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5 June, 16:20

A house has a black tar, flat, horizontal roof. The lower surface of the roof is well insulated, while the upper surface is exposed to ambient air at 300K through a convective coefficient of 10 W/m2-K. Calculate the roof equilibrium temperature for a) a clear sunny day with an incident solar radiaton flux of 500 W/m2 and the ambient sky at an effective temperature of 50K and b) a clear night with an ambient sky temperature of 50K.

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  1. 5 June, 16:46
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    Answer a) roof equilibrium temperature is 400K

    Explanation:

    The roof surface is sorrounded by ambient air whose temperature is 300K and which has a convective coefficient h of 10W/m2-K.

    This means that heat will be conducted to the roof from the air around at an heat Flux of 300K x 10W/m2-K = 3000w/m2

    For a clear solar day with solar heat Flux of 500W/m2, total heat Flux on roof will be

    Q = 500 + 3500 = 3500W/m2

    Q = h (Tr-Ta)

    Ts is temperature of roof,

    Ta is temperature of air

    3500 = 10 (Tr - 50)

    350 = Tr - 50

    Tr = 400k

    Answer b) : roof equilibrium temperature will be 350K

    Explanation:

    At night total heat Flux is only due to hot ambient air sorrounding the surface of the roof.

    Q = 3000W/m2

    Q = h (Tr-Ta)

    3000 = 10 (Tr-50)

    300 = Tr - 50

    Tr = 350K
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