1. A coating on a panel surface is cured by radiant energy from a heater. The te

Question

1. 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 Ambient at 298 K equations determine the unknowns 7,…, 5.67 × 10-8 17.417,-5188.18 1,-0.711, +7.46T, " 2352.71 5.67 × 10-2 + 1.8657,-4-2250 J,-0.711, +7.467,-11093 where J, and J, are the radiosities of the heater and coating surfaces, respectively, and T, and T, are the respective temperatures. Use Newton vector method. The initial guesses should consider that the radiosities can be between O and 1 and the emperatures greater than Ta 298 K

Explanation / 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

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