Steam at 120 °C flows steadily through a horizontal steel pipe of inner radius 2.5 cm…
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
Steam at 120 °C flows steadily through a horizontal steel pipe of inner radius 2.5 cm and wall thickness 6.0 mm. The outer surface of the pipe is exposed to still air at 25 °C. To reduce energy loss, the pipe is to be wrapped with a layer of mineral wool insulation of thermal conductivity lower than that of steel.
The design objective is to choose a thickness for the mineral wool such that, once installed, the rate of energy loss by radiation from the outer surface of the insulation does not exceed the rate of energy conducted radially outward through the steel pipe wall.
Assume the following:
• The steam temperature remains uniform at 120 °C.
• The outer surface of the mineral wool behaves as a gray body of known emissivity.
• Convection from the outer surface of the insulation to the surrounding air is negligible compared to radiation.
• The insulation is sufficiently long that end effects can be ignored.
Address the questions below.
(a) Write a symbolic expression for the rate at which energy is conducted through the steel wall per unit length of pipe, in terms of the relevant geometric parameters and material property constants.
(b) Write a symbolic expression for the rate at which energy is radiated from the exterior surface of a cylindrical layer of insulation per unit length, in terms of its outer radius Ro and given constants.
(c) Using the expressions from parts (a) and (b), derive an inequality that the insulation’s outer radius Ro must satisfy to meet the design objective stated above.
(d) Suppose the emissivity of the insulation’s exterior surface could be reduced by applying a thin, shiny aluminum foil. Explain qualitatively, without further calculations, how this change would affect the required insulation thickness and why.