Temperature Rise and Free-Convection Heat-Transfer Coefficient for Two-Dimensional Pot-Core Inductors and Transformers

Existing formulations to account for heat transfer (HT) from a magnetic core to the ambient environment usually use a constant HT coefficient obtained from the literature. The results using this method can be inaccurate. This paper presents a new more accurate formulation for determining the surface temperature using the following two characteristic parameters: the height of the core and the average convective heat flux dissipated from the side surface. Natural convection and radiation are accounted for, using finite-element-based simulations. Calculated results for the mean surface temperature rise for a given loss in the case of a vertically oriented pot core are presented. The core has no object in close proximity to it, and an adiabatic boundary condition is applied to the bottom of the core. Only the side surface of the core effectively dissipates convective heat, and the contribution of the core's top surface to convection is fairly negligible. Radiative HT is calculated assuming that the side and top surface participate in radiation. Radiative HT is on the same order as convective HT even for a low surface temperature rise. Finally, an expression is developed to correlate the mean surface temperature and total loss. The expression shows only a 3% error with respect to experimental results for a pot core. Application of the expression for non-pot-core components is also examined by conducting an experiment on a flyback converter that uses a transformer with an ER core. The error in estimating the mean surface temperature rise is about 19%. This high error is deemed to result from a large error bar that exists in the loss measurement.