Hallo CFD users,

I want to calculate the water temperature in a container which is supported on a plate with a small round heater located in its center. The container takes shape of cylinder. The heater is constantly kept at 50 degree. Since the heater area is much smaller than the bottom area of the container, and the heating temperature is not that high, the radial temperature gradients in water and supporting plate have to be taken account. However, my experience is that after a long while the temperature in water should be uniform. In case the thermal resistance between the water and plate is regarded constant, the temperature of the plate should be also uniform, which is contradictionary to another fact that the temperature gradient in heating plate should permanently exist. On that note, my experience should be wrong, i.e. the temperature difference should always exist in the water even in steady state.

I'm a little confused with this simple problem, and ask for any advice and tips. Is there any theorem or formula regarding this issue?

Thanks a lot in advance,

Ali

is it too simple to give an answer?

If you are losing heat along the surface of the cylinder then the water temperature will not be uniform. Not only that, but the temperature gradient in the water can and probably will set up convective currents that will redistribute the energy of the water from bottom to top in a way to enhance energy transfer over simple conduction. The only simplifying assumption that I can see making is that the temperature distribution is axisymmetric. But I would expect to see variations in both the radial and longitudinal directions.

Thanks for your tips. Actually I'm calculating the temperature distribution with assumption that the variations take spherical shape due to the round center heating. Finally I come to two coupled two order ordinary differential equations. I failed finding any analytical solution, so I have to resort to Matlab for numerical solution. Perhaps I shall go to FEM/FVM for the better visualization.

Anyways it seems that my experience is not reliable, but I still imagine it could be simply treated in case the container is at micrometer scale.