Chapter 8, Problem 8.17P

A flat-plate solar collector is used w heat atmospheric air flowing through a rectangular channel. The bottom surface of the channel is well insulated, while the top surface is subjected to a uniform heat flux $q_o^{"}$ , which is due to the net effect of solar radiation absorption and heat exchange between the absorber and cover plates.

(a) Beginning with an appropriate differential control volume, obtain an equation that could be used to determine the mean air temperature $T_m\left(x\right)$ as a function of distance along the channel. Solve this equation lo obtain an expression for the mean temperature of the air leaving the collector.
(b) With air inlet conditions of $\stackrel{\dot{}}{m}=0.1\text{kg/s}\text{and}{T}_{m,i}=40°C$ , what is the air outlet temperature if $L=3m,w=1m,\text{and}{q}_o^{\text{'}\text{'}}=700W/m^2$ ? The specific heat of air is $c_p=1008\text{J/kg}\cdot \text{K}$ .