# Heat Dissipation from an Annular Fin

2 views (last 30 days)
Jonathan Bird on 5 May 2020
Answered: Ayush Gupta on 10 Jun 2020
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

Ayush Gupta on 10 Jun 2020
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

### Categories

Find more on Bessel functions in Help Center and File Exchange

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!