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15 July, 14:12

A block made of a certain material has a thickness of 20 cm and a thermal conductivity of 0.04 m C. At a particular instant in time the temperature distribution with x, the distance from the left surface of the block, is T = -100 x2 + 20 x, where x is in meter. Calculate the heat flux at the left (x = 0) and right face of the block.

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  1. 15 July, 14:18
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    heat flux (Q) = 8 W/m³ uniform heat flux throughout the block

    Explanation:

    flat plate ecuation with uniform source:

    d2T / dx² = - Q / k ... from general balance if x = 0 ⇒ dT / dx = 0; Q = 0 if x = L ⇒ T = T1

    ∴ k = 0.04 W/mC; L = 0.2 m

    If T = - 100x² + 20x

    ⇒ dT / dx = - 200x + 20

    ⇒ d2T / dx² = - 200 = - Q / k

    ⇒ Q / k = 200

    ⇒ Q = 200 * 0.04 W/mC

    ⇒ Q = 8 W/m³
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