This thesis summarizes our latest findings on liquid-solid equilibria for fluids in confined spaces. In the first part of the thesis we introduce a microscopic lattice model which we have developed for the exploration of the freezing and melting phenomena in mesoporous solids with arbitrary geometries of the pore spaces. By applying this model to materials with well-ordered pore structures we (i) establish the mechanisms of the freezing and melting transitions and identify the equilibrium and metastable transition branches for different boundary conditions, (ii) illuminate the role of thermodynamic fluctuations, and (iii) find rigorous equations governing the transition temperatures for the lattice model considered. In the second part of the thesis the results obtained with the ordered pore systems are used for an in-depth analysis of the transitions occurring in geometrically disordered porous solids. First, by considering the ink-bottle pore geometry the efficacies of the different phase transition mechanisms established in the first part are elucidated. As a particularly important result, it is shown that thermodynamic fluctuations may alter the transition mechanisms. In the light of these findings the freezing and melting behaviors in statistically disordered porous materials are discussed. In the third part of the thesis several experimentally-relevant topics are considered and the potentials of the microscopic model for evaluation of the experimental data are demonstrated.

Fresh water shortage and hot weather are common challenges in many countries of the world. In the other hand, the air conditioning systems which are used for indoor cooling cause peak electricity demand during high temperatures hours. This peak hour demand is very important since it is more expensive and mainly is supplied by fossil fuel power plants with lower efficiencies compare to base load fossil fuel or renewable owe plants. Moreover, these peak electricity load fossil fuel power plants cause higher green house gas emission and other environmental effects. So, all these show that any solution for these problems could make life better in those countries and all over the world.In this thesis, a new idea for a Power storage, Cooling storage, and Water production Combined Cycle (PCWCC) is introduced and reviewed. PCWCC is combination of two thermal cycles, Ice Thermal Energy Storage (ITES) and desalination by freezing cycle, which are merged together to make a total solution for fresh water shortage, required cooling, and high peak power demand. ITES is a well known technology for shifting the electricity demand of cooling systems from peak hours to off-peak hours and desalination by freezing is a less known desalination system which is based on the fact that the ice crystals are pure and by freezing raw water and melting resulted ice crystals, pure water will be produced. These two systems have some common processes and equations and this thesis shows that by combining them the resulted PCWCC could be more efficient than each of them. In this thesis, the thermodynamic equations and efficiencies of each PCWCC sub-systems are analyzed and the resulted data are used in finding thermodynamics of PCWCC itself. Also, by using reMIND software, which uses Cplex to find the best combinations of input/output and related processes, the cost of produced fresh water and cooling from PCWCC is compared with total cost of fresh water and cooling produced by each sub-systems of PCWCC in three sample cities all over the world, Kerman, Dubai, and Texas. These cities are chosen since they have similar ambient temperature trend with different electricity and fresh water tariff's. The results show that, the PCWCC is economical where there is a significant electricity price difference between ice charging and ice melting hours, off-peak and peak hours, of the day or when the fresh water price is high compare to electricity price. The results also show that how the revenue from fresh water could cover the used electricity cost and make some income as well.