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Computer Aided Thermal Design Laboratory www.msharpmath.com / 00 서울대학교 기계항공공학부 담당 : 김 찬 중 열전달 강의 4 2013. 03. 26.

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Presentation on theme: "Computer Aided Thermal Design Laboratory www.msharpmath.com / 00 서울대학교 기계항공공학부 담당 : 김 찬 중 열전달 강의 4 2013. 03. 26."— Presentation transcript:

1 Computer Aided Thermal Design Laboratory / 00 서울대학교 기계항공공학부 담당 : 김 찬 중 열전달 강의

2 Computer Aided Thermal Design Laboratory / 00 2 스펙트럼 흑체방사도 ■ 플랑크(Planck)의 식 ■ 스테판-볼츠만 법칙 (Stefan-Boltzmann law)

3 Computer Aided Thermal Design Laboratory / 00 3 예제 2 #> c1 = e8; c2 = 14388; lam = 3; c1 = 3.742e+008 c2 = lam = 3 #> solve.T {1000} ( 800 = c1 / ( lam^5*(exp(c2/(lam*T))-1) ) ); ans =

4 Computer Aided Thermal Design Laboratory / 00 4 흑체복사함수 #> double fb(z) = int.x(600,z) ( 3.742e8/x^5/(exp(14388/x)-1))/_sigma; #> fb(3000); ans = #> fb(4000); ans =

5 Computer Aided Thermal Design Laboratory / 00 5 흑체복사함수 double fb(z) = int.x(600,z) ( 3.742e8/x^5/(exp(14388/x)-1))/_sigma; double fbinv(gsum) { dz = 100; z = 600; sum = fb(z); if( sum > gsum ) return z; while( 1 ) { z += dz; sum = fb(z); if( sum > gsum ) { z -= dz; dz /= 10; continue; } if( |gsum-sum| < ) break; } return z; } double fb12(z1,z2) = int.x(z1,z2) ( 3.742e8/x^5/(exp(14388/x)-1))/_sigma; // example 5-4 #> T = 5800; fb12(0.4*T,0.76*T); T = 5800 ans =

6 Computer Aided Thermal Design Laboratory / 00 6 흑체복사함수, 예제 3,4 // example 5-3 #> T = 1500; T = 1500 #> fbinv(0.1); ans = 2195 #> lam1 = ans/T; lam1 = #> fbinv(0.9); ans = 9373 #> lam2 = ans/T; lam2 = // example 5-4 #> T = 5800; fb12(0.4*T,0.76*T); T = 5800 ans =

7 Computer Aided Thermal Design Laboratory / 00 7 ans = [ e ] [ e ] [ e ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] #> fbm++( ( 700:100:4000)' ) | fbm++( (4100:100:7500)' ) | (fbm++( (8000:500:19500)' ) _ fbm++( (20000:5000:55000)' )); matrix fbm(double z) = [ z, int.x(600,z) ( 3.742e8/x^5/(exp(14388/x)-1))/_sigma ];

8 Computer Aided Thermal Design Laboratory / 00 8 double paracir(ri,rj,L=1) { double fij ; ri /= L ; rj /= L ; x = 1+(1+rj^2)/ri^2 ; fij = (x-sqrt(x*x-4*(rj/ri)^2))/2; return fij; } double pararec(x,y,H=1) { double fij; x /= H; y /= H; x2 = sqrt(1+x*x); y2 = sqrt(1+y*y); fij =0.5*log((1+x^2)*(1+y^2)/(1+x^2+y^2)) -x*atan(x)-y*atan(y) +x*y2*atan(x/y2)+y*x2*atan(y/x2); fij *= 2/pi/x/y; return fij; } double edgerec(x,y,L=1) { double fij; x = L/x; y = L/y; z = x*y/sqrt(x^2+y^2) ; fij = atan(x)/x+atan(y)/y-atan(z)/z +0.25*log( (1+x^(-2))*(1+y^(-2))/(1+z^(-2)) *((1+z^2)/(1+x^2))^(1/x^2)* ((1+z^2)/(1+y^2))^(1/y^2) ); fij *= x/pi; return fij; } 형상계수

9 Computer Aided Thermal Design Laboratory / 00 9 #> paracir(12,6,15) ; ans = 예제 10

10 Computer Aided Thermal Design Laboratory / #> j1 = 23224; r2 = (1-0.8)/(pi*0.06^2*0.8); e2 = _sigma*300^4; #> r12 = 240.3; r13 = 24.3; r23 = 140; #> solve.q1.j2.j3 ( q1 = (j1-j2)/r12+(j1-j3)/r13, (e2-j2)/r2 = (j2-j1)/r12+(j2-j3)/r23, 0 = (j3-j1)/r13+(j3-j2)/r23 ); j1 = r2 = e2 = r12 = r13 = 24.3 r23 = 140 ans = [ ] [ ] [ ] #> solve [ q1=1, j2=2, j3=3 ] ( q1 = (j1-j2)/r12+(j1-j3)/r13, (e2-j2)/r2 = (j2-j1)/r12+(j2-j3)/r23, 0 = (j3-j1)/r13+(j3-j2)/r23 ); #> q1;j2;j3; q1 = j2 = j3 = 예제 11


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