Optimization of Heating and Cooling System Locations by Taguchi’s Method to Maximize or Minimize the Natural Convection Heat Transfer Rate in a Room

Using Taguchi's method, the best heat transfer locations for the heating and cooling systems are optimized. To investigate the flow field and heat transfer, the double multi-relaxation time lattice Boltzmann method is used. Sixteen different positions for heating and cooling systems are investigated, the full factorial method for the proposed model considers 44=256\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${4}^{4}=256$$\end{document} experiments, but using the Taguchi method can significantly reduce the number of experiments. In this study, with respect to the number of parameters and levels, the orthogonal array L16\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{16}$$\end{document} of Taguchi's method is proposed which reduces the number of experiments to 16. Various simulations are performed based on the design of the experiments, and the process output changes are measured by a factor called the signal-to-noise ratio. The optimal positions of the heating and cooling systems to maximize and minimize the Nusselt number are found. Also, using analysis of variance (ANOVA), the effective parameters and the percentage of participation of each of them on the Nusselt number are evaluated. In addition, the results show that the height position of the heating system has the greatest effect on the Nusselt number, while the longitudinal position of the cooling system has the least effect.