b$)$ A diffuse, gray radiation shield of $60mm$ diameter and emissivities of ${}_{2,i}=0\mathrm{.}01$ and ${}_{2,0}=0\mathrm{.}1$ on the

inner and outer surfaces, respectively, is concentric with along tube transporting a hot process fluid.

The tube surface is black with a diameter of $20mm.$ The region interior to the shield is evacuated. The

exterior surface of the shield is exposed to a large room whose walls are at $17C$ and experiences

convection with air at $27C.$ The convective heat transfer coefficient $\text{'}h\text{'}(\frac{W}{m^2}(K))$ may be obtained

from the below equation

${}^{0\mathrm{.}5}=0\mathrm{.}6+0\mathrm{.}387\{\frac{Ra}{[1+(\frac{0\mathrm{.}559}{P}r{)}^{0\mathrm{.}5625}{]}^{1\mathrm{.}777}}{\}}^{0\mathrm{.}167}$