This is a transient convection problem that utilizes dimensionless numbers for the solution.
A 10 cm thick pure gold plate is initially at 85ËšC. Both top and bottom boundary surfaces are exposed to an ambient gas at 15ËšC 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.
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A 10 cm thick pure gold plate is initially at 85ËšC. Both top and bottom boundary surfaces are exposed to an ambient gas at 15ËšC 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, Ï„:
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:
=15ËšC + (85ËšC - 15ËšC)(0.34)=38.8ËšC
© BrainMass Inc. brainmass.com December 24, 2021, 11:36 pm ad1c9bdddf>https://brainmass.com/physics/convection/transient-convection-problem-utilizes-dimensionless-numbers-584806