$11$A$.3$ Transpiration cooling

$($a$)$ Calculate the temperature distribution between the two shells of Example $11\mathrm{.}4-4$ for radial mass flow rates of zero and ${10}^{-5}\frac{g}{s}$ for the following conditions

$R=500$ microns $T_R=300C$

$R=100$ microns $T_{}=100C$

$k=6\mathrm{.}13{10}^{-5}ca\frac{l}{c}m*s*C$

hat$(C{)}_p=0\mathrm{.}25ca\frac{l}{g}*C$

$($b$)$ Compare the rates of heat conduction to the surface at $R$ in the presence and absence of convection.