The effect of conductive baffles on natural convection in a power-law fluid-filled square cavity

This research involves the numerical study of the conjugate natural convection of a power-law fluid in a two-dimensional square cavity with a pair of conducting baffles. The lower wall of the cavity contains a heat source with constant heat flux, while a pair of conductive baffles is embedded on its upper wall. The left and right side walls and some parts of the lower wall of the cavity are thermally insulated and its upper wall is kept at a low temperature. The governing equations along with the corresponding boundary conditions are solved using the numerical finite difference method based on the control volume formulation and SIMPLE algorithm. The effects of pertinent parameters on flow and temperature fields and heat transfer rate are investigated. From the results of the numerical solution, increasing the Rayleigh number and baffles thermal conductivity enhance the thermal performance of the cavity. So that for Ra=106,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ Ra = 10^{6} , $$\end{document} with an increase in the thermal conductivity ratio from 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 1 $$\end{document} to 100,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 100, $$\end{document} the average Nusselt number increases by about 14% for both cases n=0.6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ n = 0.6 $$\end{document} and n=1.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ n = 1.2 $$\end{document}. As well as a decrease in power-law index, except in low Rayleigh numbers, increases the heat transfer rate. Based on the results, the increase of the average Nusselt number is about 283% for a power-law index reduction in the range of 0.6≤n≤1.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 0.6 \le n \le 1.2 $$\end{document} at Ra=106\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ Ra = 10^{6} $$\end{document}. Also, an increase of the length of the baffles deteriorates the thermal performance of the cavity at high Rayleigh numbers, while enhances it at low Rayleigh numbers.