The concrete slab of a basement is 11 m long, 8 m wide, and 0.20 m thick. During the winter, temperatures are nominally 17 C and 10 C at the

Question

The concrete slab of a basement is 11 m long, 8 m wide, and 0.20 m thick. During the winter, temperatures are nominally 17 C and 10 C at the top and bottom surfaces, respectively. If the concrete has a thermal conductivity of 1.4 W/m K, what is the rate of heat loss through the slab

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Delwyn 1 year 2021-09-02T14:24:26+00:00 1 Answers 334 views 0

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    2021-09-02T14:25:26+00:00

    Answer:

    Q = – 4312 W = – 4.312 KW

    Explanation:

    The rate of heat of the concrete slab can be calculated through Fourier’s Law of heat conduction. The formula of the Fourier’s Law of heat conduction is as follows:

    Q = – kA dt/dx

    Integrating from one side of the slab to other along the thickness dimension, we get:

    Q = – kA(T₂ – T₁)/L

    Q = kA(T₁ – T₂)/t

    where,

    Q = Rate of Heat Loss = ?

    k = thermal conductivity = 1.4 W/m.k

    A = Surface Area = (11 m)(8 m) = 88 m²

    T₁ = Temperature of Bottom Surface = 10°C

    T₂ = Temperature of Top Surface = 17° C

    t = Thickness of Slab = 0.2 m

    Therefore,

    Q = (1.4 W/m.k)(88 m²)(10°C – 17°C)/0.2 m

    Q = – 4312 W = – 4.312 KW

    Here, negative sign shows the loss of heat.

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