Question #256766
A horizontal metal plate which is completely insulated except for one exposed surface of 100 sq. ft. is heated electrically to maintain a temperature of 200 °F on the exposed surface. Heat is transferred from this surface by both radiation and conduction through air (assumed to be without motion) to a second plate of similar size maintained at a surface temperature of 100 °F. The distance between the parallel plates is 0.25-in., and each plate has an imissivity of 0.20. What is the watts input to the warmer plate?
1
Expert's answer
2021-10-30T11:20:12-0400

Solution;

Given;

As=100sq.ft=9.29m2A_s=100sq.ft=9.29m^2

Th=200°F=93.33°c=366.33KT_h=200°F=93.33°c=366.33K

Tc=100°F=37.78°c=310.78KT_c=100°F=37.78°c=310.78K

L=0.25in=6.35×103mL=0.25in=6.35×10^{-3}m

ξ=0.20\xi=0.20

We know;

QT=Qrad+QconvQ_T=Q_{rad}+Q_{conv}

Qrad=ξAsσ(Th4Tc4)Q_{rad}=\xi A_s\sigma(T_h^4-T_c^4)

Where;

σ=5.67×108Wm2/K4\sigma=5.67×10^-8Wm^{-2}/K^4

By substitution;

Qrad=0.20×9.29×5.67×108(366.34310.784)Q_{rad}=0.20×9.29×5.67×10^{-8}(366.3^4-310.78^4)

Qrad=914.48WQ_{rad}=914.48W

Now;

Qconv=hAs(ThTc)Q_{conv}=hA_s(T_h-T_c)

Where h is the convectional heat transfer coefficient,value is;

h=3.5W/m2°ch=3.5W/m^2°c

Hence;

Qconv=3.5×9.29(93.3337.78)Q_{conv}=3.5×9.29(93.33-37.78)

Qconv=1806.21WQ_{conv}=1806.21W

Therefore;

QT=914.48+1806.21Q_T=914.48+1806.21

QT=2720.69WQ_T=2720.69W





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