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22 December, 17:24

2.) A plane wall is made of brick with a thermal conductivity of 1.5 W / (m⸳K). The wall is 20 cm thick and has a surface area of 10 m2. One side of the wall is exposed to outside air blowing against the wall resulting in a heat transfer coefficient of 20 W / (m2 ⸳K). The other side is exposed to an air-conditioned room with a convective heat transfer coefficient of 5 W / (m2 ⸳K). a. What are the thermal resistances corresponding to conduction through the wall and convection at each wall surface? b. For every 1 o C of temperature difference between the outside and inside air, how much additional cooling power is required from the air conditioner?

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  1. 22 December, 17:39
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    The answers to the question are

    a. The thermal resistances corresponding to conduction through the wall and convection at each wall surface is 2.167*10^ (-2)

    b. 46.15 W. That is for every 1 °C of temperature difference between the outside and inside air, 46.15 W additional cooling power is required from the air conditioner.

    Explanation:

    For a wall with convective heat transfer on either side, the total thermal resistance is given by

    R = (1 / (h1*A) + L / (A*k) + 1 / (h2*A))

    Where R = Total thermal resistance

    h1 = 20 W / (m2*K)

    h2 = 5 W / (m2*K)

    A = Wall surface area = 10 m^2

    L = Wall thickness = 20 cm = 0.2 m

    Therefore, R = 2.167*10^ (-2)

    (b) The heat transferred for every 1 °C difference between the inside and outside temperatures is given by

    Q = (T2 - T1) / R where T2 and T1 are the inside and outside temperatures respectively. Hence for (T2 - T1) = 1 °C we have

    Q = (1 °C/2.167*10^ (-2)) = 46.15 W
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