Ley de enfriamiento de Newton con temperatura variable

Abstract

En este trabajo se presenta un estudio teórico-experimental sobre la ley de enfriamiento de Newton, con temperatura variable. En el estudio teórico se resolvió una ecuación diferencial ordinaria lineal la cual permite calcular la temperatura de un objeto a lo largo de un periodo de tiempo. Para la sección experimental del estudio se realizaron dos modelos experimentales, donde se uso un modelo senoidal para la temperatura ambiente y se comparo con la respuesta teórica, después de 22 y 52 horas respectivamente. En el estudio se compararon los resultados experimentales con las soluciones de las ecuaciones diferenciales, en diferentes lapsos de tiempo. El objetivo del presente, fomenta la reflexión por parte de los estudiantes y docentes, dando libre camino, a la modificación del modelo de temperatura y otros análogos para el estudio de ecuaciones diferenciales ordinarias y sus aplicaciones.

This work presents a theoretical-experimental study on the applicability of Newton’s cooling law in prolonged time periods, considering a sinusoidal variable ambient temperature. In the theoretical study, a linear ordinary differential equation that describes the heat transfer between an object and its environment was solved. The solution of this equation allows calculating the object’s temperature over time, considering a variable ambient temperature. In the experimental part, two experimental models were built to evaluate Newton’s cooling law. A sinusoidal model was used to represent the ambient temperature, which represents a non-traditional initial condition. The experimental results were compared with the theoretical solution obtained in the first part of the study, considering 22 and 52 hours. The objective of this work is to evaluate the validity of Newton’s cooling law in situations that have not been explored in depth previously. The incorporation of a sinusoidal temperature as an initial condition provides a new perspective on the study of this phenomenon and opens the door to the modification of temperature models and other analogous models in the field of ordinary differential equations and their applications.