Psychrometric chart is a basic tool for analysis of processes in airconditioning systems. While psychrometric calculators and numerical psychrometric charts are widely available, there is a lack of numerical algorithms for solving the sizing problem by using psychrometric analysis. After introducing a classification of modelling problems in direct and inverse (based on the relation between physical and computational causality), this paper defines the design problem as a set of inverse problems of control and parameter optimization. A non-linear model is obtained by assembling the models of the elementary processes. The paper proposes to solve the direct and control problems by using a method similar to Newton-Raphson's, and the parameter optimization problem by using least-squares. Open-source implementation, published on Zenodo repository, and interactive, reproducible environment, available on Binder web service, accompany this paper (