Experimental estimate of the continuous one-dimensional kernel function in a rectangular duct with forced convection

The continuous, one-dimensional kernel function in a rectangular duct subject to forced convection with air was experimentally estimated using liquid crystal thermography techniques. Analytical relationships between the kernel function for internal flow and the temperature distribution resulting from a known heat flux distribution were manipulated to accomplish this objective. The kernel function in the hydrodynamically fully developed region was found to be proportional to the streamwise temperature gradient resulting from a constant heat flux surface. In the hydrodynamic entry region of the rectangular duct, a model for the kernel function was proposed and used in its experimental determination. The kernel functions obtained by the present work were shown to be capable of predicting the highly nonuniform surface temperature rise above the inlet temperature resulting from an arbitrary heat flux distribution to within the experimental uncertainty. This is better than the prediction obtained using the analytically derived kernel function for turbulent flow between parallel plates, and the prediction obtained using the conventional heat transfer coefficient for constant heat flux boundary conditions. The latter prediction fails to capture both the quantitative and qualitative nature of the problem. The results of this work are relevant to applications involving the thermal management of nonuniform temperature surfaces subject to internal convection with air such as board-level electronics cooling. Reynolds numbers in the turbulent and transition range were examined.