## 1 Introduction  
Currently, the dynamic development of engineering systems of parametric models can be observed. The parametric models, built from variables with a known interpretation connected with the equations of the laws of physics, are able to more and more accurately reflect the studied dependencies. The development of this type of model is limited only by the scope of natural science and computing capabilities. The parallel development of the mathematical models and numerical simulation algorithms can be easily observed in many fields of engineering, in particular in chemical engineering [1] and mechanical engineering [2]. Advanced computational techniques for the process design and optimization can have a positive impact on their quality and profitability. Literature studies indicate the development of the parametric mathematical models of heat and mass transfer phenomena, which can be applied to HVAC (heat, ventilation, and air-conditioning) systems. The design research is oriented toward the systems operating under specific environmental conditions, as well as the simulation analysis of the system performance at various operating points in order to increase the efficiency of heat and mass exchange units. Therefore, the latest achievements in the use of the mass and heat transfer models are presented. In their work, [PERSON] et al. [3] numerically analyzed the M-cycle cooling tower operation. In this research, critical heat and mass transfer process conditions were considered. Moreover, some critical factors with the highest impact on the system performance were established. Finally, a higher than 100% wet-bulb effectiveness for water cooling was achieved. [PERSON] and co-workers [4] designed some theoretical models of buoyancy-driven flows by area heat sources. According to the analyzed dependencies, a new law of thermal stratified flow for the transition zone was obtained. The numerical simulation approach was used to verify the correctness of the approximate theoretical solutions. In [5], a highly specialized liquid desicant air-conditioning system for bus spray-paint booths was considered. The adoption of the liquid desiccant dehumidifier can reduce the cooling load by 62.1% and be helpful in avoiding reheating. [PERSON] and co-workers [6] presented and analyzed a feasible hybrid cooling system for application to office spaces in hot and humid climates. The designed approach combined a phase change material thermal storage layer with a melting temperature of 25 \({}^{\circ}\)C to cool the supply air, as well as a personalized evaporative cooler to provide cooling for the occupants. Then, the designed solution was sized, implemented, and tested using the numerical simulation approach. As one of the main results, the designed solution achieved 87% energy savings compared to the conventional HVAC systems. [PERSON] et al. [7] applied reinforcement learning algorithms for load shifting in a cooling supply system. The work concluded that the obtained convergence speed is not suitable for complex planning learning of thermal energy networks in real time. Nonetheless, some standardized interfaces can facilitate the systematic testing of new computational tools for real-life energy systems. In [8], a highly specialized case study was considered. A detailed computational model was used for the prediction of domestic hot water (DHW) heat. The prediction accuracy was improved by the additional artificial variables introduced. The different prediction techniques can be used to select the best DHW heat model. In the mentioned research, the obtained mathematical parametric models consisted of the nonlinear differential-algebraic relations (differential-algebraic equations (DAEs)). Some special aspects related to the highly nonlinear DAE systems, like their numerical solution and optimization, are the subject of both theoretical and simulation research. The latest scientific achievements in the numerical simulation of the DAE systems have been reported in the literature.