Consider two solid elements exchanging heat due to the temperature gradient between them by heat conduction. Such problems are always modelled with one mechanism only. Example: The transient behaviour of a pipe shell is to be modelled and the shell is discretised radially in n element. Element 1 is the most inner element. It "receives" heat from the flow through the pipe by convective transfer and it conducts heat towards the next-outer element. Consider element 2. Should the energy balance contain conduction with the neighbours 1 and 3 only (first row), or should the pairs 1-2 and 2-3 also be connected through thermal radiation (2nd row)?
Note: I am applying an energy balance for a closed system in the form of dU = sum(heatflows) in a transient way here. Caloric equation of state of dU.
If applying the same thought to convection I believe I understand the reason why it is not done: the convection coefficient is mostly an empiric value which probably includes all relevant means of heat exchange.