The net heat exchange by radiation from plate 1 with radius b to plate 2 with ra

Question

The net heat exchange by radiation from plate 1 with radius b to plate 2 with radius a that are separated by a distance c is given by: q = sigma pi b^2 F_1 - 2 (T_1^4 - T_2^4) Where T_1, and T_2 are the absolute temperatures of the plates, sigma = 5.669 times 10^-8 W/(m^2-K^4) is the Stefan-Boltzmann constant, and F_1-2 is a shape factor which for the arrangement in the figure, is given by: F_1-2 = 1/2 [Z - Squareroot Z^2 - 4X^2 + 4X^2 Y^2Z] Where X = a/c, Y = c/b, and Z = 1 + (1 +X^2)Y^2. Write a script file that calculates the heat exchange q. For input the program asks the user to enter values for T_1, T_2, a, b, and c. For output the program prints a summary of the geometry and temperatures and then print the value of q. Use the script to calculate the results for T_1 = 400 K, T_2 = 600 K, a = 1 m, b = 2 m, and c = 0.1, 1, and 10 m.

Explanation / Answer

Matlab Code:

clear, clc

sigma=5.669e-8;

T1=input('Enter the temperature of plate 1: ');

T2=input('Enter the temperature of plate 2: ');

a=input('Enter the radius of plate 1: ');

b=input('Enter the radius of plate 2: ');

c=input('Enter the distance between plate 1 and plate 2: ');

X=a./c; Y=c/b; Z=1+(1+X.^2).*Y.^2;

F_1_2 = 0.5*(Z-sqrt(Z.^2-4*X.^2.*Y.A2));

q=sigma*pi*b^2*F_1_2*(T1^4-T2^4);

fprintf( For circular plate 1 with radius %i m and temperature %i,a,T1)

fprintf(' deg K and circular plate 2 with radius %i m and temperature',b)

fprintf(' %i deg K ',T2)

table=[c ;q];

fprintf(‘ Radiation ’)

fprintf(' Separation Heat Exchange ')

fprintf(' (m) (Watts) ’)

fprintf(' %4.1f %6.0f ,table)

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