Internal heat generation in a discrete heat source: Conjugate heat transfer analysis

In the present work, we conduct an asymptotic and numerical analysis for the cooling process of a discrete heat source, which is placed in a rectangular-channel laminar cooling flow. In our physical model, the heated strip is embedded in a substrate, generating continuously a uniform volumetric heat rate. We assume that this heat-generation mechanism is due to an electrical current in the heat source. Hence, heat losses to the cooling fluid and to the substrate material during this process are presented. The governing equations of the cooling flow and the participating solid are reduced to an integro-differential equation that predicts the temperature variations of the heat source. We show that the conjugate heat transfer process is controlled by a conjugate nondimensional parameter, here denoted by α, which determines the basic heat transfer regimes between the cooling flow and the discrete heat source.