Heat Dissipation from an Annular Fin

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

Answer 1

[Ayush Gupta]

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