I am working at present on free convection heat transfer from a heated horizontal surface through a liquid to a thin cooled fin project. The problem is that the solution is not converging.

A brief review

In immersion cooling of electronic equipment there is often a heated horizontal surface directly exposed to a liquid with a free surface. Vertical fins attached to a cooled surface then project vertically downwards into the liquid. Boiling occurs at the heated surface in many real situations but in some cases and under some operating conditions there is no boiling and the heat transfer from the heated surface to the liquid and then to the fins is by free convection.

In this analysis this particular case of free convection from the hot surface directly exposed to a liquid with a free surface to vertical fins attached to a cooled surface that project vertically downwards into the liquid is considered.

The fluid is fc72, the fin is made of Copper and the free surface is considered to be a solid of very low conductivity.

Assumptions:

The cooled surface and the fin are at same temperature.

thickness of the fin is small compared to the distance between the fins and the effect of the fin thickness on the solution is therefore negligible.

This is the description of the problem. It would be helpful if anybody can help me out. If the solution for this problem exist I would like some help regarding this problem.

Dear Kaushikg

Your problem(fluid flow over the heated horizontal surface) is hydrodynamically unstable, so that difficult convergence is originated from the its basic nature. This kind of problem is similar to the fluid flow of rotating inner cylinder, in point of hydrodynamic stability view.

Sometimes, that kind of problem does not have steady state solution. Instead, it shows periodic behavior along the time span.

How about to solve the problem by time marching method ? Then, you might see two types of phisical behavior. One is to reach steady state after some transient(oscillating with or without periodicity) behavior. And the other is to show the periodical behavior continuously. If it shows the latter behavior(continuously periodic), the real physical situation may not have steady state solution. It might have only periodical solution.

Sincerely, Jinwook.