
What is the effect of having the little cardboard thing around a coffee cup? Do they serve as an applicable amount of insulation, or just keep your hand from being too hot? What about the effects of a cap?
First Model
- Heat Transfer in Solid's physics - the water (coffee) was assumed to be a solid; it couldn't move due to density differences. I assumed the cup was antisymmetric, so you only get a slice.
- Natural Convection from air on the boundaries. The top boundary was from modeled as a plate above, the bottom of the cup was modeled as a horizontal plate below (these are actually quite different - when the heat comes from the top it can raise away, but on the bottom it cannot), and from a vertical plate on the side.
- The fluid was assumed to be water with an initial temperature of 212 F, and the cup was assumed to be paper with an initial temperature of 50F. The ambient temperature was also assumed to be 50 F.
- Density, heat capacity, and thermal conductivity values from library materials or the internet.
- (Pro tip - creating both sides of the geometry with antisymmetric settings causes terrible convergence to non-physical values.)
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| Initial Temperature Profile |
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| Temperature Profile of a point Halfway up the r=0 axis of the cup. x-axis is time in seconds, y-axis is temperature in F. |
What we observe is that the temperature at the center of the coffee changes 14 F in 30 min, while huge temperature gradients appear in the fluid. Temperature gradients would then effect the density, so some sort of circulation would result.
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| What's the effect of a 3% change in density? Source Data |
Anywhos, using coupled fluid dynamics with heat transfer has already taken 2 hours to simulate 28.9s; so I think I just should have borrowed a thermal camera from Dr. Hiato and done the experiment. To do the effects of the cardboard holder (which this entire shinding is about) I will need to find a better method.
The solver crashed sometime during the night; something about an illegal mathematical expression, so I don't have the correct physics / model because it I get an illegal mathematical expression that probably means I am not converging (I could simply be taking too large of a step size initially). I did get the velocity profile of the first two time steps, 0 and 10s. Initially it looks like that I am getting small currents (10 microns/s) near the top of the cup (these have to circulate, I think that is why the velocity is highest in the middle), and at 10s they are much larger.
The interesting thing from these results is why the velocity current of the top extend all the way to the symmetry axis?