传热学实验--墙角matlab导热问题

1、word文档可自由复制编辑二维导热物体温度场的数值模拟姓名小明学号111111班级能动学院能动一、问题描述有一墙角模型，尺寸如图1所示，导热系数0.53W/(mK),墙角内外壁为第一类边界条件。求解该模型的温度分布及导热量。图1lmq=01.5m二、计算原理根据热平衡法列出节点方程，各方向导入单元体的热量之和为零。内节点和绝热边界点(图1点划线上的点)的方程形式不同。图2tj*lt屮Lttl-l.JIL*ijtl-lJtlj订A,AxAs内节点绝热边界图2所示的内节点和绝热边界节点方程如下内节点：+=九1NSEW(tt)Ax(tt)Ax(tt)Ay(tt)AyTOC o 1-5 h z*v*v

2、*v*v*i,j+li,j+i,jji,j+i+1ji,j+i1jI,J=0AAyAxA绝热边界点：+=1NSEW(t_t)Ax(tt)Ax(tt)Ayjij+ji,j+0+iJi,j2Ay2AyAx=0三、计算过程用Matlab7.1语言编写计算程序，初取网格步长Ax=Ay=0.1mfunctionTfori=l:16Tfi,1)=30;-endforj=l:12Tfl,j)=30；-endform=6:16forn=6:12TimJn)=0;end-end1(16,2:5)=24,13,12,6;1(2:5,12)=24,18,12,6;whi1e1for1=2:15forj=2:5tem

3、p=Tfijj);I(i,j)=(I(i-bj)+T(i+bj)+T(i,j-1)+1(r,j+1)/4;eps=Tijj)-temp;end-endifepsle-8break;nTnTSend-end-while1forj=2:5temp=Tj);1(116,j)=C*T(15,jJ+Kiej-O+TClG,j+l)/4;eps=T16j)-temp;-endifepsle-8break;endendSMTSwhile1fori=2:5forj=2:11temp=Tijj);1(1,j)=(T(i-lTj)+T(i+bjJ+Td.j-O+KL,j+1)/4;eps=Tijj)-temp;e

4、nd-endifepsle-8break;end-endwhile1Eifori=2:5temp=Tfi,12);Kx,121=(5*1(1,ll)+T(i-b1)+1(i+l,12)/4;eps=Tij12)-temp;endifepsle-8break;end-endpcolor(TJ);shadinginterpfigurecontour;TJ10);运彳丁结果：30.0030.0030.0030.0030.0030.0030.0030.0030.0030.0030.0030.0030.0028.9327.8926.900526.9026.0225.3024.7924.4624.1324

5、.0624.0530.0027.8525.7223.7021.8720.3919.3918.7918.4318.2218.0918.0830.0026.7223.4720.2917.3615.0013.6212.8612.4612.2312.1012.0830.0025.5921.1316.6412.308.&37.216.596.306.156.066.0530.0024.4918.8212.856.550.000.000.000.000.000.000.0030.0024.2718.4512.466.290.000.000.000.000.000.000.0030.0024.1518.25

6、12.256.160.000.000.000.000.000.000.0030.0024.0818.1312.146.080.000.000.000.000.000.000.0030.0024.0518.0712.076.050.000.000.000.000.000.000.0030.0024.0218.0412.046.020.000.000.000.000.000.000.0030.0024.0118.0212.026.010.000.000.000.000.000.000.0030.0024.0118.0112.016.010.000.000.000.000.000.000.0030.0024.0018.0112.016.000.000.000.000.000.000.000.0030.0024.0018.0012.006.000.000.000.000.000.000.000.0030.0024.0018.0012.006.000.000.000.000.000.000.000.00图1：各个点的温度数值图2：分层设色等温线分布图3：等温线分布（每两条线间隔为三度）四、小结本次数值模拟是运用matlab程序用