## 2 Materials and Methods
### Numerical Modelling  
The numerical modelling was implemented by the authors in the BASIC computational program. The decision to use such computational modelling was driven by the very essence of the BASIC programming method, i.e., a base program for the main calculus algorithm and special specific subroutines for the thermo-physical phenomena and for the physical properties of the thermal agents. Such an approach has two major advantages: first, the separate validation of the subroutines; and secondly, the validation of the main calculus algorithm once the subroutines are validated and the overall computational model is validated. The authors' vast experience of modelling the subroutines (for example, convection coefficient determination, radiation calculus, mass transfer module including dew point temperature-pressure correlation, and combustion and flue gases composition and physical properties) has been previously validated by direct comparison with the results obtained in laboratory testing. By compiling the boilers' specific geometry from the two thermal agents' flow point of view and from the thermal heat and mass transfer point of view with the validated subroutines, two modelling programs were written: one for the corrugated pipe boiler (CORCOND) and another one for the finned pipe boiler (FINCOND). The specific geometry of the corrugated pipes condensing boiler is presented in Figure 3, along with the main flow specific geometries for the flue gases (critical for determining the heat and mass transfer conditions). It is important to mention that the corrugated pipe coil solution of the condensing boiler is one of the most efficient and demonstrated over the years not only exceptional thermal performances, but also functional durability, and has, along with the other boiler components, an outstanding overall working performance. The second boiler type, with finned pipes, also has very good thermal performance. It is a broadly used solution, in various geometries, and it can be made from various materials. The constructive geometry selected for this study is presented in Figure 4, along with some important discretization details. The furnace is represented by the volume between the premix plane surface radiation burner and the main finned pipes heat exchanger body. There are also lateral cooling pipes in the furnace, as presented in Figure 4. For the first convective finned pipes row, there is considered to be only heat transfer, due to the impossibility of draining the formed condensate. Considering its important thermal load, the first row is divided in two calculus sections: the upper part, and the lower part (also due to the fin geometry that differs between the two sections). The first convective body with condensation is the second row of finned pipes, and the second condensing body is the final plane pipes fascicle. Figure 4: Heat and mass transfer zone discretization for the finned pipe boiler. (Source: Own Elaboration). Figure 3: General view of the corrugated pipe boiler body and constructive details. Geometrical characteristics: D\({}_{\text{int}}\) = 151 mm; h = 4 mm; b = 2 mm; s = 4 mm. (Source: Own Elaboration). In both cases, the modelling program considered first the convective heat transfer, and after determining a range of parameters as fuel consumption, water temperatures, and flue gases temperatures, it moves to the second step of computation, over-imposing the condensation process. The condensation process will modify the flue gases composition and, consequently, the flue gases heat transfer conditions. The modelling program considers and computes those changes and their thermal implications and reassess the heat and mass transfer conditions (i.e., by modifying the partial pressure of the water vapor in the flue gases, the dew point, the mass transfer parameters, the flow speeds, the convective coefficients, etc.). The computational program was based on the logical schematics of a verification calculus of a boiler. The main steps followed were:  
1.