Comparative Numerical Analysis of Newton and Modified Newton’s Law of Cooling

Abstract

The aim of this research was to comprehend how an object decays in temperature under different conditions by conducting a comparative numerical analysis of the classical Newtons Law of Cooling and a reformulated Newtons Law of Cooling. The main purpose of this study was to apply numerical solutions to two cooling models and compare their performance with the Fourth Order Runge-Kutta method (RK4) and Dormand-Prince method. Both models were solved analytically to get analytical solutions to be used as reference solutions in order to evaluate the accuracy of the numerical methods. The sensitivity and stability of the methods were tested by numerical simulation using various step sizes and absolute error analysis was done to measure the differences between numerical and analytical solutions. To show the cooling behaviour of the two models with time, graphical representations were used. The results showed that the RK4 and Dormand-Prince can be used to provide an accurate approximation of the analytical solutions, and that the Dormand-Prince method has a better accuration by the fact that it has the ability to control the step size. Furthermore, the modified Newton Law of Cooling was a better representation of the observed colling patterns than the classical model, which pointed to its greater flexibility in predicting real colling behaviour. On the whole, this paper has shown that numerical techniques are effective in the formulation of the cooling problems and how the modified model was useful in the realistic representation of the thermal behaviour, which may be considered to be a systematic way of conducting a thermal analysis in the future in the context of engineeering.