tpbvp - yinit =[S T0[x,y = numinteg(yinit Tsh_nlin =...

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Sheet1 Page 1 function tpbvp global c h Tinf % Constants k = 42 b = 0.5 d = 0.2 Tinf = 500 l = 2 epsilon = 0.1 sigma = 5.7e-8 h = 0.5 Tr = 675 % Computed constants A = b*d P = 2*(b+d) c = (sigma*epsilon*P)/(k*A) % Boundary conditions T0 = 1000 T4 = 350 % Part a) % Finite difference approach with nonlinear equations and rootfinding % Initial guess T = zeros(3,1) Tinit = zeros(3,1) Tinit(1) = Tr Tinit(2) = Tr Tinit(3) = Tr % Nonlinear root finding Tfd_nlin = fsolve(@finitediff,Tinit,optimset('fsolve')) % T = % 739.9453 % 592.5973 % 474.1394 % Part b) % Finite difference approach with linearized system of equations diag = 2+4*c*Tr^3*h^2 rhs = c*(3*Tr^4+Tinf^4)*h^2 Amat = [diag -1 0 -1 diag -1 0 -1 diag] bvec = [T0+rhs rhs T4+rhs] Tfd_lin = Amat\bvec
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Sheet1 Page 2 % Part c) % Shooting method with rootfinding % Initial guess Sinit = -800 % Nonlinear root finding S = fzero(@shoot,Sinit)
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Unformatted text preview: yinit = [S T0] [x,y] = numinteg(yinit) Tsh_nlin = y(2:4,2) %------------------------------------------------% function zero = finitediff(T) T1 = T(1) T2 = T(2) T3 = T(3) zero(1) = -2*T1-0.0475e-8*T1^4+T2+1029.6875 zero(2) = T1-2*T2-0.0475e-8*T2^4+T3+29.6875 zero(3) = T2-2*T3-0.0475e-8*T3^4+379.6875 %------------------------------------------------% function zero = shoot(Sinit) Tinit = 1000 yinit = [Sinit Tinit] [x,y] = numinteg(yinit) zero = y(5,2)-350 %------------------------------------------------% function [x,y] = numinteg(yinit) xspan = linspace(0, 2, 5) [x,y] = ode45(@eqn,xspan,yinit) %------------------------------------------------% function dydx = eqn(x,y) global c h Tinf S = y(1) T = y(2) Sheet1 Page 3 dSdx = c*(T^4-Tinf^4) dTdx = S dydx = [dSdx dTdx]...
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This note was uploaded on 09/05/2011 for the course EGM 3344 taught by Professor Raphaelhaftka during the Spring '09 term at University of Florida.

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tpbvp - yinit =[S T0[x,y = numinteg(yinit Tsh_nlin =...

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