"Applying Graph Theory and Multi-Variables G-Function to Solved the Problem Related to Cooling a Sphere "

Abstract

We have observed that the separation of variables method and graph theory in mathematics can be applied to several types of problems on bounded three-dimensional domains. The problem must be linear and have homogeneous boundary-conditions. In this paper, we present the result of classical problem in three dimensions by applying modified integral form, of Newton's law of cooling for sphere, which is encountered in ordinary differential equations texts. Also show that, the rate at which a body cools is proportional to the difference of its temperature and the temperature of the environment. The assumed symmetries in the problem will permit us to reduce the dimension of the problem to spatial dimension and time with the help of Bipartite Graphs in Graph theory.