Natural convection is one of the heat transfer configurations that have been widely investigated due to its broad applications in various fields. However, the focus is mainly on the convection process in vertical parallel plate arrays which has experienced a number of challenges. 2-D analyses between two parallel plates have been widely used for numerical and theoretical investigation of thermal performance and flow characteristics of plate arrays. It enables the description of various isothermal wall parameters such as plate height, plate temperature, and plate spacing. The study has also been extended to 2D multi-channel plate arrays, showing lowest heat transfer at the edge channels. For the 3D configuration of vertical heat sink, i.e., parallel-plate array with a base plate at one end, the dragged fin-base corner flow and the side flow around the open end lead to significant 3D features.
Recently, a team of researchers at National Tsing Hua University: Professor Shwin-Chung Wong and his Master students Shih-Han Chu and Ming-Hsuan Ai numerically analyzed the 3D characteristics of natural convection exhibited in isothermal vertical plate arrays. For vertical plate arrays at varying ratio of the lengths and heights, the authors considered the effects due to the virtual chimney with hot-plume buoyancy as well as the side wall effects. Their research work is published in the journal, International Journal of Thermal Sciences.
The research team commenced their analysis on single-channel configurations followed by multi-channel plate arrays. The plates used were of varied plate length and height ratios (L/H). The variations of the heat transfer coefficients for different L/H ratios were observed. Furthermore, heat transfer performance in the hot plumed 3D multichannel plate arrays and the 2D cases were compared and contrasted by taking into account the enhancement contributed by the extra plume buoyancy.
The authors successfully observed that the heat transfer coefficient was significantly distributed non-uniformly along the plates and in particular the plate ends. The heat transfer coefficient dropped inward as a result of boundary layer development. But the plume buoyancy in the inner plates resulted in a gradual re-rise of heat transfer therein. Consequently, the effect of the plume buoyancy varied with respect L/H ratios. However, the overall heat transfer coefficient approached that of 2D cases with a difference less than 4% as L/H ≥2.
According to the authors, the non-uniformity in the distribution of the heat transfer coefficients was mainly due to the effects of the side flows. The plume shrinkages associated with the plate-end side flow also resulted in average transfer coefficients of 3D multichannel plates to be lower than that of the 2D channels. Also, the plume buoyancy was very weak at the channel edges thereby inducing complex flows in outer channels.
Some interesting points have been found regarding Elenbaas’ 2D empirical formula, which were obtained from 3D measurements for single channels. First, the single-channel measurements ignored the collective multichannel plume buoyancy which increased with the channel number, thereby significantly under-estimated the heat transfer in multichannel plates. Also, when Elenbaas corrected the side-flow effect in his 3-D square-plate data to obtain a 2-D empirical correlation, he assumed the side flow would always favor heat transfer. However, 3D simulations indicated this assumption caused 14% under-estimations in the 3D-to-2D correction for medium and large plate spacings due to weakened 3D plume buoyancy with side flow. It was also found that Elenbaas’ experimental strategy led to about 14% over-estimations of the heat transfer coefficient for medium and large plate spacings. The two independent errors fortuitously canceled so that the Elenbaas’ 2D formula is still reliable for single-channel plates.
Wong, S., Chu, S., & Ai, M. (2018). Revisit on natural convection from vertical isothermal plate arrays II—3-D plume buoyancy effects. International Journal of Thermal Sciences, 126, 205-217.Go To International Journal of Thermal Sciences