Solve using matlab code A coating on a panel surface is cured by radiant energy
ID: 1526737 • Letter: S
Question
Solve using matlab code A coating on a panel surface is cured by radiant energy from a heater. The temperature of the coating is determined by radiative and convective heat transfer processes. If the radiation is treated as diffuse and gray, the following nonlinear system of simultaneous equations determine the unknowns J_K, T_k, J_c. T_c panel 5.67 times 10^-8 T_c^4 + 17.41T_c -J_c = 5188.18 J_c = 0.71 J_k = 7.46T_c = 2352.71 5.67 times 10^-8 T_j^A +1.865T_h - J_h =. 2250 J_k = 0.71 J_c + 7.46T_k = 11093 where J_h, and J_c are the grandiosities of the heater and coating surfaces, respectively, and T_h and T_c are the respective temperatures. Show that the following iteration functions can be used for solving the nonlinear system of equations with the fixed-point iteration method:T_c = [J_e -. 17, 41T_c + 5188.18/5.67 times 10^-8]1/4, T_k = [2250 J_k - 1.865 T_h/5.67 x 10^-8]^1/4 J_c = 2352.71 +0.71J_k -746T_c JA_h = 11093+ 0.71J_c -7, .46T_h solve the nonlinear system of equations with the fixed-point iteration method using the iteration functions from part Use the following initial values: T_k = T_c = 298 K, J_c = 3000 W/m^2, and J = 5000 w/m^2 Carry out 100 iterations, and plot the respective values to observe their convergence. The final answers should be T = 481 K, J = 6222 W/m^2 T_k = 671 K, J_h = 10504 W/m^2Explanation / Answer
Matlab Code
n = 20; % set some number of iterations , may need adjusting
f = inline ( '[5.67E-8*x(4)^4+ 17.41*x(4)-x(3)-5188.18 ; x(3)-0.71*x(1)+7.46*x(4)-2352.71;5.67E-8*x(2)^4+ 1.865*x(2)-x(1)-2250;x(1)-0.71*x(3)+7.46*x(2)-11093]' ); % the vector function
% the matrix of partial derivatives
Df = inline ( '[0,0,-1,4*5.67E-8*x(4)^3+17.41;-0.71,0,1,7.46;-1,4*5.67E-8*x(2)^3+1.865,0,0;1,7.46,-0.71,0]' );
x = [0.2;298;0.2;298]; % starting guess
for i = 1: n
Dx = -Df ( x ) f( x ); % solve for increment
x = x + Dx; % add on to get new guess;
end
disp(x);
Sample Output
>> Untitled
1.0e+04 *
1.0504
0.0671
0.6222
0.0481