Laminar natural convection in a 2-D pentagonal house with sloping roof heated by constant heat flux

Natural convection in a pentagonal house with a protruding cooler for summer is numerically investigated. The sloping roof is subjected to constant heat flux, and the cooler maintains at a uniform cold temperature. The remaining walls of the house are insulated. Local multi-quadratic radial basis function (LMQRBF) method is applied in solution of Navier–Stokes equations in stream function-vorticity form. The working fluid in the house is air with Pr = 0.71. The effects of Rayleigh number (10³ ≤ Ra ≤ 10⁶), heat flux of the roof (0.1 ≤ q ≤ 2.0), and the cooler’s vertical position (0.65 ≤ H/L ≤ 0.85) are explored. Streamlines, isotherms, velocity profiles, and the distribution of Nusselt number are displayed. Numerical results indicate that for the top and right wall of the cooler, the heat transfer is stronger than that for the bottom wall. It reveals that all the governing parameters efficiently impact the generation and evolution of the secondary and tertiary vortex in the gable roof. It is also observed that the variation of average Nusselt number on the right wall with Rayleigh number is under the combined influence of the heat flux and the cooler’s vertical position.