Analyses of Convection Heat Transfer From Discrete Heat Sources in a Vertical Rectangular Channel

Steady-state experiments are performed to study the convection heat transfer from four in-line simulated chips in a vertical rectangular channel using water as the working fluid. The experimental data cover a wide range for laminar flow under natural, mixed, and forced convection conditions with the Reynolds number based on the channel hydraulic diameter ranging from 40 to 2220 and on the heat source length ranging from 50 to 2775. The heat flux ranges from $0.1W∕cm2to0.6W∕cm2$⁠. The effects of heat flux, flow rates, and chip number are investigated and results indicate that the Nusselt number is strongly affected by the Reynolds number. To develop empirical correlations, the appropriate value of the exponent $n$ of $ReD$ is determined to collapse all the lines into a single line to show the independence of heat flux. Based on experimental results, the empirical correlations are developed for relations using $Nuℓ$⁠, $ReD$⁠, and $GrD$⁠. The results are compared to predictions from a three-dimensional numerical simulation, and a numerical correlation is also developed.