Lattice-Boltzmann Modeling of Natural Convection Between a Square Outer Cylinder and an Inner Isosceles Triangular Heating Body

Abstract

The present study confirms the robustness and the computational effectiveness of the lattice-Boltzmann method in simulating natural convection between a triangular isosceles heating body and a square outer cylinder isothermally cooled/(insulated) from its vertical/(horizontal) walls. The heated body is symmetrically placed on the vertical centerline of the cavity with the summit opposite to its horizontal base pointing upwards. A detailed parametric study is conducted to investigate the effect of three positions (MB, MM, and MT) of the heating body on fluid flow and heat transfer characteristics for a wide range of Rayleigh number (10³ ≤ Ra ≤ 10⁷) and Pr = 7 (water). The method used is validated against previous works using classical numerical methods to solve Navier–Stokes and energy equations in similar geometries with a circular heating body. In the conductive and convective regimes, useful correlations for the total Nusselt number are deduced as for the three positions of the heating block.

Notes

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