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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 :

Hashirriaz830

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 [tex]\alpha[/tex]_s = 0.65

air temperature T∞ = 16°C ...= 289K

heat transfer rate [tex]G_s[/tex] = 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:  

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

[tex]\alpha[/tex][tex]G_s[/tex]-[tex]h(T_s-[/tex]T∞)-∈σ([tex]T_{s} -T_{surf} )[/tex]=0

2562-7[tex]T_s[/tex]-7.371*10^-9=0

Use iteration method to solve for [tex]T_s[/tex]

[tex]T_s[/tex]=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.  

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