基于雅克比迭代算法室内温度分布问题的研究——封闭空间内点热源的散热情况

Research on Indoor Temperature Distribution Based on Jacobi Iterative Algorithm—Heat Dissipation of Point Heat Source in Closed Space

摘要: 本文章在给定环境下，求出室内的稳态、动态温度分布。通过傅立叶导热定律，采用热平衡法建立区域节点离散方程，利用雅克比迭代算法进行分析求解。通过围护结构耗热量公式计算出房间的基本耗热量，推导以房间温度为变量的能量守恒方程，求得出水口水温，然后确定定解条件，建立稳态导热内节点离散方程，并利用雅克比迭代的方法表达连续介质各点在同一时刻的温度分布。把进水口流量分成等差值情况进行分析讨论，在不同流量下，依据能量守恒方程，便可通过假设出水口温度求出室内平均温度，进而分别求出每种流量下的室内温度分布。

Abstract: In this paper, the steady and dynamic temperature distribution in a given environment is solved. According to Fourier heat conduction law, the discrete equation of regional nodes is established by heat balance method, and the Jacobian iterative algorithm is used for analysis and solution. The basic heat consumption of the room is calculated by the heat consumption formula of the enclosure structure, the energy conservation equation with the room temperature as the variable is derived, and the water temperature of the nozzle is obtained. Then, the definite solution conditions are determined, and the discrete equation of the internal nodes of the steady-state heat conduction is established. The temperature distribution of each point in the continuous medium at the same time is expressed by the Jacobian iteration method. According to the energy conservation equation, the indoor average temperature can be calculated by assuming the outlet temperature under different flow rates, and then the indoor temperature distribution under each flow rate can be calculated respectively. The numerical solution and temperature contrast chart of some temperature regions under different flow rates are given.