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Adsorption heat transformation (AHT) systems can play a major role in protecting our environment by decreasing the usage of fossil fuels and utilizing natural and alternative working fluids. The adsorption isotherm is the most important feature in characterizing an AHT system. There are eight types of International Union of Pure and Applied Chemistry (IUPAC) classified adsorption isotherms for different “adsorbent-adsorbate” pairs with numerous empirical or semi-empirical mathematical models to fit them. Researchers face difficulties in choosing the best isotherm model to describe their experimental findings as there are several models for a single type of adsorption isotherm. This study presents the optimal models for all eight types of isotherms employing several useful statistical approaches such as average error; confidence interval (CI), information criterion (ICs), and proportion tests using bootstrap sampling. Isotherm data of 13 working pairs (which include all eight types of IUPAC isotherms) for AHT applications are extracted from literature and fitted with appropriate models using two error functions. It was found that modified Brunauer–Emmet–Teller (BET) for Type-I(a) and Type-II; Tóth for Type-I(b); GAB for Type-III; Ng et al. model for Type-IV(a) and Type-IV(b); Sun and Chakraborty model for Type-V; and Yahia et al. model for Type-VI are the most appropriate as they ensure less information loss compared to other models. Moreover; the findings are affirmed using selection probability; overall; and pairwise proportion tests. The present findings are important in the rigorous analysis of isotherm data.

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Computational fluid dynamics (CFD) is one of the promising methods that can precisely predict non-uniform air flow and contaminant distribution in indoor environments. The overarching objective of this study was to develop a mathematical model for describing the photocatalytic oxidation (PCO) reaction mechanism of gas phase toluene with titanium dioxide (TiO2)-bound indoor building materials. This mathematical model was developed based on Langmuir-Hinshelwood type kinetics and for the integration with CFD simulations as a wall surface boundary condition. The effects of gas phase toluene concentration, illuminance and humidity on the toluene oxidation reaction were considered with locally TiO2-doped building materials. Especially, humidity dependence was explicitly integrated as a competitive adsorption model between toluene and water vapour. Moreover, surface compositions of TiO2 and the substrate (ceramic tile in this study), and the physical adsorption properties of those materials, were modelled and integrated into the mathematical model. A 0.02 m3 chamber experiment and adsorption isotherm measurements were conducted to identify the model parameters. CFD analysis was carried out according to experimental scenarios, and an optimization procedure for the model parameters was proposed for their application as the boundary conditions in the CFD analysis.