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Old Apr 15th 2016, 03:44 AM   #1
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Transient Heat loss problem

I am working on a project where I have to calculate the energy/heat loss over a period of time of a box filled with warm water. Normally I would use the following formula:
T=Tamb+(Ti-Tamb)e^((alpha*As*t)/(m*c))
Where:
T = Temperature after x amount of time
Tamb = Temperature of surroundings
Ti = Temperature of contents of box
alpha = Thermal diffusivity
As = Surface area
t = time in seconds
m = mass in kg
c = specific heat

The problem I am facing is that this box is semi submerged in cold water which has a different temperature than the surrounding air. Also I know that somehow I have to take into account that the heat lost to the water will be different that to the air.

What would be the best way to go about tackling this problem?
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Old Apr 15th 2016, 04:37 AM   #2
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You need to determine whether the bath of water that the box is submerged in can be thought of as an infinite heat sink - so it maintains a constant temperature - or not. If you can assume it's infinite then you can treat it as a heat sink just like you would treat the air, so you use your formula twice - first with area of the box exposed to the air and then second adding the effects of the area of the box exposed to the water. It also appears that you are treating the box as having a uniform temperature, which makes the math relatively easy, but is that a reasonable assumption? Or - do you need to determine the gradient of temperature inside the box?
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Old Apr 15th 2016, 05:03 AM   #3
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Thanks ChipB for that reply, the surrounding water can indeed be seen as heat sink so that solves that part of the problem. The assumption has been made that the fluid inside the box is at a constant temperature when being loaded and unloaded (which I will need to take a closer look at as well) but I will need to make some form of temperature gradient inside the box.

What would be the best way to tackle that as the box is a flat rectangle with dimensions which have yet to be determined. The box will also have surge barriers inside I recon I will have to take those in to account as well for the temperature gradient as well as heat loss, right?
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