In Chapter $3$ we will learn that the steady state temperature distribution

$T(r)$ for a hollow cylinder whose surfaces are exposed to fluids at a

different temperature is given by

$\frac{1}{r}\frac{d}{dr}(rk\frac{dT}{dr})=0,(T(r_1)=T_{s,1},T(r_2)=T_{s,2})$

where $$k$$ is the thermal conductivity. Determine the heat transfer rate

$a$ using

$q=-k(2r_{2}L)\frac{dT}{dr}{|}_r=r_2$

if $k=164\frac{W}{m}K,r_1=3mm,r_2=5mm,L=1m,T_1=100C,$ and $T_2=25C.$

Express you answer in kW $.$