Chapter 1, Problem 1.39P

On a cold winter day, the outside wall of a home is exposed to an air temperature of $\text{—2°C}$ when the inside temperature of the room is at $\text{22°C}$. As a result of this temperature gradient, there is heat loss through the wall to the outside. Consider the convective heat transfer coefficients for the air inside the room and at the outside wall surface to be, respectively, 12.0 and $\text{28}{\text{.0 W/m}}^{\text{2}}\text{K}$. If the composite room wall is modeled as a plane wall with a thermal resistance per unit area of $\text{0}{\text{.5 m}}^{\text{2}}\text{K/W}$, determine the temperature at the outer surface of the wall as well as the rate of heat flow through the wall per unit area. If the homeowner were to consider using a fiberglass insulation layer on the inside wall surface for reducing this heat loss by 50%, what is the required thickness of this layer and the outside wall temperature for this case?