Uniform and Non-uniform Thermoelement Subject to Lateral Heat Convection

A general energy equation of quasi-one-dimensional heat flow in a longitudinal thermoelement (TE) of a curved side that is subjected to an electric field and convection heat transfer on the curved surface is developed. The energy equation is solved for the temperature distribution in two cases; uniform cross-section TE and non-uniform cross-section TE. Analytical solutions for a uniform cross-section TE with uniform electrical and thermophysical properties are obtained, whereas numerical solutions are provided for a non-uniform cross-section TE. Two parameters playing a vital role in the thermal performance of the TE are identified: the heat resistance ratio (HRR) and the energy growing ratio (EGR). The HRR represents the ratio of the longitudinal conduction maximum thermal resistance to the lateral convection maximum thermal resistance. The EGR represents the ratio of Joule’s electrical heating to Fourier’s heat conduction. The effects of varying these two parameters, as well as the TE geometry, have been thoroughly investigated.