You should specify your request because you mention air and in the same sentence fluid movement.
So air as a gas or as a fluid?
For convection, it is a transport of matter and it concerns fluids (liquid and gas) while for conduction it is a phenomenon called "from one step to the next". For example, the conduction takes place from a heating bar to a profile and then to a plate
Unless we are in the case of an ultra-thin layer of air, I don't see how we could consider conduction instead of convection for a gas. And even in the case of the thin air layer, I'm not sure that the results can actually be comparable.
Even in a confined space, most heat transfer within an air volume is done by convection, static air being rather a good thermal insulator. Replacing convection with conduction will not give a satisfactory result, neither in the time domain with regard to the evolution of physical quantities, nor at the 3D level for the temperature or velocity fields within the fluid (especially since it would be considered static...). The principle of heat exchange in the globalized form that you are considering is found in certain applications for estimating the performance of heating/insulation of buildings, and gives only a few average indications of temperature, or energy consumption. And such a "global" approach implies defining "equivalent" thermal coefficients, which can only be evaluated on the basis of an experiment or a simulation. And here we are back to square one.