Fractional single-phase-lagging heat conduction model for describing anomalous diffusion

Abstract

The fractional single-phase-lagging (FSPL) heat conduction model is obtained by combining scalar time fractional conservation equation to the single-phase-lagging (SPL) heat conduction model. Based on the FSPL heat conduction model, anomalous diffusion within a finite thin film is investigated. The effect of different parameters on solution has been observed and studied the asymptotic behavior of the FSPL model. The analytical solution is obtained using Laplace transform method. The whole analysis is presented in dimensionless form. Numerical examples of particular interest have been studied and discussed in details.

Keywords

• Single-phase-lagging (SPL) heat conduction model
• Fractional single-phase-lagging (FSPL) heat conduction model
• Laplace transform
• Fractional conservation equation
• Asymptotic behavior
• Anomalous diffusion