傳熱學(xué)MATLAB溫度分布大課后復(fù)習(xí)完整編輯版

.\東南大學(xué)能源與環(huán)境學(xué)院課程作業(yè)報(bào)告作業(yè)名稱：傳熱學(xué)大作業(yè)——利用matlab程序解決熱傳導(dǎo)問(wèn)題精品文檔放心下載院系：能源與環(huán)境學(xué)院專業(yè)：建筑環(huán)境與設(shè)備工程學(xué)號(hào)：姓名：2014年11月9日.\一、題目及要求原始題目及要求各節(jié)點(diǎn)的離散化的代數(shù)方程源程序不同初值時(shí)的收斂快慢上下邊界的熱流量（λ=1W/(m℃））計(jì)算結(jié)果的等溫線圖計(jì)算小結(jié)題目：已知條件如下圖所示：二、各節(jié)點(diǎn)的離散化的代數(shù)方程各溫度節(jié)點(diǎn)的代數(shù)方程ta=(300+b+e)/4;tb=(200+a+c+f)/4;tc=(200+b+d+g)/4;td=(2*c+200+h)/4謝謝閱讀te=(100+a+f+i)/4;tf=(b+e+g+j)/4; tg=(c+f+h+k)/4;th=(2*g+d+l)/4謝謝閱讀ti=(100+e+m+j)/4; tj=(f+i+k+n)/4; tk=(g+j+l+o)/4; tl=(2*k+h+q)/4謝謝閱讀.\tm=(2*i+300+n)/24; tn=(2*j+m+p+200)/24; to=(2*k+p+n+200)/24; tp=(l+o+100)/12感謝閱讀三、源程序【G-S迭代程序】【方法一】函數(shù)文件為：function[y,n]=gauseidel(A,b,x0,eps)精品文檔放心下載D=diag(diag(A));L=-tril(A,-1);U=-triu(A,1);G=(D-L)\U;f=(D-L)\b;y=G*x0+f;n=1;whilenorm(y-x0)>=epsx0=y;y=G*x0+f;n=n+1;end命令文件為：A=[4,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0;謝謝閱讀-1,4,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0;感謝閱讀0,-1,4,-1,0,0,-1,0,0,0,0,0,0,0,0,0;謝謝閱讀.\0,0,-2,4,0,0,0,-1,0,0,0,0,0,0,0,0;精品文檔放心下載-1,0,0,0,4,-1,0,0,-1,0,0,0,0,0,0,0;感謝閱讀0,-1,0,0,-1,4,-1,0,0,-1,0,0,0,0,0,0;精品文檔放心下載0,0,-1,0,0,-1,4,-1,0,0,-1,0,0,0,0,0;感謝閱讀0,0,0,-1,0,0,-2,4,0,0,0,-1,0,0,0,0;謝謝閱讀0,0,0,0,-1,0,-1,0,4,0,0,0,-1,0,0,0;精品文檔放心下載0,0,0,0,0,-1,0,0,-1,4,-1,0,0,-1,0,0;精品文檔放心下載0,0,0,0,0,0,-1,0,0,-1,4,-1,0,0,-1,0;感謝閱讀0,0,0,0,0,0,0,-1,0,0,-2,4,0,0,0,-1;感謝閱讀0,0,0,0,0,0,0,0,-2,0,0,0,24,-1,0,0;謝謝閱讀0,0,0,0,0,0,0,0,0,-2,0,0,-1,24,-1,0;感謝閱讀0,0,0,0,0,0,0,0,0,0,-2,0,0,-1,24,-1;謝謝閱讀0,0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,12];精品文檔放心下載b=[300,200,200,200,100,0,0,0,100,0,0,0,300,200,200,100]';謝謝閱讀[x,n]=gauseidel(A,b,[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]',1.0e-6)感謝閱讀xx=1:1:4;yy=xx;[X,Y]=meshgrid(xx,yy);Z=reshape(x,4,4);Z=Z'contour(X,Y,Z,30)=139.6088150.3312153.0517153.5639謝謝閱讀.\108.1040108.6641108.3119108.152384.142967.909663.379362.421420.155715.452114.874414.7746【方法2】>> t=zeros(5,5);t(1,1)=100;t(1,2)=100;t(1,3)=100;t(1,4)=100;t(1,5)=100;t(2,1)=200;t(3,1)=200;t(4,1)=200;t(5,1)=200;fori=1:10t(2,2)=(300+t(3,2)+t(2,3))/4;謝謝閱讀t(3,2)=(200+t(2,2)+t(4,2)+t(3,3))/4;精品文檔放心下載t(4,2)=(200+t(3,2)+t(5,2)+t(4,3))/4;謝謝閱讀t(5,2)=(2*t(4,2)+200+t(5,3))/4;謝謝閱讀t(2,3)=(100+t(2,2)+t(3,3)+t(2,4))/4;精品文檔放心下載t(3,3)=(t(3,2)+t(2,3)+t(4,3)+t(3,4))/4;謝謝閱讀t(4,3)=(t(4,2)+t(3,3)+t(5,3)+t(4,4))/4;精品文檔放心下載t(5,3)=(2*t(4,3)+t(5,2)+t(5,4))/4;感謝閱讀t(2,4)=(100+t(2,3)+t(2,5)+t(3,4))/4;精品文檔放心下載.\t(3,4)=(t(3,3)+t(2,4)+t(4,4)+t(3,5))/4;t(4,4)=(t(4,3)+t(4,5)+t(3,4)+t(5,4))/4;t(5,4)=(2*t(4,4)+t(5,3)+t(5,5))/4;t(2,5)=(2*t(2,4)+300+t(3,5))/24;t(3,5)=(2*t(3,4)+t(2,5)+t(4,5)+200)/24;t(4,5)=(2*t(4,4)+t(3,5)+t(5,5)+200)/24;t(5,5)=(t(5,4)+t(4,5)+100)/12;t'endcontour(t',50);ans=100.0000200.0000200.0000200.0000200.0000100.0000136.8905146.9674149.8587150.7444100.0000102.3012103.2880103.8632104.3496100.000070.626461.946559.801859.6008100.000019.003314.890314.539314.5117.\【Jacobi迭代程序】函數(shù)文件為：function[y,n]=jacobi(A,b,x0,eps)謝謝閱讀D=diag(diag(A));L=-tril(A,-1);U=-triu(A,1);B=D\(L+U);f=D\b;y=B*x0+f;n=1;whilenorm(y-x0)>=epsx0=y;y=B*x0+f;n=n+1;end命令文件為：A=[4,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0;感謝閱讀-1,4,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0;謝謝閱讀0,-1,4,-1,0,0,-1,0,0,0,0,0,0,0,0,0;感謝閱讀0,0,-2,4,0,0,0,-1,0,0,0,0,0,0,0,0;謝謝閱讀-1,0,0,0,4,-1,0,0,-1,0,0,0,0,0,0,0;感謝閱讀0,-1,0,0,-1,4,-1,0,0,-1,0,0,0,0,0,0;感謝閱讀0,0,-1,0,0,-1,4,-1,0,0,-1,0,0,0,0,0;感謝閱讀.\0,0,0,-1,0,0,-2,4,0,0,0,-1,0,0,0,0;感謝閱讀0,0,0,0,-1,0,-1,0,4,0,0,0,-1,0,0,0;感謝閱讀0,0,0,0,0,-1,0,0,-1,4,-1,0,0,-1,0,0;感謝閱讀0,0,0,0,0,0,-1,0,0,-1,4,-1,0,0,-1,0;精品文檔放心下載0,0,0,0,0,0,0,-1,0,0,-2,4,0,0,0,-1;謝謝閱讀0,0,0,0,0,0,0,0,-2,0,0,0,24,-1,0,0;精品文檔放心下載0,0,0,0,0,0,0,0,0,-2,0,0,-1,24,-1,0;精品文檔放心下載0,0,0,0,0,0,0,0,0,0,-2,0,0,-1,24,-1;感謝閱讀0,0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,12];精品文檔放心下載b=[300,200,200,200,100,0,0,0,100,0,0,0,300,200,200,100]';精品文檔放心下載[x,n]=jacobi(A,b,[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]',1.0e-6);精品文檔放心下載xx=1:1:4;yy=xx;[X,Y]=meshgrid(xx,yy);Z=reshape(x,4,4);Z=Z'contour(X,Y,Z,30)=97Z=139.6088150.3312153.0517153.5639謝謝閱讀108.1040108.6641108.3119108.1523謝謝閱讀84.142967.909663.379362.4214感謝閱讀20.155715.452114.874414.7746謝謝閱讀.\四、不同初值時(shí)的收斂快慢1、[方法1]在Gauss迭代和Jacobi迭代中，本程序應(yīng)用的收斂條件均為norm(y-x0)>=eps，即使前后所求誤差達(dá)到e的-6次方時(shí)，跳出循環(huán)得出結(jié)果。感謝閱讀將誤差改為0.01時(shí)，只需迭代25次，如下[x,n]=gauseidel(A,b,[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]',0.01)運(yùn)行結(jié)果為精品文檔放心下載將誤差改為0.1時(shí)，需迭代20次，可見(jiàn)隨著迭代次數(shù)增加，誤差減小，變化速度也在減小。感謝閱讀[方法2]通過(guò)i=1:10判斷收斂，為迭代10次，若改為1:20，則迭代20次。謝謝閱讀2、在同樣的誤差要求下，誤差控制在e的-6次方內(nèi)，Gauss迭代用了49次達(dá)到要求，而Jacobi迭代用了97次，可見(jiàn)，在迭代中盡量采用最新值，可以大幅度的減少迭代次數(shù)，迭代過(guò)程收斂快一些。感謝閱讀在Gauss中，初值為100，迭代46次達(dá)到精確度1.0e-6,初值為50時(shí)，迭代47次，初值為0時(shí)，迭代49次，初值為200時(shí)迭代50次，可見(jiàn)存在一個(gè)最佳初始值，是迭代最快。這一點(diǎn)在jacobi迭代中表現(xiàn)的尤為明顯。感謝閱讀五、上下邊界的熱流量：上邊界t=200℃,t=10℃，所以，熱流量Φ1=λ*[200-100x+200-tx+200-tx+200-tx+200-t*x]dabc=1*（100/2+(200-139.6088)+(200-150.3312)+(200-153.0517)+(200-153.5639)/2)=230.2264W感謝閱讀下邊界熱流量Φ2=|λ*[ti-tmx+tj-tox+tk-tpx+tl-tq*x]-yyyy2h*(100-10*x+tn-t*x+to-t*x+tm-t*x+tp-t*x)|y2yyyy2.\=|1*((84.1429-20.1557)+(67.9096-15.4521)+(63.3793-14.8744)+(62.4214-14.7746)/2)-10*(90/2+(20.1557-10)+(15.4521-10)+(14.8744-10)+(14.7746-10)/2)|=|-489.925|W=489.25W感謝閱讀六、溫度等值線Gauss:Yacobi:.\七、計(jì)算小結(jié)導(dǎo)熱問(wèn)題進(jìn)行有限差分?jǐn)?shù)值計(jì)算的基本思想是把在時(shí)間、空間上連續(xù)的溫度場(chǎng)用有限個(gè)離散點(diǎn)溫度的集合來(lái)代替，即有限點(diǎn)代替無(wú)限點(diǎn)，通過(guò)求解根據(jù)傅里葉定律和能量守恒兩大法則建立關(guān)于控制面內(nèi)這些節(jié)點(diǎn)溫度值的代數(shù)方程，獲得各個(gè)離散點(diǎn)上的溫度值。謝謝閱讀要先劃分查分網(wǎng)格，在建立差分代數(shù)方程組，用MATLA