Heat Dissipation from an Annular Fin

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Jonathan Bird
Jonathan Bird 2020-5-5
回答： Ayush Gupta 2020-6-10
I'm trying to find the rate of heat dissipation from an annular fin as a function of the fin radius. The rate of heat dissipation is found as follows:
q = (2*pi*k*n*w*theta_0*Rb)*((besselk(1,n*Rb)*besseli(1,n*Re)-besseli(1,n*Rb)*besselk(1,n*Re))/(besselk(0,n*Rb)*besseli(1,n*Re)+besseli(0,n*Rb)*besselk(1,n*Re)));
Where Rb and Re are the inner and outer radii respectively. k, n, w, theta_0 and Rb are all known values. How could I work out the rate of heat dissipation as a function of the outer radius Re for say Re = Rb to Re = 100*Rb and plot this?
Many thanks

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回答（1 个）

Ayush Gupta
Ayush Gupta 2020-6-10
This equation can be simplified by fixing the known values and the relation between Re and Rb, Refer to the code below:
x = [0:0.5:20];
result = [0:0.5:20];
for i = 1:length(x)
result(i) = cali(x(i));
end
plot(x,result)
function out = cali(Rb)
k = 1;
n= 1;
k = 1;
w = 1;
thefixedta_0 = 1;
Re = 100*Rb;
out = (2*pi*k*n*w*thefixedta_0*Rb)*((besselk(1,n*Rb)*besseli(1,n*Re)-besseli(1,n*Rb)*besselk(1,n*Re))/(besselk(0,n*Rb)*besseli(1,n*Re)+besseli(0,n*Rb)*besselk(1,n*Re)));
end

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