Constructal multi-scale structure of PCM-based heat sinks

This paper inquires the effectiveness of a PCM-based heat sink as a reliable solution to portable electronic devices. This sink is composed of a PCM with low thermal conductivity and fins to boost its conductivity. The optimization is subjected to fixed heat sink volume filled with PCM between vertical equidistant fins. New fins are installed in the unheated space existing in each enclosure which is not involved in thermal distribution from vertical fins to the PCM. Based on the same principle, new fins generations are augmented stepwise to the multi-scale structure. The steps of adding fins will continue up to the point that the objective function reaches its maximal value, i.e., maximizing the longest safe operation time without allowing the electronics to reach the critical temperature. The results indicate that in each length of the enclosure, the optimum volume fraction and the best fins distance values exist in which the heat sink performance becomes maximum, and adding more fins lowers the performance of the heat sink. Increasing the enclosure’s length by 2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{n}$$\end{document} does not change them. For an enclosure with constant length, the optimal number of steps for adding fins within the enclosure is a function of the fin thickness. The results indicate that increasing the thickness changes the optimal number of adding fins inside the enclosure (normally a decrease). As the fin thickness is lowered, there will be a higher effect by adding vertical fins in the enclosure. Numerical simulations cover the Rayleigh number range 2×105≤RaH≤2.7×108\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\times 10^{5}\le \hbox {Ra}_{\mathrm{H}} \le 2.7\times 10^{8}$$\end{document}, where H is the heat sink height.