Mathematical Understanding of How a Car Engine Cooling System Works

Rafael Pantoja Rangel; Manuel Arciga Vargas; Alexander Yakhno; Karla Liliana Puga Nathal

doi:doi:10.11648/j.pamj.20221105.11

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Mathematical Understanding of How a Car Engine Cooling System Works

Rafael Pantoja Rangel, Manuel Arciga Vargas, Alexander Yakhno, Karla Liliana Puga Nathal

Published in Pure and Applied Mathematics Journal (Volume 11, Issue 5)

Received: 7 September 2022 Accepted: 28 September 2022 Published: 17 October 2022

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Abstract

The research is related to the modeling of Newton's cooling law (in its ideal form) through the numerical, graphical and analytical approaches to the automobile heating and cooling system (CHSV) and comparing it with the model of the exponential solution of the ordinary differential equation, from starting the car engine until the fan is activated several times and then turned off, with the aim that students relate school mathematics with problem situations in their context, an environment that is not common to deal with in the subject of Mathematics for Engineering II in the Mechanical Metal Engineering career at the Technological University of the Costa Grande de Guerrero, Mexico. In this sense, the use of technology is proposed to present the student with a strengthened scenario with the MaxiDAS DS808 Scanner and Oscilloscope automotive tool, with which the data of the time and temperature variables are obtained, exported and processed with the GeoGebra software, to obtain the plot and the functions that model the CHSV. The theory that supported the study was the Ontosemiotic approach to Mathematical Cognition and Instruction (EOS). The students worked with a didactic sequence, into which the activities to be developed during the experimental phase were integrated. Due to the COVID-19 pandemic, the sequence was placed on the LMS INSTRUCTURE CANVAS platform, where the developed products, explanatory videos and the comics "In search of a mathematical model" were recorded. Videoconferences were generated in Google Meet as an interactive student-teacher and student-student medium, to provide explanations of the subject and doubts. The research was of the qualitative type and the learning processes of 21 students were studied, the evidence was reviewed and as a result it is stated that it was possible to model the heating and cooling system of the engine, as well as understand the numerical, graphical and analytical approaches, as an alternative solution to the exponential solution of Newton's law of cooling, in its ideal form.

Published in	Pure and Applied Mathematics Journal (Volume 11, Issue 5)
DOI	10.11648/j.pamj.20221105.11
Page(s)	78-83
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Newton's Law of Cooling, Modeling, EOS Theory, Problem Situation, Function Adjustment

References

[1]	Arciga, M. (2022). Numerical, graphical and analytical approach to the heating and cooling system of an automobile to propitiate its learning (Master's thesis in mathematics education). University Center for Basic Sciences and Engineering, University of Guadalajara.
[2]	Artigue, M. (1989). Ingénierie didactique. Publications mathématiques et informatique de Rennes, 1989 (Rennes Mathematics and Informatics Publications, 1989) (S6), 124-128.
[3]	Blanchard, P. (1994). Teaching differential equations with a dynamical systems viewpoint. College Mathematics Journal, 25 (5), 385-393. doi: 10.2307/2687503.
[4]	Arslan, S., Chaachoua, H., and Laborde, C. (2004). Reflections on the teaching of differential equations. What effects of the teaching of algebraic dominance? In Niss, M. A. (Ed.), Proceedings of the 10th International Conference in Mathematics Education 10, 54-69.
[5]	Olivieri, N., Núñez, P., Rodríguez, E. (2010). Rolling of a sphere on an inclined plane. Improvements to the experiment developed in the "Packard plane". Lat. Am. J. Phys. Educ., 4 (2), 383-387. http://www.lajpe.org/may10/21_Nestor_Olivieri.pdf. ISSN 1870-9095.
[6]	Pantoja, R. (2020). The photograph of hours of arbol applied as a mediator to propicate learning of the calculation of areas. Brazilian Journal of Development. 6 (3), 9923-9940. ISSN 2525-8761. DOI: 10.34117/bjdv6n3-028.
[7]	Pantoja, R. Guerrero, L., Ulloa, R. Nesterova, E. (2016). Modeling in problem situations of daily life. Journal of Education and Human Development, 5 (1), 62-76. Retrieved: http://jehdnet.com/.
[8]	Pantoja, R., López, M. E. (2021). Analysis of everyday life objects in motion using video, Tracker and GeoGebra to understand parametric equations. Education Research Journal, 11 (5), 83 –96. ISSN: 2026-6332.
[9]	Pantoja, R., Sánchez, M. T., López, M. E., Pantoja-González, R. (2021). Examples to relate school mathematics to everyday life mediated by video, Tracker and GeoGebra. South Florida Journal of Development, Miami, 2 (3), 4417-4434. ISSN 2675-5459, DOI: 10.46932/sfjdv2n3-046.
[10]	Buchanan, J. L., Manar, T. J and Lewis, H. (1991). Visualization in differential equations, Visualization in Teaching and Learning Mathematics, USA, 139-146.
[11]	Moreno, J. and Laborde, C. (2003). Linkage between Systems and Records of Representation of Differential Equations within an Environment of Dynamic Geometry. Minutes of the Colloquium on Integration of Technologies in the Teaching of Mathematics. (1), 1-11.
[12]	Oliver, E., Aguilar, M., Pizano, I., Carapia, L., & Jiménez, M. (2018). The use of GeoGebra for numerical solution of integrals as an application for arc length calculation. Pistas Educativas, 33 (104), 125-140.
[13]	Godino, J. (2002). An Ontological and Semiotic Approach to Cognition in Mathematics. Research on Didactics of Mathematics, 22. Recovered from: http://www.ugr.es/~jgodino/funciones-semioticas/04_enfoque_ontosemiotico.pdf
[14]	Hitt, F. (2013). Learning Mathematics in Collaborative Problem and Problem Situation Settings, and their Resolution. Quebec, Canada: UQAM, Mathematics Department.
[15]	Hitt, F. and Quiroz, S. (2017). Learning Mathematics through Mathematical Modeling in a Socio-cultural Environment tied to the Theory of the Activity. Journal of Comombian Education, (73), 151-175. Recovered in: https//www.redalyc.org/articulo.oa?id=413651843-0008.
[16]	Godino, J., Batanero, C. (1994). Institutional and Personal Meaning of Mathematics Objects. Research in Didactics of Mathematics. Recovered from: http://www.ugr.es/~jgodino/funciones-semioticas/03_SignificadosIP_RDM94.pdf.

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APA Style

Rafael Pantoja Rangel, Manuel Arciga Vargas, Alexander Yakhno, Karla Liliana Puga Nathal. (2022). Mathematical Understanding of How a Car Engine Cooling System Works. Pure and Applied Mathematics Journal, 11(5), 78-83. https://doi.org/10.11648/j.pamj.20221105.11

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ACS Style

Rafael Pantoja Rangel; Manuel Arciga Vargas; Alexander Yakhno; Karla Liliana Puga Nathal. Mathematical Understanding of How a Car Engine Cooling System Works. Pure Appl. Math. J. 2022, 11(5), 78-83. doi: 10.11648/j.pamj.20221105.11

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AMA Style

Rafael Pantoja Rangel, Manuel Arciga Vargas, Alexander Yakhno, Karla Liliana Puga Nathal. Mathematical Understanding of How a Car Engine Cooling System Works. Pure Appl Math J. 2022;11(5):78-83. doi: 10.11648/j.pamj.20221105.11

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@article{10.11648/j.pamj.20221105.11,
  author = {Rafael Pantoja Rangel and Manuel Arciga Vargas and Alexander Yakhno and Karla Liliana Puga Nathal},
  title = {Mathematical Understanding of How a Car Engine Cooling System Works},
  journal = {Pure and Applied Mathematics Journal},
  volume = {11},
  number = {5},
  pages = {78-83},
  doi = {10.11648/j.pamj.20221105.11},
  url = {https://doi.org/10.11648/j.pamj.20221105.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20221105.11},
  abstract = {The research is related to the modeling of Newton's cooling law (in its ideal form) through the numerical, graphical and analytical approaches to the automobile heating and cooling system (CHSV) and comparing it with the model of the exponential solution of the ordinary differential equation, from starting the car engine until the fan is activated several times and then turned off, with the aim that students relate school mathematics with problem situations in their context, an environment that is not common to deal with in the subject of Mathematics for Engineering II in the Mechanical Metal Engineering career at the Technological University of the Costa Grande de Guerrero, Mexico. In this sense, the use of technology is proposed to present the student with a strengthened scenario with the MaxiDAS DS808 Scanner and Oscilloscope automotive tool, with which the data of the time and temperature variables are obtained, exported and processed with the GeoGebra software, to obtain the plot and the functions that model the CHSV. The theory that supported the study was the Ontosemiotic approach to Mathematical Cognition and Instruction (EOS). The students worked with a didactic sequence, into which the activities to be developed during the experimental phase were integrated. Due to the COVID-19 pandemic, the sequence was placed on the LMS INSTRUCTURE CANVAS platform, where the developed products, explanatory videos and the comics "In search of a mathematical model" were recorded. Videoconferences were generated in Google Meet as an interactive student-teacher and student-student medium, to provide explanations of the subject and doubts. The research was of the qualitative type and the learning processes of 21 students were studied, the evidence was reviewed and as a result it is stated that it was possible to model the heating and cooling system of the engine, as well as understand the numerical, graphical and analytical approaches, as an alternative solution to the exponential solution of Newton's law of cooling, in its ideal form.},
 year = {2022}
}

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TY  - JOUR
T1  - Mathematical Understanding of How a Car Engine Cooling System Works
AU  - Rafael Pantoja Rangel
AU  - Manuel Arciga Vargas
AU  - Alexander Yakhno
AU  - Karla Liliana Puga Nathal
Y1  - 2022/10/17
PY  - 2022
N1  - https://doi.org/10.11648/j.pamj.20221105.11
DO  - 10.11648/j.pamj.20221105.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 78
EP  - 83
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20221105.11
AB  - The research is related to the modeling of Newton's cooling law (in its ideal form) through the numerical, graphical and analytical approaches to the automobile heating and cooling system (CHSV) and comparing it with the model of the exponential solution of the ordinary differential equation, from starting the car engine until the fan is activated several times and then turned off, with the aim that students relate school mathematics with problem situations in their context, an environment that is not common to deal with in the subject of Mathematics for Engineering II in the Mechanical Metal Engineering career at the Technological University of the Costa Grande de Guerrero, Mexico. In this sense, the use of technology is proposed to present the student with a strengthened scenario with the MaxiDAS DS808 Scanner and Oscilloscope automotive tool, with which the data of the time and temperature variables are obtained, exported and processed with the GeoGebra software, to obtain the plot and the functions that model the CHSV. The theory that supported the study was the Ontosemiotic approach to Mathematical Cognition and Instruction (EOS). The students worked with a didactic sequence, into which the activities to be developed during the experimental phase were integrated. Due to the COVID-19 pandemic, the sequence was placed on the LMS INSTRUCTURE CANVAS platform, where the developed products, explanatory videos and the comics "In search of a mathematical model" were recorded. Videoconferences were generated in Google Meet as an interactive student-teacher and student-student medium, to provide explanations of the subject and doubts. The research was of the qualitative type and the learning processes of 21 students were studied, the evidence was reviewed and as a result it is stated that it was possible to model the heating and cooling system of the engine, as well as understand the numerical, graphical and analytical approaches, as an alternative solution to the exponential solution of Newton's law of cooling, in its ideal form.
VL  - 11
IS  - 5
ER  -

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Author Information

Rafael Pantoja Rangel

University Center for Exact and Engineering Sciences, University of Guadalajara, Jalisco, Mexico
Manuel Arciga Vargas

Basic Science Department, Technological University of the Guerrero Costa Grande, Guerrero, Mexico
Alexander Yakhno

University Center for Exact and Engineering Sciences, University of Guadalajara, Jalisco, Mexico
Karla Liliana Puga Nathal

Basic Science Department, Technological Institute of Guzmán City, Jalisco, Mexico

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Plain Text BibTeX RIS

APA Style

Rafael Pantoja Rangel, Manuel Arciga Vargas, Alexander Yakhno, Karla Liliana Puga Nathal. (2022). Mathematical Understanding of How a Car Engine Cooling System Works. Pure and Applied Mathematics Journal, 11(5), 78-83. https://doi.org/10.11648/j.pamj.20221105.11

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ACS Style

Rafael Pantoja Rangel; Manuel Arciga Vargas; Alexander Yakhno; Karla Liliana Puga Nathal. Mathematical Understanding of How a Car Engine Cooling System Works. Pure Appl. Math. J. 2022, 11(5), 78-83. doi: 10.11648/j.pamj.20221105.11

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AMA Style

Rafael Pantoja Rangel, Manuel Arciga Vargas, Alexander Yakhno, Karla Liliana Puga Nathal. Mathematical Understanding of How a Car Engine Cooling System Works. Pure Appl Math J. 2022;11(5):78-83. doi: 10.11648/j.pamj.20221105.11

Copy | Download

@article{10.11648/j.pamj.20221105.11,
  author = {Rafael Pantoja Rangel and Manuel Arciga Vargas and Alexander Yakhno and Karla Liliana Puga Nathal},
  title = {Mathematical Understanding of How a Car Engine Cooling System Works},
  journal = {Pure and Applied Mathematics Journal},
  volume = {11},
  number = {5},
  pages = {78-83},
  doi = {10.11648/j.pamj.20221105.11},
  url = {https://doi.org/10.11648/j.pamj.20221105.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20221105.11},
  abstract = {The research is related to the modeling of Newton's cooling law (in its ideal form) through the numerical, graphical and analytical approaches to the automobile heating and cooling system (CHSV) and comparing it with the model of the exponential solution of the ordinary differential equation, from starting the car engine until the fan is activated several times and then turned off, with the aim that students relate school mathematics with problem situations in their context, an environment that is not common to deal with in the subject of Mathematics for Engineering II in the Mechanical Metal Engineering career at the Technological University of the Costa Grande de Guerrero, Mexico. In this sense, the use of technology is proposed to present the student with a strengthened scenario with the MaxiDAS DS808 Scanner and Oscilloscope automotive tool, with which the data of the time and temperature variables are obtained, exported and processed with the GeoGebra software, to obtain the plot and the functions that model the CHSV. The theory that supported the study was the Ontosemiotic approach to Mathematical Cognition and Instruction (EOS). The students worked with a didactic sequence, into which the activities to be developed during the experimental phase were integrated. Due to the COVID-19 pandemic, the sequence was placed on the LMS INSTRUCTURE CANVAS platform, where the developed products, explanatory videos and the comics "In search of a mathematical model" were recorded. Videoconferences were generated in Google Meet as an interactive student-teacher and student-student medium, to provide explanations of the subject and doubts. The research was of the qualitative type and the learning processes of 21 students were studied, the evidence was reviewed and as a result it is stated that it was possible to model the heating and cooling system of the engine, as well as understand the numerical, graphical and analytical approaches, as an alternative solution to the exponential solution of Newton's law of cooling, in its ideal form.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Understanding of How a Car Engine Cooling System Works
AU  - Rafael Pantoja Rangel
AU  - Manuel Arciga Vargas
AU  - Alexander Yakhno
AU  - Karla Liliana Puga Nathal
Y1  - 2022/10/17
PY  - 2022
N1  - https://doi.org/10.11648/j.pamj.20221105.11
DO  - 10.11648/j.pamj.20221105.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 78
EP  - 83
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20221105.11
AB  - The research is related to the modeling of Newton's cooling law (in its ideal form) through the numerical, graphical and analytical approaches to the automobile heating and cooling system (CHSV) and comparing it with the model of the exponential solution of the ordinary differential equation, from starting the car engine until the fan is activated several times and then turned off, with the aim that students relate school mathematics with problem situations in their context, an environment that is not common to deal with in the subject of Mathematics for Engineering II in the Mechanical Metal Engineering career at the Technological University of the Costa Grande de Guerrero, Mexico. In this sense, the use of technology is proposed to present the student with a strengthened scenario with the MaxiDAS DS808 Scanner and Oscilloscope automotive tool, with which the data of the time and temperature variables are obtained, exported and processed with the GeoGebra software, to obtain the plot and the functions that model the CHSV. The theory that supported the study was the Ontosemiotic approach to Mathematical Cognition and Instruction (EOS). The students worked with a didactic sequence, into which the activities to be developed during the experimental phase were integrated. Due to the COVID-19 pandemic, the sequence was placed on the LMS INSTRUCTURE CANVAS platform, where the developed products, explanatory videos and the comics "In search of a mathematical model" were recorded. Videoconferences were generated in Google Meet as an interactive student-teacher and student-student medium, to provide explanations of the subject and doubts. The research was of the qualitative type and the learning processes of 21 students were studied, the evidence was reviewed and as a result it is stated that it was possible to model the heating and cooling system of the engine, as well as understand the numerical, graphical and analytical approaches, as an alternative solution to the exponential solution of Newton's law of cooling, in its ideal form.
VL  - 11
IS  - 5
ER  -

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