$1$

A $12$ mm outside diameter pipe carries a cryogenic fluid at $90$ K $.$ Another pipe of $15$ mm outside diameter and at $290$ K surrounds it coaxially and the space between the pipes is completely evacuated.

$($a$)$ Determine the radiant heat flow for $3\mathrm{.}5$ m length of pipe if time surface emissivity for both surfaces is $0\mathrm{.}25.$

$($b$)$ Calculate the $\%$ reduction in heat flow if a shield of $13\mathrm{.}5$ mm diameter and $0\mathrm{.}06$ surface emissivity is placed between pipes.