I am trying to calculate the power of a radiator and the final temperature. the equation is Planck's law I do not know what is wrong with it. could you please help me

h=6.626176e-34; %J/s

c=2.99792458e8; %m/s

k=1.380649e-23; %J/K

A=20*1e-4; %m^2

er=0.95; %radation emissivity according to measurement Fig.1 e & f

T=300; %Kelvin,because of the cover and vacuum condition of cooling.

tc=1; % tc=transmittance of the cover

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%calculations:

%% radiator

%direction

syms theta

f = (1/2)*sin(2*theta);

intf = int(f,0,pi/2);

%wavelength, Planck's law, Blackbody Values For Vector Lam

Lam=(0:inf).*1e-6; % meters

dLam = Lam(2) - Lam(1); % Delta Lambda

I1 =(2*h*c^2)./((Lam.^5).*(exp((h.*c)./(k.*T.*Lam))-1));

% plotI1 = I1*1e-12;

% plotLam = Lam/1e-6;

% plot(plotLam,plotI1,'linewidth',4)

Ibb=trapz(Lam,I1);

%the power of radiator

Pr = 2*A*pi*intf*Ibb*er; % W. m-2

[Torsten]

And what's wrong with the code ?

[Zahra Kamali Khanghah]

Lam=(0:inf )in the range 0 to infinity it is the error : Requested array exceeds the maximum possible variable size.

in the other ranges the answer is not correct

[Torsten]

Instead of Inf, use a large value such that I1 is approximately 0.

Lam = 0:Inf would be a vector of infinite length that MATLAB cannot create.

[Zahra Kamali Khanghah]

thanks. As the final answer should be somthing around 330, could you tell me what is the reseason I cannot get it like a usual number?

[Torsten]

Before calculating Pr, use the line

intf = double(intf)

But you should be able to get intf as 0.5 without symbolic calculations...

Answer 1

[Neelanshu]

Hi Zahra,

I understand from your query that you are interested in finding the reason why you're not getting a numeric value for the power of the radiator.

You can follow these steps to ensure you get a numeric value for the power :

• As Torsten pointed out you need to change the "Lam" variable range to a vector of finite range and convert "intf" variable to double datatype.

intf = double(intf)

• Additionally you have to choose a very small starting value for "Lam" variable instead of 0. In MATLAB, division by zero leads to a NaN value for I1, which propagates when it undergoes numerical integration.

% Define wavelength range, starting from a small positive number to avoid division by zero

Lam = linspace(1e-10, 1e-6, 10000); % Meters

By making these adjustments, you should be able to obtain a numeric value for the power.

Hope this helps.