Lumped Parameter Thermal Model of Heat-Generating General Geometry in Cylindrical Coordinate System

In this study, an equivalent thermal network for a general geometry with internal heating in cylindrical coordinates is derived. The equivalent thermal circuit consists of three thermal resistances: two resistances to the external heat flow and one resistance to compensate for the internal heating. The inclusive expressions can analytically derive the well-known equivalent thermal network of a hollow cylinder and one of the conventional thermal resistances to the external heat flow, as a special case. Simulations are performed for an insulator geometry bounded by equilateral triangles and a circle sector. The developed network outperforms the cylindrical approximation with a large radius ratio in terms of accurate estimation of average temperature and heat flow. For example, when an external heat flow and internal heat generation coexist and the radius ratio is 0.85, the error rate of the temperature rise in the developed network is 1.58%, whereas it is 10.8% in the cylindrical approximation network. The computation time of the developed network is less than 1 s, which is much shorter than that of the finite element method. The developed model is adaptable for any application, with or without heat generation, which is expected to be applied to the homogenization process of the winding and insulator.