Chapter 13, Problem 13.119P

The surface of a radiation shield facing a black hot wall at 400 K has a reflectivity of 0.95. Attached to the back side of the shield is a 25-mm-thick sheet of insulating material having a thermal conductivity of $0.016\text{W/m}\cdot \text{K}$ . The overall heat transfer coefficient (convection and radiation) at the surface exposed to the ambient air and surroundings al 300 K is $10{\text{W/m}}^2\cdot \text{K}$ .

(a) Assuming negligible convection in the region between the wall and the shield, estimate the heat loss per unit area from the hot wall.
(b) Perform a parameter sensitivity analysis on the insulation system, considering the effects of shield reflectivity, ${\rho }_s$ , and insulation thermal conductivity, k. What influence do these parameters have on the heat loss from the hot wall? What is the effect of an increased overall coefficient on the heal loss? Show the results of your analysis in a graphical format.