I solved a 2-d flow problem for the flow field first and then used the veloocties in the heat transfer equations. My tmeperature rise was only a few degrees, therefore, I did not re-solve the flow field equations due to the very small changes in the thermal properties of the fluid. My question is; Is this correct or is it necessary for me to couple the equations?

thanks

Is a few degrees important to your process or product? Will it give an inferior heat treat to a metal?

As to the coupling, why not just try it? If the flow patterns don't change (you define how small the change must be before it can be ignored), the temperatures after the second pass will change by an ignorable amount.

You'll learn a lot more by trying it than asking for a rule to follow.

My reply above was sort of sharp - sorry about that.

But, if you can spend the time, you'll learn a good bit by correcting the properties for the temperature change and re-running the problem. Or, if your fluid is a gas, try the problem using a compressible algorithm.

Good luck.

Based on what I remember from coursework: for low Mach numbers, the energy equation is decoupled from the continuity and momentum equations so that you can first solve the continuity and momentum equations and use this solution to solve for the temperature distribution via the energy equation. I.e., for low Mach, there is no exchange between kinetic and internal energy. However, I don't think this holds if bouyancy is included. For instance, if you have a high temperature boundary surrounded by low temperature ones, free convection is going to occur and can significantly affect the temperature distribution. In this case I believe the equations are coupled. Hope this helps.