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Dynamic simulations have been successfully applied to the modelling of building heating, ventilating and air-conditioning (HVAC) plant operation. These simulations are generally driven using time-series data as input. Whilst time-series simulations are effective, they tend to be expensive in terms of computer execution time. A possible method for reducing simulation time is to develop a probabilistic picture of the model, by characterising the model as being in one of several states. By determining the probability for being in each model state, predictions of long-term values of quantities of interest can then be obtained using ensemble averages. This study aims to investigate the applicability of the Markov modelling method for the above stated purpose in the simulation of HVAC systems. In addition, the questions of the degree of accuracy which can be expected, and the amount of time-savings which are possible are investigated. The investigation has found that the Markov modelling technique can be successfully applied to simulations of HVAC systems, but that assumptions commonly made concerning the independence of driving variables may often not be appropriate. An alternative approach to implementing the Markov method, taking into Z): account dependencies between driving variables is suggested, but requires further development to be fully effective. The accuracy of results has been found to be related to the sizes of the partial derivatives of the calculated quantity with respect to each of the variables on which it depends, the sizes of the variables' ranges, and the number of states assigned to each variable in developing the probabilistic picture of the model's state. A deterministic error bound for results from Markov simulations is also developed, based on these findings.

The finite element method is used to predict numerically steady state, two-dimensional laminar and turbulent thermal buoyant and convective recirculating flows. The governing equations are solved by the finite element method using Galerkin Weighting functions, with velocity, pressure, and temperature as dependent variables. Turbulent separating, recirculating flow in the complex geometry of a room with variable inlets, outlets and convective chimney ducts is investigated. The room is ventilated/air-conditioned utilising the solar energy via a flat plate collector and solar absorption airconditioning system. For this purpose the Navier-Stokes, continuity and general energy equations are solved in a coupled form and in an uncoupled form and solutions are compared amongst themselves and with the experimental results of hot wire anemometers and thermocouples. The parts where turbulent flows occurred especially in the convective duct and the room, the flows are analysed using the Prandtl- Kolmöjorov model to depict the effective viscosity. The analogy between thermal and momentum diffusivity via Prandtl number is used to depict the turbulent conductivity from the turbulent viscosity. The length scale of turbulence is specified as an algebraic function of position from empirical data and experience of other researchers . The kinetic energy is expressed as a function of velocity at the nodes together with the turbulence intensity which varies from ~5% - ~20%. This turbulence model is used to predict the flow including its recirculations in the solar ventilated/air-conditioned room, and the fully turbulent convective channel. The analysis includes temperature and heat transfer predictions in this complex geometry of combined free and forced convection, together with buoyancy effects and turbulent transport and recirculations. Results obtained are compared with the experimental data which showed very good agreement.