Novel model of thermo-magneto-viscoelastic medium with variable thermal conductivity under effect of gravity

• Published in: Applied mathematics and mechanics Vol. 41; no. 5; pp. 819 - 832
• Main Author: Said, S. M.
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.05.2020; Springer Nature B.V; Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt; Department of Mathematics, Faculty of Science and Arts, Qassim University,Buridah 51931, Al-mithnab, Kingdom of Saudi Arabia
• Edition: English ed.
• Subjects: Applications of Mathematics; Classical Mechanics; Eigenvalues; Fluid- and Aerodynamics; Gravitation; Gravitational effects; Heat conductivity; Heat transfer; Linear functions; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Thermal conductivity; Thermal energy; Thermal shock; Viscosity; gravity field; variable thermal conductivity; 74B10; eigenvalue approach; thermo-viscoelastic; O343
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-020-2603-9

The basic equations for a homogeneous and isotropic thermo-magnetoviscoelastic medium are formulated based on three different theories, i.e., the Green- Lindsay (G-L) theory, the coupled (CD) theory, and the Lord-Shulman (L-S) theory. The variable thermal conductivity is considered as a linear function of the temperature. Using suitable non-dimensional variables, these basic equations are solved via the eigenvalue approach. The medium is initially assumed to be stress-free and subject to a thermal shock. The numerical results reveal that the viscosity, the two-temperature parameter, the gravity term, and the magnetic field significantly influence the distribution of the physical quantities of the thermoelastic medium.