1. In steady state without heat sources, the rate of heat transfer is the same through the spherical surface of any radius

Therefore, does not depend on , i.e.

2. The Fourier Law for heat flux:

3.

4.

5.

()

6. Find the constants of integration from the boundary conditions:

Subtruct

7. Write solution:

Note: steady state solution does not depend on conductivity k

8.

does not depend on r

2.1 #10

> restart;

> T1:=80;T2:=T1/4;

> r2:=2.0;r1:=r2/5;

> k:=0.5;

> T:=T1+(T1-T2)*(1/r-1/r1)/(1/r1-1/r2);

> plot(T,r=r1..r2);

> Q:=4*(3.14)*k*(T1-T2)/(1/r1-1/r2);