I am modelling heat transfer across a wall that separates a compartment from environment. What is the right choice for boundary conditions ?

If Biot number (Bi) << 1, heat flux needs to be prescribed; if Bi >> 1, temperature needs to be set. Anywhere in between, heat transfer coefficient needs to be determined or the wall needs to be modelled as well.

If the case is transient (as in experiments), the wall between the compartment and environment gets hot. This changes wall's material properties (usually therm. conductivity) and, therefore, the Biot and the Nusselt number. As a consequence, it can happen that heat transfer coefficient needs to be defined as time dependent function of temperature.

Regarding modelling the external environment, one needs to assess the impact of the compartment onto surrounding fluid. This can be done by simple energy balance assessment. In most case, the external side can be treated as constant when the energy density on the external walls is small and time duration of the experiment is short.

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