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25 April, 15:06

The hot combustion gases of a furnace are separated from the ambient air and its surroundings, which are at 25 oC, by a brick wall 0.15 m thick. The brick has a thermalconductivity of 1.2 W/m. K and a surface emissivity of 0.8. Under steady state conditions an outer surface temperature of 100 oC is measured. Free convection heat transfer to the air adjoining this surface is characterized by a convection coefficient h = 20 W/m2. K. What is the inner surface temperature of the brick?

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  1. 25 April, 15:21
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    T1 = 625.54 K

    Explanation:

    We are given;

    T_α = Tsur = 25°C = 298K

    h = 20 W/m². K,

    L = 0.15 m

    K = 1.2 W/m. K

    ε = 0.8

    Ts = T2 = 100°C = 373K

    T1 = ?

    Assumption:

    -Steady - state condition

    -One - dimensional conduction

    -No uniform heat generation

    -Constant properties

    From Energy balance equation;

    E°in - E°out = 0

    Thus,

    q"cond - q"conv - q"rad = 0

    K[ (T1 - T2) / L] - h (Ts-T_α) - εσ (Ts⁴ - Tsur⁴)

    Where σ is Stephan-Boltzmann constant and has a value of 5.67 x 10^ (-8)

    Thus;

    K[ (T1 - T2) / L] - h (Ts-T_α) - εσ (Ts⁴ - Tsur⁴) = 1.2[ (T1 - 373) / 0.15] - 20 (373 - 298] - 0.8x5.67x10^ (-8) [373⁴ - 298⁴] = 0

    This gives;

    (8T1 - 2984) - (1500) - 520.31 = 0

    8T1 = 2984 + 1500 + 520.31

    8T1 = 5004.31

    T1 = 5004.31/8

    T1 = 625.54 K
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