Chapter 3, Problem 3.14P

Consider the composite wall of Problem 3.13 under conditions for which the inside air is still characterized by $T_{\infty ,i}=20°\text{C}$ and $h_i=30{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ However, use the more realistic conditions for which the outside air is characterized by a diurnal (time) varying temperature of the form
   $\begin{array}{l}{T}_{\infty ,0}\left(\text{K}\right)=273+5\sin \left(\frac{2\pi }{24}t\right)0\le t\le 12h\\ T_{\infty ,o}\left(\text{K}\right)=273+11\sin \left(\frac{2\pi }{24}t\right)12\le t\le 24h\end{array}$

with $h_o=60{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ Assuming quasi-steady conditions for which changes in energy storage within the wall may be neglected, estimate the daily heat loss through the wall if its total surface area is $200{\text{m}}^{\text{2}}.$