A comparative study of 2-D and 3-D conjugate natural convection from a vertical rectangular fin array with multilayered base subjected to distributed high heat flux

Abstract

This paper presents a comparative numerical study of 2-D and 3-D steady, laminar conjugate natural convection heat transfer from a vertical rectangular aluminium fin array subjected to a distributed high heat flux related to the cooling of a 105 W LED street lighting luminaire. The effect of radiation is also considered in the aforementioned models. The 2-D model uses the Stream function-Vorticity-Temperature approach. The finite-difference methodology is used to discretize the governing equations. The discretization method in the 3-D model is finite-volume. The solution algorithm is SIMPLE (Semi-Implicit Method for Pressure-linked Equations). A detailed parametric study based on a realistic lamp data is conducted to observe the effect of heat flux, fin spacing, fin height, fin width, fin thickness and fin material (aluminium, brass, copper, mild steel) on the fluid (air) velocity and temperature distributions, heat transfer and LED junction temperature. A novel finding of this work is the revelation of asymmetric flow and thermal fields in the successive channels of the fin array, as predicted by the 3-D model. In contrast with the existing studies in which fin base is treated as isothermal, an optimal fin spacing is found to exist corresponding to the maximum heat transfer coefficient in the present study. The difference between 2-D and 3-D model-predicted average heat transfer coefficients increases with increase in fin height to fin spacing ratio. The contribution of radiation heat transfer is about 8–14% of the total heat transfer in the range of dimensions of the fin array considered in this work. A penalty function based optimization study is carried out to maximize the average heat transfer coefficient while maintaining the LEDs below the safe limit of 353 K. Finally, correlations for predicting the average heat transfer coefficient in the vertical rectangular fin array heat sink, and the maximum LED temperature as a function of luminaire wattage and geometric parameters of the fin array have been presented.