二維導(dǎo)熱物體溫度場(chǎng)地?cái)?shù)值模擬

1、二維導(dǎo)熱物體溫度場(chǎng)的數(shù)值模擬作 者：學(xué)號(hào)：學(xué)院（系）：能源與動(dòng)力工程學(xué)院專 業(yè)：能源動(dòng)力系統(tǒng)及自動(dòng)化班 級(jí)：二維導(dǎo)熱物體溫度場(chǎng)的數(shù)值模擬一：物理問題有一個(gè)用磚砌成的長(zhǎng)方形截面的冷空氣通道，其截面尺寸和示意圖如圖1-1 所示，假設(shè)在垂直紙而方向上冷空氣及磚墻的溫度變化很小，可以近似地予以忽 略。在下列兩種情況下試計(jì)算：(1)磚墻橫截面上的溫度分布；(2)垂直于紙 面方向的每米長(zhǎng)度上通過磚墻的導(dǎo)熱量。第一種情況：內(nèi)外壁分布均勻地維持在0弋及30 C：第二種情況：內(nèi)外表面均為第三類邊界條件，且已知：g =3OC,/q =10W/m2-Croo2=10C,/i2=4W/m2-C磚墻的導(dǎo)熱系數(shù)2 = O

2、.53W/加 C方1 wl二：數(shù)學(xué)描述該結(jié)構(gòu)的字熱問題可以作為二維問題處理，并且其截而如圖所示，由于 對(duì)稱性，僅研究其1/4部分即可。其網(wǎng)絡(luò)節(jié)點(diǎn)劃分如圖上述問題為二維矩形域內(nèi)的穩(wěn)態(tài).無內(nèi)熱源、常物性的導(dǎo)熱問題，對(duì)于這樣的物理問題，我們知道，描寫其的微分方程即控制方程，就是字熱微分方程：d2td2t八+ =0dr dy-第一類邊界條件：內(nèi)外壁分布均勻地維持在c及3(rc；J二30C二 0C第三類邊界條件：內(nèi)外表而均為第三類邊界條件，且已知:俎=30r, 4 = io w/m2c方82 = 10C,力2 = 4 w/m2-c磚墻的導(dǎo)熱系數(shù)兄=0- 53 W / mC三：方程的離散如上圖所示，用一系

3、列與坐標(biāo)軸平行的網(wǎng)絡(luò)線把求解區(qū)域劃分成許多子區(qū)域，以網(wǎng)格線的交點(diǎn)作為需要確定溫度值的空間位置，即節(jié)點(diǎn)，節(jié)點(diǎn)的位置已該 點(diǎn)在兩個(gè)方向上的標(biāo)號(hào)m、n來表示。每一個(gè)節(jié)點(diǎn)都可以看成是以它為中心的小區(qū)域的代表，如上（叫n）:對(duì)于（m, n）為內(nèi)節(jié)點(diǎn)時(shí)：由熱平衡法可以得到, 當(dāng) Ax 二 Ay 時(shí):tmn = -（t,+L + tm）n+I +14對(duì)于（m, n）為邊界節(jié)點(diǎn)吋：恒溫邊界只需特殊考慮位于絕熱平直邊界上的節(jié)點(diǎn): + ULI ）對(duì)流邊界分為角點(diǎn)、絕熱邊界點(diǎn)和對(duì)流邊界點(diǎn)。1.絕熱邊界點(diǎn):=扣“ +y J4m.n2.對(duì)流邊界點(diǎn):mynt zz?,/7 + l + 彳七 S + 七 m,n_l2 hA

4、x+ t2(hAx3.夕卜角點(diǎn):、+ 1 t丿4內(nèi)角點(diǎn)：=2（七血+1Js + ta +2 hAx(2hAx+ n,n-l + t 刃+ 1/+ t四：編程思路及流程圖取左初始試探值TA (ij) =0f unct i on 二 wendu () t=zeros (12, 16); tf二zeros (12,16); Q1x=0；01y=0；01=0; Q2x二0；Q2y二0；Q2二0; n=0;for i=1:12 t(iJ)=30； endfor j=1:16 t(1, j)=30;endtO=t;t=diedai1(t);for i=2:5for j=2:16whi le t(i, j)

5、-tO(i, j)=0. 00001; t0=t；t=diedai1(t);endendendfor i=6:12for j=2:5whi le t(i, j)-tO(i tj)=0. 00001; tO二 t；t=diedai1(t);endendendtO 二 t for i=2:1101x=Q1x+0. 53* (t(i,1)-t(i,2); end01 x=Q1 x+0. 53*(t(12,1)-t(12, 2)/2； for j=2:15Q1y=Q1y+0. 53*(t (1, j)-t(2, j); end01 y=Q1 y+0. 53*(t(1,16)-t (2,16)/2；01

6、 = (Q1x+01y)*4for i=6:11Q2x二Q2x+0 53*(t (i,5)-t(i, 6);endQ2x二Q2x+0 53*(t (12, 5)-t (12, 6)/2； for j=6:15Q2y=02y+0. 53* (t (5, j) -1 (6, j); endQ2y二Q2y+0 53*(t (5,16)-t (6,16)/2; Q2二(Q2x+02y)*4 n=2*abs(01-Q2)/(01+Q2)t0=tf;tf=d i eda i 2(tf);for i=2:5for j=2:16whi le tf(i, j)-tO(i, j)=0. 00001;t0=tf;

7、tf=d i eda i 2(tf);endendendfor i二6:12for j=2:5whi le tf(i, j)-tO(i, j)=0. 00001;tO二tf；tf=d i eda i 2(tf);endendendtO 二 tfQ1x=0;Q1y=0;Q1=0;Q2x二0；Q2y二0；Q2二0;n=0;for i=1:1101x=Q1x+10*0. 1*(30-tf(iJ);end01 x=Q1 x+10*0. 05*(30-tf (12,1);for j=2:1501 y=Q1 y+10*0. 1 * (30-tf (1, j);end01 y=Q1 y+10*0. 05*(

8、30-tf (1,16)；for i=6:11Q2x=Q2x+4*0.1*(tf(i,6)-10);end02x=02x+4*0. 05* (tf (12, 6)-10);for j=7:15Q2y=Q2y+4*0.1*(tf (6, j)-10);endQ2y=Q2y+4*0. 05*(tf (6,16)-10);Q1 = (01x+01y)*4；02=(Q2x+02y)*4;n=2*abs (Q1-Q2)/(01+Q2)for i=7：12for j=7：16 tf(i, j)=10;endendsubplot (211);pcolor (t)shading i nterp；co Iorm

9、ap (hot)hold oncontour (t, 3, k)hold offcolorbark=caxis；subplot (212);pcolor (tf)shading i nterp;co Iormap(hot)hold oncontour (tf, 3, * k*)hold offcaxis (k)colorbarfunct ion t1=dieda i1(t)for i=2:5for j=2:15t(i, j) = (t(ifj+1)+t(i-1, j)+t(i+1, j)/4;endt(i,16) = (2*t(i,15)+t(i-1,16)+t(i+1,16)/4；endfo

10、r i=6:11for j=2:5t(i, j) = (t(i,j+1)+t(i-1, j)+t(i+1, j)/4;endendfor j=2:5t(12, j) = (2*t(11, j)+t(12, j-1)+t(12, j+1)/4；endt1=t;function t1=diedai2(t)t(1J) = (t(1,2)+t(2,1) +2*10*0.1 *30/0.53)/ (2*(10*0.1/0. 53+1);for j=2：15t(1, j) = (2*t (2, j) +t(1, j-1)+t (11 j+1) +2*10*0. 1 *30/0. 53)/(2* (10*0

11、. 1/0. 53+2); endt(1J6) = (2*t(2,16) +2*t(1,15)+2*10*0.1 *30/0. 53)/(2*(10*0. 1/0. 53+2);for i=2:11t(ij) = (2*t (if2)+t(i-1,1)+t(i+1,1)+2*10*0.1 *30/0. 53)/ (2* (10*0.1/0. 53+2); endt(12,1) = (2*t (12, 2) +2*t (11,1)+2*10*0.1 *30/0. 53)/ (2* (10*0. 1/0. 53+2);for i=2:5for j=2:15t(i, j) = (t(i,j+1)+t

12、(i-1 J)+t(i+1, j)/4；endt(i,16) = (2*t(i,15)+t(i-1,16)+t(i+1,16)/4；endt (6, 6) = (2* (t (6, 5)+t (5, 6) )+t (7, 6) +t (6, 7)+2*4*0.1 *10/0. 53)/ (2* (4*0. 1 /0. 53+3); for j=7：15t (6, j) = (2*t (5, j) +t (6, j-1)+t (6, j+1) +2*4*0. 1 *10/0. 53)/ (2* (4*0. 1 /0. 53+2)； endt (6,16) = (2*t (5,16) +2*t (

13、6,15) +2*4*0. 1 *10/0. 53)/ (2* (4*0. 1/0. 53+2);for i=7：11t(i,6)= (2*t (i, 5) +t (i -1,6) +t (i +1,6) +2* 10*0.1 *4/0. 53)/ (2* (4*0. 1 /0. 53+2); endt(12,6) = (2*t(12,5) +2*t(11,6) +2*4*0. 1 *10/0. 53)/(2*(4*0. 1/0. 53+2);for i=6:11for j=2:5t(i, j) = (t(i, j-1)+t(i, j+1)+t(i-1J)+t(i+1, j)/4;endend

14、for j=2:5t (12, j) = (2*t (11, j) +t (12, j-1) +t (12, j+1 )/4；endt1=t;輸出結(jié)果如下：恒溫邊界ColuJins 1through 10A30. 000030.000030. 000030.000030. 000030.000030.000030.000030.000030.000030. 000029.03452& 069027.117426. 221425.455624.894024.525524.300124.168430. 000028.069026.124124. 179022.312820.706819.59511

15、8.907718.506718.279930. 000027.117624.179321.161818. 144215.463613.871813. 003612.539112.290730. 000026. 222022.313718.144913. 6384913177.42496.6960S. 35646.186330.000025.456820. 708715.46559.13280Q00030. 000024.896419.598913. 87567.42720000030. 000024.53001S.9J5013.01096 70050000030. 000024.308418.

16、520212.55266. 36370000030. 000024.183618.304712.31566. 20180000030. 000024.12141& 199312. 20326.12790000030. 000024.102718.167912.1702S. 106500000Columns 11through1630. 000030.000030. 000030.000030. 000030.000021. 093524.051724. 028924.016721.01092a. 0091IB. 153818.084618.047G18.027218.017618.014812

17、.157412.085812.047412.027312.017712.0148S. 09946.05366.02956.0169S.01096.0092|000000000000000000000000000000000000000000Q1 =241.7157Q2241.7145n.=5.0064e-006對(duì)流誤差邊界Comma nd Win dowColunins 】through029.893129.691529.490229.291829.102628. 93242&791528.683828.606528.553529.691529.109228.526727.951027.399

18、826. 903326.494726.185225.965125.815229.490328.527127.556626.685626.642324. 786524.098723.597323.253423.026029.292327.952226.586826.192623.797522. 501521.616520.S51920.426220. 156329.103727.402825.616123.800321. 853519.906718.613817.S68717.439217.185928.934526.909124. 794322. 609219.910616. 654015.164214.570114.276814. 114428.795226. 504924.113021.531418. 625915. 1709000028.680926. 202223.621420.877717.890511. 5832000028.616：25.992623.292620. C67517.475214. 2987000028.569325.859323.088920.224517.2443U. 1499000028.543425.