Consider a 3-m × 3-m × 3-m cubical furnace whose top and side surfaces closely approximate black surfaces at a temperature of 1200 K. The base surface has an emissivity of ε = 0.7, and is maintained at 800 K. Determine the net rate of radiation heat transfer to the base surface from the top and side

Question

Consider a [latex] 3-m imes 3-m imes 3-m [/latex] cubical furnace whose top and side surfaces closely approximate black surfaces at a temperature of 1200 K. The base surface has an emissivity of [latex] \varepsilon = 0.7 [/latex], and is maintained at 800 K. Determine the net rate of radiation heat transfer to the base surface from the top and side surfaces.

Accepted Answer

The base surface of a cubical furnace is surrounded by black surfaces at a specified temperature. The net rate of radiation heat transfer to the base surface from the top and side surfaces is to be determined.

Assumptions 1 Steady operating conditions exist. 2 The top and side surfaces of the furnace closely approximate black surfaces. 3 The properties of the surfaces are constant.

Properties The emissivity of the base surface is [latex] \varepsilon = 0.7 [/latex]

Analysis The base surface is completely surrounded by the top and side surfaces. Then using the radiation relation for a surface completely surrounded by another large (or black) surface, the net rate of radiation heat transfer from the top and side surfaces to the base is determined to be

[latex] \dot{Q}_{ ext {rad,base }}=\varepsilon A \sigma\left(T_{ ext {base }}^{4}-T_{ ext {surr }}^{4} ight) [/latex]

[latex] = (0.7)\left(3 imes 3 m ^{2} ight)\left(5.67 imes 10^{-8} W / m ^{2} \cdot K ^{4} ight)\left[(1200 K )^{4}-(800 K )^{4} ight] [/latex]

[latex] = 5 9 4 , 4 0 0 W[/latex]

Question 1.130: Consider a 3-m × 3-m × 3-m cubical furnace whose top and sid...

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