Investigate on Non-Fourier Heat Conduction in Sand Using Models based on Fractional Calculus

Abstract

In this article, the study of the non-Fourier heat conduction in casting sand that is located inside a container under an instantaneous heat flux. According to inefficiencies of Fourier model to model the behavior of this problem due to differences in heat transfer between the phases and the ability of the models based on fractional calculus to model the anomalous behavior in different materials, in this paper, a model based on fractional calculus have been used. This model has recently entered the field of physics. Thermal properties, initial and boundary conditions of the problem is assumed to be known. The governing equations have been solved in a try and error algorithm to find the phase lag and fractional order using an implicit discretization method. The results show that neither the super-diffusion fractional model nor sub-diffusion fractional model can model the heat transfer in the sand. Based on the present results, it can observe also that in the initial moment, sub-diffusion conditions and after that super-diffusion conditions govern on the problem. Using simultaneously sub-diffusion and super-diffusion models, the numerical results are able to cover the experimental data for the temperature distribution within the container.

Keywords

• non-fourier heat transfer
• fractional calculus
• fractional models
• super diffusion-sub diffusion model