二维导热物体温度场的数值模拟

1、Ah喩钏復*灣University(/ Stienw pnd 丁的呦翎廿 Pcfjing金属凝固过程计算机模拟二维导热物体温度场的数值模拟Solidworks十字接头的传热分析作者:张杰学号:S20156019学院:北京有色金属研究总院专业:材料科学与工程成绩:2015年12月二维导热物体温度场的数值模拟+ 1%Ml,hj-1图1二维均质物体的网格划分用有限差分法模拟二维导热物体的温度场，首先将二维物体划分为如图1所示的网格，Ax与与可以是不变的常量，即等步长,也可以是变量（即在区域内的 不同处是不同的），即变步长？如果区域内各点处的温度梯度相差很大，则在温度变 化剧烈处，网格布得密些，在温度

2、变化不剧烈处，网格布得疏些？至于网格多少，步长 取多少为宜，要根据计算精度与计算工作量等因素而定 ？在有限的区域内，将二维不稳定导热方程式应用于节点（i , j）可写成： 刃P、（oT c2T YPCp=人 I 2- +Fi ,jW2f cTTP-T P=+0(叵丫 J； ,j-2TiP j+T： ,j S 丿i ,j, 2(Ax)+ o(Ax)25丿i ,jTiPj-2T Pj+TP+咻y)2 比込X、也y（亦2 2当Aj也X、也y较小时，忽略0（肛）、o2x）、。（与）项。当2 = 3时,即X、y方向网格划分步长相等？最后得到节点（i，j）的差分方程：TiPr =TiPj+Fobi； ,j

3、 +昭,j +TPj/TPj_4-4TiPj ）式中假设边界为对流和辐射边界，对流用以下公式计算：PPCpAxTiPjTi卩严0（2巧,j+TiPj汀TiPjd-4TiP）广心（Tf ,j）MATLAB编程模拟表1计算机模拟参数模拟参数输入几何尺寸/m0.35初始温度/ C15定温边界/ C100密度/kg/m37840导热系数/w/（m C）30比热 /J/(kg C)610工件节点数/个25时间步长/min0.1时间步数/个100几何步长/mm35在MATLAB中编程求解，程序如下：cic;clear;format Io ng%参数输入moni_canshu=xlsread模拟参数输入.x

4、lsx,1,B2:B11); %读取exce中的模拟参数 s=moni_canshu(1);%几何尺寸,mt0=moni_can shu (2);% 初始温度，Ctf=mo ni_can shu(3); % 辐射(空气)边界，C rou=mon i_ca nshu(4);% 密度,kg/m3 lamda=moni_canshu(5);%导热系数,w/(m C) Cp=moni_can shu(6);% 比热,J/(kgC) n=moni_canshu(7);%工件节点数，个1000 dt=60*mo ni_can shu(8); % 时间步长，min to s m=moni_canshu(9)

5、;%时间步数，个100 dx=s/( n-1);% 计算 dx f0=lamda*dt/(rou*Cp*dx*dx); %计算f0%初始参数矩阵，初始温度for iii=1: nfor jjj=1: nTold(iii,jjj)=t0;endendTold(1,:)=tf;Told( n,:)=tf;Told(:,1)=tf;Told(:, n)=tf;%写文件表头xlswrite(data.xlsx,坐标位置, sheet1：A1); asc=97;for ii=1: nbiaotou仁第nu m2str(ii)点;asc=asc+1;xlswrite(data.xlsx：biaotou1：

6、sheet1：char(asc) 1); xlswrite(data.xlsx：biaotou1：sheet1：A num2str(ii+1); end%模拟运算for jj=1:2co pyfile( data.xlsx：,data1.xlsx)Tn ew(1：1: n)=tf;Tn ew( n：1: n)=tf;Tn ew(1: n：1)=tf;Tn ew(1: n：n )=tf;for i=2: n-1for j=2: n-1Tn ew(i,j)=Told(i,j)+fO*(Told(i-1,j)-4*Told(i,j)+Told(i+1,j)+Told(i,j-1)+Told(i,j+

7、1); endendTold=T new;p color(Told);% 绘图shad inginterpcolorma p(jet)p ause(0.1)saveas(gcf,第num2str(jj*0.1) s温度图像.jpg); xlswrite(data1.xlsx；Told,sheet1；B2);cop yfile(data1.xlsx：第nu m2str(jj*0.1) s数 据.xlsx) delete(data1.xlsx);end模拟结果：坐标位置第1点第2点第3点第4点第5点第6点第7点第8点第9点第10点第11点第12点第13点第1点96.2896.2896.2896.2

8、896.2896.2896.2896.2896.2896.2896.2896.2896.28第2点96.2885.7374.9068.6665.9465.0564.8464.8064.7964.7964.7964.7964.79第3点96.2874.9055.9145.0440.3638.8538.4938.4338.4238.4238.4238.4238.42第4点96.2868.6645.0431.6425.9424.1323.7123.6423.6323.6323.6323.6323.63第5点96.2865.9440.3625.9419.8517.9517.5217.4517.4417

9、.4417.4417.4417.44第6点96.2865.0538.8524.1317.9516.0315.5915.5215.5115.5115.5115.5115.51第7点96.2864.8438.4923.7117.5215.5915.1615.0915.0815.0815.0815.0815.08第8点96.2864.8038.4323.6417.4515.5215.0915.0215.0115.0115.0115.0115.01第9点96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第10点96.286

10、4.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第11点96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第12点96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第13点96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第14点96.2864.7938.4223.6317.4415.51

11、15.0815.0115.0015.0015.0015.0015.00第15点96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第16点96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第仃点96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第18点96.2864.8038.4323.6417.4515.5215.0915.0215.0115.0115.01

12、15.0115.01第19点96.2864.8438.4923.7117.5215.5915.1615.0915.0815.0815.0815.0815.08第20点96.2865.0538.8524.1317.9516.0315.5915.5215.5115.5115.5115.5115.51第21点96.2865.9440.3625.9419.8517.9517.5217.4517.4417.4417.4417.4417.44第22点96.2868.6645.0431.6425.9424.1323.7123.6423.6323.6323.6323.6323.63第23点96.2874.90

13、55.9145.0440.3638.8538.4938.4338.4238.4238.4238.4238.42第24点96.2885.7374.9068.6665.9465.0564.8464.8064.7964.7964.7964.7964.79第25点96.2896.2896.2896.2896.2896.2896.2896.2896.2896.2896.2896.2896.28坐标位置第14点第15点第16点第17点第18点第19点第20点第21点第22点第23点第24点第25点第1点96.2896.2896.2896.2896.2896.2896.2896.2896.2896.2896

14、.2896.28第2点64.7964.7964.7964.7964.8064.8465.0565.9468.6674.9085.7396.28第3点38.4238.4238.4238.4238.4338.4938.8540.3645.0455.9174.9096.28第4点23.6323.6323.6323.6323.6423.7124.1325.9431.6445.0468.6696.28第5点17.4417.4417.4417.4417.4517.5217.9519.8525.9440.3665.9496.28第6点15.5115.5115.5115.5115.5215.5916.0317

15、.9524.1338.8565.0596.28第7点15.0815.0815.0815.0815.0915.1615.5917.5223.7138.4964.8496.28第8点15.0115.0115.0115.0115.0215.0915.5217.4523.6438.4364.8096.28第9点15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第10点15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第11点15.0015.0015.0015.00

16、15.0115.0815.5117.4423.6338.4264.7996.28第12点15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第13点15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第14点15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第15点15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第16点

17、15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第仃点15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第18点15.0115.0115.0115.0115.0215.0915.5217.4523.6438.4364.8096.28第19点15.0815.0815.0815.0815.0915.1615.5917.5223.7138.4964.8496.28第20点15.5115.5115.5115.5115.5215.5916.0317.9524.1338.8565.0596.28第21点17.4417.4417.4417.4417.4517.5217.9519.8525.9440.3665.9496.28第22点23.6323.6323.6323.6323.6423.7124.1325.9431.6445.0468.6696.28第23点38.4238.4238.4238.4238.4338.4938.8540.3645.0455.9174.9096.28第24点64.7964.7964.7964.7964.8064.8465.0565.9468.6674