In Chapter $3$ we will learn that the steady state temperature distribution $T(x)$ for a cooling fin

is described using an equation of the form

$\frac{d^2}{d{x}^2}T(x)-\frac{4h}{kD}(T(x)-T_{})=0,(T(0)=T_b,T(x)=T_{})$

where $h$ is the heat transfer ; $k$ is the thermal conductivity; $D$ is the diameter of the cooling

fin; and $T_{}$ is the temperature of the ambient air. Determine the rate of heat transfer q using

$q=-\frac{k{D}^2}{4}\frac{T}{x}{|}_x=0$

if $k=157\frac{W}{m}$ K$.$ Express you answer in watts.