Numerical solution of transient fractional Non-Fourier heat conduction using generalized Cattaneo model and improved Talbot method

In recent years, the field of non-Fourier heat transfer has found great interest among investigators.The reason returns to different observed anomalous behaviors in thermal response of many systems in engineering applications. On the other hand, fractionalcalculus has proved its great ability in modeling anomalous and intermediate behaviors in transport phenomena. In this work, we have employed this ability for modeling the intermediate processes of heat transfer.To do this, the classical concept of time lagging fordescribing non-Fourier thermal transport is first generalized to fractional time lagging. This has been done through employing fractional Taylor series formula on single-phase-lag heat conduction constitutive model which results to the introduction of fractional Cattaneo(single fractional phase-lag) model. Next, it is aimed to show the capabilities of this model in capturing the intermediate behaviors of thermal transport in a physical system. Therefore, it is necessary to find appropriate ways of solving the resulting governing equation. Forthis reason, the Laplace transformation approach is used and then Talbot’s approache is used for obtaining Inversion Laplace transformation. The results show the ability of fractional single-phase lag model in capturing the non-Fourier thermal behavior observed in a homogeneous material.

کلیدواژه ها:

Numerical Inversion of Laplace ، Non- Fourier heat transfer ، Integral transformations ، fractional calculus ، Single Phase Lagging (PH)