A cryogenic fluid flows through a tube \(20 \mathrm{~mm}\) in diameter, the outer surface of which is diffuse and gray with an emissivity of 0.05 and temperature of \(77 \mathrm{~K}\). This tube is concentric with a larger tube of \(50-\mathrm{mm}\) diameter, the inner surface of which is diffuse and gray with an emissivity of 0.05 and temperature of \(300 \mathrm{~K}\). The space between the surfaces is evacuated. Determine the rate of heat gain by the cryogenic fluid per unit length of the inner tube. If a thin-walled radiation shield that is diffuse and gray with an emissivity of 0.05 (both sides) is inserted midway between the inner and outer surfaces, calculate the change (percentage) in rate of heat gain per unit length of the inner tube. To what degree will the heat transfer change if the shield emissivity is 1.0 (both sides)?