Numerical analysis for Prandtl number dependency on natural convection in an enclosure having a vertical thermal gradient with a square insulator inside

Abstract

The natural convection in a horizontal enclosure heated from the bottom wall, cooled at the top wall, and having a square adiabatic body in the center is studied. Three different Prandtl numbers (0.01, 0.7 and 7) are considered for the investigation of the effect of the Prandtl number on natural convection. Adiabatic boundary conditions are employed for the side walls. A twodimensional solution for unsteady natural convection is obtained, using an accurate and efficient Chebyshev spectral methodology for different Rayleigh numbers varying over the range of 10 3 to 10 6. It had been experimentally reported that the heat transfer mode becomes oscillatory when Pr is out of a specific Pr band beyond the critical Ra. In this study, we reproduced this phenomenon numerically. It was found that when Ra=10 6, only the case for intermediate Pr (=0.7) reached a non-changing steady state and the low and high Pr number cases (Pr=0.01 and 7) showed a periodically oscillatory fashion hydrodynamically and thermally. The variation of time-and surface-averaged Nusselt numbers on the hot and cold walls for different Rayleigh numbers and Prandtl numbers are presented to show the overall heat transfer characteristics in the system. Further, the isotherms and streamline distributions are presented in detail to compare the physics related to their thermal behavior.