Natural Convection in an Open and Wavy Porous Cavity Submitted to a Partial Heat Source

Natural convection heat transfer inside a porous cavity having a wavy wall is investigated numerically. The cavity has an opening on the top wall, its right cold wall is wavy, and a partial heat source is placed at the middle of the left wall keeping other walls as adiabatic. The primitive Darcy equations for porous media are non-dimensionalized and solved by the finite difference method; Rayleigh–Darcy number \(({\varvec{Ra}})\) $(\mathit{Ra})$ , length of heat source \(({\varvec{\epsilon }})\) $(\mathit{ϵ})$ , and parameters involving the waviness of the wall are the governing parameters for this investigation. The results are analyzed by representing contour plots of streamlines and isotherms; the heat transfer coefficients and maximum temperature of the heat source are also calculated and analyzed. The obtained results show that the increasing wall waviness leads to the formation of a circulation zone, so the \(\overline{{\varvec{Nu}}}\) $\overline{\mathit{Nu}}$ increases for \({{\varvec{Ra}}}<{{\textbf {10}}}^{\textbf{3}}\) $\mathit{Ra}<{\mathbf{10}}^{\mathbf{3}}$ , and for \({{\varvec{Ra}}}={{\textbf {10}}}^{\textbf{3}}\) $\mathit{Ra}={\mathbf{10}}^{\mathbf{3}}$ , the wavy wall’s impact reduces due to a strong buoyancy force in an open porous cavity.