A new viewpoint on theory of the scaling-law heat conduction process

Abstract

In this article, we suggest a new model for the heat-conduction problem by us?ing the scaling-law vector calculus with Mandelbrot scaling law. The linear and non-linear scaling-law heat conduction equations are considered as analogues to the work of Fourier, Laplace, and Burgers. The obtained results are considered as typical examples to deal with the Mandelbrots scaling-law phenomena in heat transport system.