The Effects of Fractional Time Derivatives in Porothermoelastic Materials Using Finite Element Method

Marin Marin, Aatef Hobiny and Ibrahim Abbas
Additional contact information
Marin Marin: Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093 Brasov, Romania
Aatef Hobiny: Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Ibrahim Abbas: Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2021, vol. 9, issue 14, 1-14

Abstract: In this work, a new model for porothermoelastic waves under a fractional time derivative and two time delays is utilized to study temperature increments, stress and the displacement components of the solid and fluid phases in porothermoelastic media. The governing equations are presented under Lord–Shulman theory with thermal relaxation time. The finite element method has been adopted to solve these equations due to the complex formulations of this problem. The effects of fractional parameter and porosity in porothermoelastic media have been studied. The numerical outcomes for the temperatures, the stresses and the displacement of the fluid and the solid are presented graphically. These results will allow future studies to gain a detailed insight into non-simple porothermoelasticity with various phases.

Keywords: porothermoelastic materials; thermal relaxation times; fractional time derivative; finite element method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/14/1606/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/14/1606/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:14:p:1606-:d:590222

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().