I don't think that it is possible to separate these effects. The primary reason is that the governing equations and therefore a mixed convection flow (assumed to be the result of some external free stream - forced convection - and the action of buoyancy - free convection). There are many systems that one could consider but I like that of a semi-infinite hot surface in a semi-infinite domain, that is a classical thermal boundary layer flow from a hot surface. If one assumes that there is an aiding uniform free stream which assist the buoyancy forces, then the boundary layer equations will yield a nonsimilar system which is also nonlinear.

The advantage of considering this case is that one can split the problem into two. First look at it just as a free convection problem with no external free stream, in which case boundary layer theory will give a self-similar solution where the streamfunction is psi = x^{3/4} f(eta) where the similarity variable is eta=y/x^{1/4}. If one forgets buoyancy and just has the external free stream, then psi=x^{1/2}f(eta) where eta=y/x^{1/2}. A quick sketch shows that the free convection "component" is fatter than the forced convection component near the leading edge, but it is the other way around far from the leading edge. However, if both effects (buoyancy and free stream) are included, then one has a nonsimilar boundary layer flow. Computations will show that the leading edge region is dominated by the forced convection component (and the fat free convection part disappears because the entrainment flow into the boundary layer is stronger than it was when only free convection was present). Far downstream the free convection component dominates while the fatter forced convection component has also disappears.

That is a complicated argument to follow, even if a good diagram has been drawn. But I hope that it shows that one cannot merely add together a forced convection mechanism to a free convection mechanism to get a simple arithmetical sum. Nonlinear interactions do not allow for that. And therefore I conclude that a mixed convection cannot be decomposed into its free and forced components because they interact with one another.

dear Hammed

https://www.youtube.com/watch?v=dATVUu2MLvM