Transient heat diffusion with a non-singular fading memory: From the Cattaneo constitutive equation with Jeffrey’s Kernel to the Caputo-Fabrizio time-fractional derivative

• Main Author: Hristov Jordan
• Format: Article
• Language: English
• Published: VINCA Institute of Nuclear Sciences 2016-01-01
• Series: Thermal Science
• Subjects: non-linear diffusion; non-singular fading memory; Jeffrey kernel; Caputo-Fabrizio derivative integral balance approach
• Online Access: http://www.doiserbia.nb.rs/img/doi/0354-9836/2016/0354-98361600019H.pdf
• ISSN: 0354-9836; 2334-7163

Starting from the Cattaneo constitutive relation with a Jeffrey’s kernel the derivation of a transient heat diffusion equation with relaxation term expressed through the Caputo-Fabrizio time fractional derivative has been developed. This approach allows seeing the physical background of the newly defined Caputo-Fabrizio time fractional derivative and demonstrates how other constitutive equations could be modified with non-singular fading memories.