Empirical correlations for mixed convection heat transfer through a fin array based on various orientations

Abstract The transfer of heat by the fins is influenced by the change of the direction of the fins. This paper investigates study the effect of the direction of longitudinal fins on a three-dimensional convection heat transfer in a rectangular channel and also study the effect of the lateral and longitudinal inclination of the rectangular channel. The Grashof range from 5 × 108 to 109, Reynolds from 1000 to 2300 and Prandtl 0.71. The bottom surface of the channel is exposed to constant heat flux, while other walls are isolated. Two cases are investigated. In case one, measurements were conducted for a lateral inclination of the channel, with a range of α = 0°,30°,60°, and 90°. Case two studied the longitudinal inclination of the channel, with the lateral inclination angle fixed at α = 90° and the longitudinal inclination angle Ө = 0°, 30°, 60°, and 70°. The dimensionless of fin height was Hf/H = 0.6, and the fin spacing was S/H = 0.17. The experimental results show that the coefficient of the heat transfer for lateral inclination (α = 0°) was greater than that for a sideways orientation (α = 90°). Additionally, the average coefficient of heat transfer for both the lateral and longitudinal inclination case is increased with the longitudinal inclination angle. The empirical equations are obtained based on the experimental results. These equations correlated the Nusselt number as a dependent variable of the orientations angles, Reynolds number, and the Grashof number, these equations are consistent with experimental results.

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