consider a static vapor bubble within a 2D domain surrounded by fluid. at the beginning, the temperature is the same in all nodes. In order to see the changes in density and temperature of the bubble, the domain (i.e. all the nodes including fluid and vapor) is heated up. How is the behavior of density and temperature along the center-line of the domain? I've simulated this problem using LBM, but the behavior of temperature is a little bit confusing (see the attached figs). i.e. the temperature increases at the beginning within the bubble and then decreases.
It seems to me this is a problem that can be solved analytically. A spherical vapor drop in a fluid taken to be infinite in dimension. Assuming it is a purely heat conduction problem ( no convection no bouyancy effects), you have 2 linear, coupled PDEs. Taking the temperature in both phases to be a function of t and r (radially ccordinate) you can find separable solutions. The key then becomes how you specify the initial conditions. For different initial conditions you can then explore how the temperature fields evolve in the drop and the fluid. You can then use the analytically results to compare with your LBM (Lattice Boltzman Method).
Thanks a lot Prof. Higgins..
I will try to solve the peoblem, analytically
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