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    This is a transient convection problem that utilizes dimensionless numbers for the solution.

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    A 10 cm thick pure gold plate is initially at 85˚C. Both top and bottom boundary surfaces are exposed to an ambient gas at 15˚C with a heat transfer coefficient of h=400 W/C-m^s Calculate the center temperature at t = 6 minutes after the start of cooling.

    © BrainMass Inc. brainmass.com December 24, 2021, 11:36 pm ad1c9bdddf
    https://brainmass.com/physics/convection/transient-convection-problem-utilizes-dimensionless-numbers-584806

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    SOLUTION This solution is FREE courtesy of BrainMass!

    A 10 cm thick pure gold plate is initially at 85˚C. Both top and bottom boundary surfaces are exposed to an ambient gas at 15˚C with a heat transfer coefficient of Calculate the center temperature at t = 6 minutes after the start of cooling.

    Solution:

    The physical constants for gold can be found by referring to any general text on heat transfer. These are found to be:

    and

    For a plate, the transient temperature charts can be utilized. The chart to be used is the transient temperature chart for a slab with thickness 2L subjected to convection at both boundary surfaces. To utilize this chart correctly, the thickness is set equal to 2L:

    2L = 10 cm.

    Rewriting,

    .

    Calculating the dimensionless time parameter, or Fourier number, τ:

    Calculating the reciprocal of the Biot number to determine the appropriate curve on the chart:

    Reading off the value from the chart using the calculated dimensionless parameters above yields:

    Thus the center temperature is at t = 6 minutes after the start of cooling is:

    =15˚C + (85˚C - 15˚C)(0.34)=38.8˚C

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 11:36 pm ad1c9bdddf>
    https://brainmass.com/physics/convection/transient-convection-problem-utilizes-dimensionless-numbers-584806

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