**4. Conclusions**

This study explored two novel approaches to model the thermal contact between the vessel and the cooktop, and thus achieving more realistic simulations. Once the numerical model was optimised, a design of experiments was performed to analyse the influence of the main parameters of the vessel during the cooking. The main conclusions of the study are as follows:


**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/math10050802/s1, Figure S1: Profile of the steel plate modelled with the thermo-mechanical analysis. The magnitude are the displacements and it is measured in m; Figure S2: Maximum, minimum and mean temperature of a model made 100% of steel and another made 100% of aluminium along the whole cooking; Figure S3: Main effects plot of steel conductivity, steel specific heat, pan and glass convective coefficients, emissivity and concavity for the: (a) maximum sensor temperature, (b) supplied energy in a cooking time of 400 s and (c) total lost energy during the whole cooking. The units of the parameters are: conductivity (W/mK); specific heat (J/kgK); convective coefficients (W/m2K); emissivity (-); Figure S4: Pareto analysis of the importance of the ouputs studied in DoE: time to reach to stationary state (a), supplied energy (b), homogenisation along the radius in the second 60 of the cooking (c) and maximum sensor temperature (d); Figure S5: Representation of the losses of a computational simplify model of: (a) Schulte and (b) steel plate (coloured areas) and the amplitude of the power density introduced (red dotted line). Blue area corresponds to conduction losses between the base of the pan and the glass. Orange and yellow area indicate the convection and radiation losses in the base and in the walls of the pan respectively.

**Author Contributions:** Conceptualization, S.L. and M.A.M.; methodology, M.A.M. and I.C.-G.; software, B.B.-S., I.C.-G. and J.G.; formal analysis, I.C.-G.; investigation, B.B.-S.; writing—original draft preparation, B.B.-S.; writing—review and editing, I.C.-G., B.C., J.G., C.F. and M.A.M.; supervision, B.C., J.G., C.F., S.L. and M.A.M.; project administration, B.C.; funding, B.C. and S.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the Spanish Ministry of Science, Innovation and Universities RETOS-COLABORATION 2017 programme (project RTC-2017-5965-6, ARQUE) and co-financed by ERDF and BSH Home Appliances Group. The Department of Industry and Innovation (Government of Aragon) provided funding through research group grant no. T24-20R (co-financed by ERDF).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
