A $2\mathrm{.}54$ cm outer diameter tube is used to transport a cryogenic liquid at $-196C$ from a plant to an adjacent unit. The tube is enclosed in an evacuated concentric pipe of $5\mathrm{.}25$ cm inner diameter and wall temperature of $-3C.$ A thin walled radiation shield is placed midway in the annular region between the tube and the pipe. Calculate heat gain by liquid per meter length of the tube.

The following emissivity data are given:

Emissivity of the tube wall $=0\mathrm{.}05$

Emissivity of the pipe wall $=0\mathrm{.}1$

Emissivity of inner surface of radiation shield $=0\mathrm{.}02$

Emissivity of outer surface of radiation shield $=0\mathrm{.}03$

OR