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.

Three‐dimensional numerical simulation of free convection and entropy generation in a cubic cavity containing a heat source

“…Their study showed that the thermal boundary conditions applied to the cavity walls and the cylinder placement direction have significant effects on the total melting time of their studied material. Gibanov et al 22 presented comparative studies of the lattice Boltzmann procedure and the finite difference approach of thermal convection heat transfer in square and cubic cavities in the presence of local energy sources of different geometrical forms. In addition to using the pure LBM method to simulate this type of thermal problem, investigations carried out in the literature have shown that the coupling of this technique with the finite difference method (FDM) can offer many advantages in terms of computational efficiency and accuracy 23–27 .…”