Question

The emissivity of galvanized steel sheet, a common roofing material, is 0.13 at temperatures around 300 K, while its absorptivity for solar irradiation is S 0.65. Would the neighborhood cat be comfortable walking on a roof constructed of the material on a day when GS 750 W/m2, T 16 C, and h 7 W/m2 K? Assume the bottom surface of the steel is insulated.

Answer 1

Answer:

Total heat transfer rate is combined convection and radiation transfer rate, multiplied with absorptivity factor. From that equation you can find temperature of the roof using iteration method.  

Explanation:

Known:

steel sheet roof emissivity ∈ = 0.13

steel sheet roof absorptivity $\alpha$_s = 0.65

air temperature T∞ = 16°C ...= 289K

heat transfer rate $G_s$ = 750 W/m2

natural convection h = 7W/m2K

Total heat transfer rate is combined heat transfer rate of convection and radiation, multiplied with absorptivity factor:  

$\alpha$$G_s$=$q_{conv} +q_{rad} =hA($T∞-$T_m$)+∈σA($T_{surf} -T_{s} )$

$\alpha$$G_s$-$h(T_s-$T∞)-∈σ($T_{s} -T_{surf} )$=0

2562-7$T_s$-7.371*10^-9=0

Use iteration method to solve for $T_s$

$T_s$=350.17 K...=77.17°C

In this particular situation, cat would not be comfortable with walking on a roof since its surface temperature is 77.17°C which may even cause burns to its paws.