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.

中文翻译：

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格子玻尔兹曼法与带加热器闭域热对流有限差分法的对比分析

目的

本文的目的是研究具有各种几何形状的局部能源的封闭方形和立方体空腔中的数值热对流传热。

设计/方法/方法

分析的区域是方形和立方体空腔，具有两个等温冷的相对垂直壁，而其他壁是绝热的。矩形、梯形或三角形的局部能量元件放置在柜体的下表面上。格子玻尔兹曼技术已被用作二维（2D）和三维（3D）公式中问题解决的主要方法，而具有非原始参数（例如流函数和涡度）的有限差分技术也已被用于用过的。

发现

已经研究了大范围的瑞利数 104-106 以及加热器的各种几何形状的速度和温度场。已经对基于 2D 和 3D 公式的两种数值技术获得的结果进行了比较分析。建立了该区域能量转移强度与能源形状和瑞利数的关系。已经发现，能量源的三角形对应于腔内速度矢量和温度的最大值，矩形对应于这些变量的最小值。随着瑞利数的增长，这些变量对于矩形和三角形加热器的值的差异也增加了。

原创性/价值

这项工作的独创性是仔细研究格子玻尔兹曼法和有限差分法在具有局部加热元件的 2D 和 3D 封闭室中的自然对流问题。