Heatline approach for visualization of heat flow and efficient thermal mixing with discrete heat sources

Abstract

Heatline approach has been implemented to visualize heat transfer and to study efficient thermal mixing of laminar natural convective flow in a square cavity with distributed heat sources. Four different cases, depending upon the location of the heat sources on the walls of the cavity, are studied. Wide range of fluids ( Pr = 0.015 – 1000 ) have been studied over a range of Rayleigh numbers ( Ra = 10 3 – 10 5 ) . Governing equations and Poisson-type of equations for streamfunction and heatfunction have been solved using penalty finite element method. Heatlines and streamlines are found to be adequate to visualize and understand heat energy distribution and thermal mixing occurring inside a cavity. Various qualitative and quantitative features on variations of local and average Nusselt numbers for test cases are adequately explained based on heatlines. The efficacy of distributed heating over conventional bottom heating for optimal thermal mixing is established via correlating with heatlines and cup-mixing temperature. The distributed heat sources are found to play major role for processing of molten materials and gaseous substances. Overall, it is shown that heatlines give suitable guidelines to assemble discrete heat sources and the heatline analysis on heat flow management with distributed heat sources is reported for the first time in this work.