Application of the New General Integral Transform for Newton’s Law of Cooling

Abstract

Integral transformations are versatile mathematical techniques that are applicable in a wide range of applications in various fields in mathematics, engineering and applied sciences. Using integral transformations, complicated functions can be transformed into more simpler functions to be analyzed and to be solved. Integral transform methods have been extensively used to solve differential equation theories and numerical calculation. Newton's law of cooling is the fundamental law that describes the rate of heat transfer by a body to its surrounding through radiation. This important law can be modelled in the form of differential equation, which is solved by many researchers by using different methods. Some researchers used integral transforms to solve this equation. In this study, we use an integral transform, providing a more flexible and powerful approach for solving differential equations, called as “New General Integral Transform” as a generalization of the Laplace transform method and some applications are given to demonstrate the effectiveness of this transform.