Chapter 1, Problem 1.79P

A rectangular forced air healing duct is suspended fromthe ceiling of a basement whose air and walls are at atemperature of $T_{\infty }=T_{sur}=5\text{°C}$ . The duct is 15 m long, and its cross section is $350\text{mm}\times 200\text{mm}$ .
(a) For an uninsulated duct whose average surface temperature is 50°C, estimate the rate of heat loss from the duct. The surface emissivity and convectioncoefficient are approximately 0.5 and $\text{4}{\text{W/m}}^{\text{2}}\cdot \text{K,}$ respectively.
(b) If heated air enters the duct at 58°C and a velocity of4 m/s and the heat loss corresponds to the result ofpart (a), what is the outlet temperature? The densityand specific heat of the air may be assumed to be $\rho =\text{1}\text{.10}{\text{kg/m}}^3$ and $c_p=1008\text{J/kg}\cdot \text{K}$ , respectively.