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I just tried changing the heating time to a very large value 100000s and got a better temperature distribution.

To give some values. The block of water is 1 m^3 and the heat flux I applied was 5000W/m^2.

I understand water takes a lot of energy to change 1 K so I figure that the errors from before were due to the very small temperature changes. (can i get confirmation on this conclusion?)

Would refining the mesh give Comsol a better temperature resolution? For 10 second simulation, I obtain random "spots" of high temperature mixed with spots of low temperature.

Hi

I assume you can estimate this rather simply from the heat capacity of water: about 4.18 kJ/kg/K hence you need 4.18MJ per degree for your 1m^2 water block, no?

with the 6m^2 of lateral faces and your 5 kW/m^2 you are entering 30 kJ/s of power which means you need some 4180/30 seconds per deg temperature rise (assuming immediate heat conduction to homogenize your medium, what is certainly neither not the case). So indeed you need several minutes to heat significantly up your m^3 of water

Perhaps you have noticed that your electric fuses for the water boiler heats up nicely after you have taken a bath, because heating water is consuming a loooot of energy ;)

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Good luck
Ivar

There are two factors causing this temperature distribution in the water. The first is that water has high heat capacity as Ivar mentioned. The second is that water has a low thermal conductivity. What that means is that it takes a lot of energy to heat water, and due to the low conductivity it is hard to maintain the high heat flux required to cause that temperature rise. Thermal diffusivity (ratio of thermal conductivity to specific heat capacity) is the parameter that affects this problem, and gold has a value that is about 1000 times bigger than that of water.

That explains why using much larger heating times works. Also, with the short heating time, the effective heated depth of water is so small that it is probably within the mesh resolution. That gives unreliable results and explains the strange temperature distribution you are getting. What you need is a boundary layer mesh with fine elements close to the boundaries. That is not enough however. Heat transfer to water will not be only due to conduction. Natural convection will, in general, be a much more significant source of heat transfer. For that you need a coupled CFD-heat transfer analysis and either fully account for the effect of temperature on density or use the Boussinesq approximation. COMSOL has examples of both types.

Nagi Elabbasi
Veryst Engineering

Hi,

Thanks a lot for your input, they really pushed me forward in my simulation progress. Unfortunately, I think I may have hit another bump in the road. I am currently trying to model a

21-nm-diameter gold particle in water
irradiated by a 6-nsec 0.13-J/cm2 laser pulse at 532 nm.
The laser has a 4 mm radius and the pulse is Gaussian.
The Gold particle has absorbance of k=4.01

My model consists of two concentric spheres. The outer sphere is water and the inner sphere is a gold particle.

I made the gold sphere boundaries the heat source and given the information above, I calculated an average incident intensity over the 6 ns to be

24.2 TW/m^2

I calculated the average value of the gaussian pulse over two standard deviations (95%) instead of multiplying the pulse by the laser intensity because I was having issues with the units when I tried

gp1*Intensity[TW/m^2]

Initial Temperatures: 293.15[K]
Surface radiosity: 0 (not sure what value to put for this one)

These are the only boundary conditions I have.

I ran the simulation and obtained results in the 350,000 K region as you can see in the picture I provided. The values obtained experimentally were 1500 K so I am way off.

Am I still missing something in my model? I have not yet added the convection process but would this be enough to drop the temperature by 2 orders of magnitude?

Sorry for asking such a large question. Heat transfer problems are not my specialty but this is a class assignment.

Hi

the radiosity is for radiative exchange, normally at a few hundred degrees of temperature difference the radiative emission of a body is relevant, so you might need to consider it, at least as an exercise. Because I'm not sure for your small sizes the scaling law would make radiative exchange so important. To be checked. Use the blackbody Stephan Boltzman law, i.e. as described here

en.wikipedia.org/wiki/Stefan–Boltzmann_law

Do not forget that it uses the difference in temperature in Kelvin ;) and with a T^4 relation it is very non linear

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Good luck
Ivar

Once again, thanks for your input.

When I tried to add in BB Radiation, I got the following error message:

Failed to evaluate variable Jacobian.
- Variable: mat.epsilon rad
- Geometry: 1
- Boundary: 5 6 7 8 11 12 14 15

These are the boundaries of my gold sphere. From what I can interpret there's a missing material property but I filled in Surface Emissivity for gold already and added it and I still got the same error.

Hi

it could be a version issue, try it on a newer v4.1 latest patch, it should work OK

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Good luck
Ivar

Hi,

I was able to fix that issue by just changing to "user-defined" emissivity rather than changing the actual material property.

The drop in temperature was significant, it dropped by 2 fold. Now my max temperature is 1.4 x10^5. Still two orders or magnitude too high.

I will now try to add in convective cooling and see how that goes.

Thanks.

Hi

convection is normally a few W/m^2/K I'm not sure that will give you a big difference, because of your small scale, but always worth to try. Often its also useful to do some hand calculations to get the orders of magnitude

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Good luck
Ivar

Hi,

Thanks a lot for your input. I was able to get the model very close to experimental data. You are right, adding in convection barely changes the temperature distributions.

It turns out I had made an error in the units, causing my input intensity to be 7 magnitudes off.

Still, your inputs were very informative and helped me learn a lot about the heat transfer process and what conditions I should be aware of.

Thanks