An invariant descriptor for conjugate forced convection-conduction cooling of 3D protruding heaters in channel flow

Abstract

In this research, the temperatures of threedimensional (3D) protruding heaters mounted on a conductive substrate in a horizontal rectangular channel with laminar airflow are related to the independent power dissipation in each heater by using a matrix G + with invariant coefficients, which are dimensionless. These coefficients are defined in this study as the conjugate influence coefficients (g +) caused by the forced convection- conduction nature of the heaters’ cooling process. The temperature increase of each heater in the channel is quantified to clearly identify the contributions attributed to the self-heating and power dissipation in the other heaters (both upstream and downstream). The conjugate coefficients are invariant with the heat generation rate in the array of heaters when assuming a defined geometry, invariable fluid and flow rate, and constant substrate and heater conductivities. The results are numerically obtained by considering three 3D protruding heaters on a twodimensional (2D) array by ANSYS/Fluent™ 15.0 software. The conservation equations are solved by a coupled procedure within a single calculation domain comprising of solid and fluid regions and by considering a steady state laminar airflow with constant properties. Some examples are shown, indicating the effects of substrate thermal conductivity and Reynolds number on conjugate influence coefficients.