PDE-Based Mathematical Models to Diagnose the Temperature Changes Phenomena on the Single Rectangular Plate-Fin

Abstract

The ideas of the studies in this article are back-grounded by the work diligently and carefully to relate the influence of two independent variables, e.g., distance and time on one dependent variable, i.e., temperature changes which are solved by a partial differential equation. In this article, we explain the particular features of a naturally physical system that it seeks to understand. The diagnosis of the temperature changes in a metal rod to consider a conduction phenomenon can be covered by all-natural physical phenomena through conduction. By making the mathematical equations based on partial differential equations (PDEs), it is shown that the temperature change is influenced by distance and time. The objectives of this study are (i) to make a prototype of the problem based on the one-dimensional heat conduction equation, (ii) to process the solution of the mathematical equation based on the parabolic partial differential equation (PDE) using the separation of variables, and (iii) to display the phenomena of the temperature changes as a function of the length in the copper bar and the time. Achieving the research objectives takes several stages in the research methods which include (a) making the prototype of the problem, (b) processing the solution of a mathematical equation, and (c) displaying the temperature changes phenomenon in the form of a curve. The results are (i) a mass balance is developed for a finite segment ∆𝑧 along the tank's longitudinal axis in order to derive a differential equation, (ii) the final complete solution in the form of a Fourier sine series, and (iii) a three-dimensional curve as an indication of the existence of the phenomenon of temperature changes. In general, it can be concluded that the making of a mathematical model based on partial differential equations with the method of separating variables as an analytical solution can be used to diagnose the phenomenon of temperature changes as a function of distance and time.

Prototyping an IoT-Platform Embedded Device to Prevent the Failure of the Battery System at the Kedungbadak-Bogor Substation

“…Secondly, when the second research objective has been obtained, it can be expected to exist the performance of the embedded device prototype through the procedures, namely measuring the voltage rating of each battery cell and response to the setting for alarm conditions when there is a decrease in the value of the battery cell voltage. The rest of this article is organized like the pattern in the previous article [44] with sorting as follows, namely, chapter 2 presents literature review, chapter 3 presents our proposed methods of the research, chapter 4 presents the results and discussion based on the two research objectives, and chapter 5 presents the determination of conclusions.…”