Suppose there is a cubic material with an internal heat source ($\Delta q / \Delta t =$ Constant), and is immersed in a sufficiently large amount of water. Now I would like to use finite difference method to simulate the steady state temperature distribution.
I think a natural convection boundary condition within the range of laminar flow can be assumed, and the maximum temperature should not exceed 100 $^\circ$C. As the surface temperature distribution is not uniform, each surface node should have its unique convective heat transfer coefficient ($h$), as this parameter depends on the temperature difference between the solid wall and the fluid.
But by looking up some heat transfer textbooks, I have never seen people address to the problem in such a way. I only found some treatments and correlation equations on the scenario of uniform temperature distribution of different geometries, while in my simulation, the temperature of different surface nodes are different. Giving it a second thought, I realized that convection heat transfer coefficient is dependent upon fluid properties, which will make it extremely complicated.
So is it possible to perform such calculations with finite difference method? Is there a method to at least estimate the convective heat transfer coefficient?