Using Numerical Analysis to Solve Some Applications of Newton's Law of Cooling

Abstract

This study explores and discusses the idea of the application of Newton's Law of Cooling in ‎solving various real-world problems using numerical analysis techniques. The law, which ‎describes and shows the rate of temperature change in an object as proportional to the ‎difference between its temperature and the ambient temperature, is modeled by a first-order ‎linear ordinary differential equation. The solution to this equation provides insights into the ‎temperature behavior over time. Two primary applications are considered: the cooling of an ‎object immersed in a liquid and the temperature dynamics within a building over 24 hours, ‎influenced by heating and cooling systems. For both cases, the mathematical models are ‎solved using numerical methods, and the results are presented with the aid of MATLAB to ‎simulate real-life scenarios. Another important thing in this study provides a valuable ‎framework for analyzing heat transfer processes, offering both theoretical understanding and ‎practical solutions for engineering and environmental applications.‎