Analytical representation of the internal shape factor of sheathed electrical heating elements

This paper focuses on the study of the internal shape factor of sheathed electrical heating elements. First, the studied geometries are presented and three dimensionless parameters are introduced. The analysis of finite elements simulations leads to the proposition of an analytical expression of the dimensionless internal shape factor. Then a non uniformity factor is proposed and it is shown that this non uniformity is in all cases inferior to 6%, and in most cases inferior to 1%. Then the proposed relation is applied to two examples, one determining the maximum heat flux for a given temperature, the second one determining the maximum temperature of the heating wire for a given heat flux.