The Effect of Two Temperature and Gravity on the 2-D Problem of Thermoviscoelastic Material Under Three-Phase-Lag

Othman, Mohamed I. A.; Zidan, Magda E. M.

doi:10.1166/jctn.2015.3947

Cited by 6 publications

(1 citation statement)

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“…El Sherif et al [18] investigated the thermo-viscoelastic cylinder effect of the magnetic field under a constant thermal shock. Othman and Zidan [19] made use of the 3PHL model to study how 2D thermoviscoelastic materials perform under the influence of gravity and two temperatures. Many applications of magneto-visco-elastic-material developed for different types of problems in thermoelasticity [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Thermal effects and initial stress on magneto‐thermo‐viscoelastic medium with two temperature under five theories

2021

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The contribution of this study is to research how the initial stress and the application of a magnetic field affects the two-dimensional complication of a general, two temperature, and thermally activated viscoelastic material in five theories.In the physical domain, normal mode analysis is employed to obtain the analytical expressions for the physical quantities. A numerical pathway is chosen to calculate the analytical expressions and their explanation is done using various graphical methods. The results predicted by different theories (L-S, G-L, G-N II, and DPL) are also examined in both the scenarios, that is, existence and nonexistence of a magnetic field, viscosity, initial stress, and two temperatures. 1Nomenclature: 𝛼 0 , 𝛼 1 , 𝛼 2 , 𝛼 3 , 𝛼 4 , the viscoelastic parameters; 𝛼 𝑡 Coefficient of linear thermal expansion, 𝜌 density; 𝐾 Coefficient of thermal conductivity, 𝜏 0 , 𝜏 1 , 𝜐 0 relaxation times; 𝑒 𝑖𝑗 Components of strain tensor, 𝜙 the volume fraction field; 𝜎 𝑖𝑗 Components of stress tensor, 𝑟 the beam radius; 𝜃 Conductive temperature, 𝑎 two temperature parameter; 𝑢, 𝑤 Displacement components, 𝛿 𝑖𝑗 Kronecker's delta; 𝑇 0 Reference temperature |(𝑇 − 𝑇 0 )∕𝑇 0 | < 1, 𝑛 * , 𝑛 0 , 𝑛 1 parameters; 𝜇 0 the magnetic permeability, 𝑝 the initial stress; 𝜏 0 the thermal relaxation time, 𝜀 0 the electric permittivity; 𝑇 Thermodynamic temperature, 𝑐 𝑒 specific heat at constant strain; 𝑒 = 𝑒 𝑘𝑘 Cubic dilatation, 𝜆, 𝜇 Lame' constants

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