pennym72 said:
I am trying to calculate the rate of thaw for a 55 gallon drum of frozen juice. I know the surface area of the drum is 20,772 sq cm. I know the starting temperature of the frozen juice (-10C) and I know the ambient temperature the drum is currently in (10C). What is the equation that will allow me to calculate the time required for the entire contents of the drum to rise to 1C. Thank you!
Starting with the assumptions that you want to:
1) Get an estimate of the time, and
2) Not mess with differential equations,
then
Here is how an engineer tackles this problem. Sorry about the English units, but that's what I'm familiar with. Start with some assumptions:
1) Assuming that the heat transfer coefficient is roughly equal to that of a single pane glass window, the R-value equals ##1.0 {hr-ft^2-deg F}/BTU##.
2) The total heat required to melt the juice is equal to the heat required to melt an equal volume of water.
3) Ice has a specific heat of 0.5.
4) The drum contains 55 gallons of juice after melting.
Then the total heat required to raise 55 gallons of water from 14 deg F to 32 deg F, and melt it at 32 deg F is ##55 gallons * 8.34 lbs/{gallon} * ((18 deg F * 0.5) + 144) = 70,200 BTU##
Since the heat to raise the temperature of the ice to 32 deg F from 14 deg F is small compared to the heat to melt the ice, simplify by assuming the average temperature of the drum is 32 deg F. Then the average temperature difference between the room and the drum is 18 deg F (10 deg C).
Then the rate of heat flow into the juice is ##22 ft^2 * 18 deg F / 1.0 {hr-ft^2-deg F}/BTU = 400 BTU/hr##.
And the time = ##70,200 BTU / 400 BTU/hr = 180 hours.##
If you could let us know how long it did take when it finally melts, we would appreciate the feedback.