Linear algebra solution to psychometric analysis of air-conditioning systems

The typical air conditioning steady-state processes are graphically represented by straight or curve lines on the psychrometric chart. Neglecting the sensible heat of the moisture results in decoupling the sensible and the latent heat, that results in linear variation of the enthalpy on the psychrometric chart. The vapor saturation curve may also be linearized by using Newton's method. If the mass flow rates of the dry air are known and if the computational causality is assigned to correspond to the physical causality (i.e. if a direct modeling problem is treated), then the steady-state models of the psychrometric processes become linear algebraic equations in the vector space defined by the dry bulb temperature and the humidity ratio. Coupling these models to describe a complex HVAC (heating ventilation air-conditioning) system results in a system of linear equations that solves a direct (or psychometric analysis) problem in which the inputs of the model are a subset of the set of independent variables of the psychical process, the outputs of the model are a subset of the set of the dependent variables of the physical process, and the unknowns are the psychometric states of the moist air. The algorithm that implements this method represents a computational alternative to graphical representations and manual solutions to psychometric analysis of air-conditioning systems.