Scale-up methods for heat transfer models with coupled conduction, convection and radiation

In order to predict the thermal behavior of systems, a theoretical and experimental study of the scaling of thermal models is undertaken. Consider a semi-infinite thin plate with transparent air flowing over one face and the other face insulated, involving uniform internal energy generation and conduction heat transfer. Externally heat is rejected to the flowing air by convection and radiation. The plate temperature can be expressed by a non-linear, singular, integro-differential equation which has to be solved numerically as the analytical solution is not available. The present results compare satisfactorily with results available in the literature. The effect of conduction and radiative transfer is also studied. For scaling purposes, the local internal energy generation along the length of the model is obtained by taking into consideration that the prototype and the model would have the same temperature at homologous locations. Experimental verification of the theoretical results is carried out by testing electrically heated plates in a wind tunnel. Within the practical limitations, encouraging comparison is observed between the theoretical and experimental results.