Comparative analysis of the lattice Boltzmann method and the finite difference technique of thermal convection in closed domains with heaters

Abstract

Purpose The purpose of this paper is to investigate numerically thermal convection heat transfer in closed square and cubical cavities with local energy sources of various geometric shapes. Design/methodology/approach The analyzed regions are square and cubical cavities with two isothermally cold opposite vertical walls, whereas other walls are adiabatic. A local energy element of rectangular, trapezoidal or triangular shape is placed on the lower surface of the cabinet. The lattice Boltzmann technique has been used as the main method for the problem solution in two-dimensional (2D) and three-dimensional (3D) formulations, whereas the finite difference technique with non-primitive parameters such as stream function and vorticity has been also used. Findings The velocity and temperature fields for a huge range of Rayleigh number 104–106, as well as for various geometry shapes of the heater have been studied. A comparative analysis of the results obtained on the basis of two numerical techniques for 2D and 3D formulations has been performed. The dependences of the energy transfer strength in the region on the shape of energy source and Rayleigh number have been established. It has been revealed that the triangular shape of the energy source corresponds to the maximum values of the velocity vector and temperature within the cavity, and the rectangular shape corresponds to the minimum values of these mentioned variables. With the growth of the Rayleigh number, the difference in the values of these mentioned variables for rectangular and triangular shapes of heaters also increases. Originality/value The originality of this work is to scrutinize the lattice Boltzmann method and finite difference method for the problem of natural convection in 2D and 3D closed chambers with a local heated element.