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12 November, 00:56

A one-dimensional plane wall of thickness 2l = 100 mm experiences uniform thermal energy generation of q˙ = 800 w/m3 and is convectively cooled at x = ±50 mm by an ambient fluid characterized by [infinity] t[infinity] = 26.0°c. if the steady-state temperature distribution within the wall is t (x) = a (l2-x2) + b where a = 10°c/m2 and b = 30°c, what is the thermal conductivity of the wall? what is the value of the convection heat transfer coefficient, h?

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  1. 12 November, 01:17
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    The thermal conductivity of the wall = 40W/m. C

    h = 10 W/m^2. C

    Explanation:

    The heat conduction equation is given by:

    d^2T / dx^2 + egen / K = 0

    The thermal conductivity of the wall can be calculated using:

    K = egen / 2a = 800/2*10

    K = 800/20 = 40W/m. C

    Applying energy balance at the wall surface

    "qL = "qconv

    -K = (dT/dx) L = h (TL - Tinfinity)

    The convention heat transfer coefficient will be:

    h = - k * (-2aL) / (TL - Tinfinty)

    h = (2 * 40 * 10 * 0.05) / (30-26)

    h = 40/4 = 10W/m^2. C

    From the given temperature distribution

    t (x) = 10 (L^2-X^2) + 30 = 30°

    T (L) = (L^2 - L^2) + 30 = 30°

    dT / dx = - 2aL

    d^2T / dx^2 = - 2a
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