Spatially heterogeneous heating and cooling is common in practical applications, such as in the ventilation and heating or cooling of buildings. However, simple models of the resulting buoyancy field typically account for either localised or distributed heat sources independently, without necessarily incorporating effects arising from their interaction.
As a canonical means of investigating the latter, this thesis studies the flow and thermal stratification of a closed domain subjected to different combinations of line and distributed surface heating and cooling in time and space. Our observations of steady and transient states are drawn from a set of direct numerical simulations in which the ratio Γ of the strength of the distributed sources to the localised sources is varied. We show that $\HfRb$ plays a decisive role in determining the system's statistically steady state, particularly in restricting the emergence of two-layer stratifications to Γ<1, and demonstrate the importance of an increasing lateral dependence of the buoyancy field with increasing distributed heating at Γ<1.
Especially the dynamic of transient states following a step change in Γ<1 is crucially determined by lateral heat transport at a finite velocity.
Building on existing approaches that typically assume uniform buoyancy within each layer, we develop a steady state model that incorporates a lateral buoyancy gradient and exhibits a better agreement with observations.

Predicting the effects of different heating distributions finds application in inverse problems of estimating boundary heat fluxes from interior temperature measurements and are of particular interest in building design and heating control. We performed a parameter estimation based on a simple two-dimensional model, however, the results show a large standard deviation from the true values. This suggests that compensating for systematic modelling errors, for example via a Bayesian approach, may be necessary to infer heterogeneous boundary conditions from simple stratification models.