Mathematical Understanding of How a Car Engine Cooling System Works
Rafael Pantoja Rangel,
Manuel Arciga Vargas,
Alexander Yakhno,
Karla Liliana Puga Nathal
Issue:
Volume 11, Issue 5, October 2022
Pages:
78-83
Received:
7 September 2022
Accepted:
28 September 2022
Published:
17 October 2022
DOI:
10.11648/j.pamj.20221105.11
Downloads:
Views:
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.
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 ...
Show More
Fixed Point Results in Fuzzy Metric Spaces, Fuzzy 2 & 3 Metric Spaces
Ankita Pagnis,
Zaheer Kareem Ansari,
Arun Garg
Issue:
Volume 11, Issue 5, October 2022
Pages:
84-95
Received:
28 September 2022
Accepted:
21 October 2022
Published:
11 November 2022
DOI:
10.11648/j.pamj.20221105.12
Downloads:
Views:
Abstract: Fixed point theory is one of the most dynamic areas of research for the last hundred years with many applications in various fields of pure and applied mathematics as well as in physical, economics and life sciences. Fixed point theory plays very important role dynamic and linear programming. Fixed point results are proved by many mathematicians in last four to five decades and further scopes are there to enhance these results. In recent years, we observed the fuzzification in almost every direction of mathematics such as arithmetic, topology, graph theory, probability theory, Image processing, stochastic processes and logic theory etc. It may not be wonder that fuzzy fixed point theory has become an area of interest for mathematicians. There are many view points of the notion of metric space in fuzzy topology. Many mathematicians used different conditions on self-mappings and proved several fixed point theorems for contractions in fuzzy metric spaces. We are interested in the results in which the distance between the objects is fuzzy, the objects themselves may be fuzzy or not. In this research article we prove some fixed point theorems for fuzzy 2-metric and fuzzy 3-metric spaces.
Abstract: Fixed point theory is one of the most dynamic areas of research for the last hundred years with many applications in various fields of pure and applied mathematics as well as in physical, economics and life sciences. Fixed point theory plays very important role dynamic and linear programming. Fixed point results are proved by many mathematicians in...
Show More
