Theoretical analysis of an annular fin with power law temperature-dependent emissivity: A minimization approach

Abstract

This study focused on examining the distribution of temperature and thermal stress in annular fins. This was done by developing an energy balance equation that incorporated temperature-dependent emissivity, using a power law to account for both linear and non-linear relationships. The energy equation was scaled using appropriate dimensional variables, and the resulting dimensionless equation was solved using a partition minimization technique, yielding results in the form of a polynomial. In order to assess the efficacy of the solution approach, the acquired results were compared with those documented in the literature and were found to be highly consistent. The influence of different thermo-physical properties on temperature distribution and thermal stress were investigated. It was observed that these properties have a direct impact on both temperatures of the fin and stress associated. The study demonstrated that an increase in the order of nonlinearity in emissivity results in more heat dissipation from the system as well as causing more radial stress to the fin, thereby accurately reflecting the practical phenomenon of emissivity that a constant form may not capture. Therefore, engineers are advised to consider these parameters, such as emissivity, which varies with temperature, when designing.