Two-dimensional heat transfer with memory property in a fractal space

Abstract

This paper considers a temperature-dependent thermal conductivity with memory property in a fractal space. The two-scale fractal derivative is adopted to model the temperature field in the spatial dimensions, and Caputo fractional derivative is used to describe its memory property. The variational iteration method is employed to solve the mixed model with great success. This paper offers a new window for studying intractable problems arising in porous media or unsmooth boundaries.