Prediction of the temperature in a fin cooled by natural convection and radiation

Predictions and measurements of the temperature along a fin cooled by natural convection and radiation are reported. The physical situation considered is a horizontal fin with a cylindrical cross-section. One end of the fin is maintained at a constant elevated temperature, and the fin is sufficiently long so that heat loss from the tip is negligible. Heat is transferred by conduction along the fin and dissipated from the surface via natural convection and radiation. The effect of natural convection is described with a published correlation for a horizontal cylinder, and a simple model is used for the radiative heat transfer. A finite difference formulation that allows for variable fluid property effects is used to determine the temperature distribution along the fin. A comparison is made to experimental results, and the agreement between the model and experiment is very good. Results show that the heat loss due to radiation is typically 15–20% of the total.