case study, the thermal conductivity of the fin material and convective heat transfer coefficient over the surface are treated as a variable and they are as a function of the local fin surface temperature. With the aforementioned condition, the energy equations for both the fin and primary surface become nonlinear. The decomposition method is suggested to solve these highly nonlinear equations to obtain a closed form temperature distribution. The result of temperature distribution determined by the present analysis is compared with that of the numerical values. With the adaptation of the simplified case, the present method is also compared with the exactly closed form results. From both of these comparisons, an exact matching of results is found. The fin performances, namely, fin efficiency, surface efficiency and augmentation factor are evaluated for a wide range of thermogeometric parameters.