Experimental Study of Mass Conservation Processes: a Look at the Teaching of Differential Equations from Modeling and Numerical Analysis

Abstract

Physical phenomena are typically described in different areas of knowledge using mathematical models. These models permit the assessment of variables associated with the process without building experimental setups. In order to achieve this goal, it is necessary to formulate a differential equation that, depending on the number of variables, can be partial or ordinary type. In this context, the present work evaluates the mass balance for an open system from a numerical and mathematical perspective, and then experimentally validates the results obtained. The analytical solutions of the mathematical models are performed through variable separation, while the numerical solutions are obtained from the fourth-order Runge-Kutta method. The experimental results confirm that the applied differential equation accurately represents the process under consideration and predicts the filling times at which the system reaches the steady-state condition. Furthermore, it describes the system's transient process with an error of less than 4%. Moreover, the influence of operational variables, including the diameters and thermophysical properties of the fluid, on the time required for the system to reach a steady state is quantified numerically. Finally, the present study has proved that how an actual situation reproduced experimentally can be modeled using differential equations and how this strategy facilitates the learning and applying theoretical models in mathematical learning environments. Copyright © 2024 Praise Worthy Prize S.r.l. - All rights reserved.