Variation of Parameters Method for Thermal Analysis of Straight Convective- Radiative Fins with Temperature Dependent Thermal Conductivity

In this study, thermal performance across straight convecting- radiating fin with temperature dependent thermal conductivity is considered. The variation of parameters (VPM) is adopted to analyze the nonlinear higher order differential equations arising due to thermal conductivity and heat transfer coefficient on temperature distribution. Pertinent parameters such as thermo geometric and radiation parameters effect on temperature profile are investigated. Result obtained illustrates that quantitative increase of thermo geometric parameter causes a significant increase in temperature distribution due to increase in ratio of convective to conduction heat transfer which influence is significant toward fin base while increasing radiation parameter leads to decrease in temperature distribution due to increasing heat transfer from fins surface to ambient environment . Comparative analysis of result obtained in study against literature proves to be in satisfactory agreement. Therefore study provides useful insight to fins operational performance in applications such as radiators, boilers, refrigeration devices, oil pipelines amongst others.