Hyperbolic Two Temperature Fractional-Order Thermoelastic Model Subjected to Thermal Loading with Two Relaxation Times

2020 ◽  
Vol 15 (2) ◽  
pp. 217-229
Author(s):  
E. Bassiouny ◽  
Rajagopalan R
Keyword(s):  
Fractional Order ◽  
Thermal Loading ◽  
Relaxation Times ◽  
Thermoelastic Model ◽  
Two Temperature

scholarly journals A Fractional-Order Model of Biopolyester Containing Naturally Occurring Compounds for Soil Stabilization

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Nadka Tzankova Dintcheva ◽  
Marilena Baiamonte ◽  
Rosalia Teresi ◽  
Gioacchino Alotta ◽  
Emanuela Bologna ◽  
...  
Keyword(s):  
Fractional Order ◽  
Soil Degradation ◽  
Agricultural Sector ◽  
Soil Stabilization ◽  
Relaxation Times ◽  
Experimental Tests ◽  
Order Model ◽  
Naturally Occurring ◽  
Fractional Order Model ◽  
Melting Properties

Currently, the use of polymers and biopolymers as soil-stabilizer additives for control of the soil degradation, deterioration, and desertification and for improving the arid and semiarid soils has been expanded significantly in the agricultural sector. This research was conducted to determine the effect of naturally occurring compounds, such as quercetin (Q) and sodium montmorillonite (NaMMt) at different weight ratios, in biopolyester, such as polylactic acid (PLA), aiming to formulate ecosustainable materials to control the soil degradation and to protect the environment. As known, the use of sophisticated analytical tools to describe the material rheology and melting properties is nowadays very popular among physicists and material scientists. Certainly, several experimental tests conducted on polymeric- and biopolymeric-based materials, such as rubbers, foams, and hydro/aero gels, show that the relaxation time spectra are a continuous function, and as a consequence, multiple relaxation times are involved in the rheological description of the materials, yielding the need for nonconventional relaxation functions. Indeed, in this work, the considered fractional-order model could be considered a powerful tool to describe and to predict the melting properties of the complex polymer-based systems containing different additives.

scholarly journals The Motion of the OH Group in p-Chlorophenol and its Influence on the 35Cl NQR Parameters

1986 ◽  
Vol 41 (1-2) ◽  
pp. 408-411 ◽  
Author(s):  
Mariano J. Zuriaga ◽  
Carlos A. Martin
Keyword(s):  
Activation Energy ◽  
Relaxation Times ◽  
Lattice Relaxation ◽  
Frequency Difference ◽  
Spin Lattice Relaxation ◽  
Normal Behaviour ◽  
Spin Lattice ◽  
35Cl Nqr ◽  
Two Temperature ◽  
Nqr Parameters

The 35Cl NQR transition frequencies and the spin-lattice relaxation times, T1, for both lines in p-chlorophenol have been measured in the temperature range 90 - 310 K. The frequency difference and the temperature derivatives for both lines clearly show the existence of two temperature intervals with distinct lattice contributions to the EFG. Similarly, T1, data show a normal behaviour due to spin-phonon interactions up to 240 K. Above this temperature T1 begins to shorten in an exponential manner. The hindered motions of the OH group are proposed as responsibles of these effects, and an activation energy of 26 kJ mol-1 is determined.

scholarly journals Characterization of the Vibration and Strain Energy Density of a Nanobeam under Two-Temperature Generalized Thermoelasticity with Fractional-Order Strain Theory

2021 ◽  
Vol 26 (4) ◽  
pp. 78
Author(s):  
Hamzah Abdulrahman Alharthi
Keyword(s):  
Fractional Order ◽  
Numerical Solutions ◽  
Generalized Thermoelasticity ◽  
Strain Theory ◽  
Aspect Ratios ◽  
The Laplace Transform ◽  
Beam Thickness ◽  
Novel Model ◽  
Two Temperature

In this work, fractional-order strain theory was applied to construct a novel model that introduces a thermal analysis of a thermoelastic, isotropic, and homogeneous nanobeam. Under supported conditions of fixed aspect ratios, a two-temperature generalized thermoelasticity theory based on one relaxation time was used. The governing differential equations were solved using the Laplace transform, and their inversions were found by applying the Tzou technique. The numerical solutions and results for a thermoelastic rectangular silicon nitride nanobeam were validated and supported in the case of ramp-type heating. Graphs were used to present the numerical results. The two-temperature model parameter, beam size, ramp-type heat, and beam thickness all have a substantial influence on all of the investigated functions. Moreover, the parameter of the ramp-type heat might be beneficial for controlling the damping of nanobeam energy.

Fractional order two-temperature thermoelasticity with finite wave speed

2012 ◽  
Vol 223 (12) ◽  
pp. 2685-2701 ◽  
Author(s):  
Abhik Sur ◽  
M. Kanoria
Keyword(s):  
Fractional Order ◽  
Wave Speed ◽  
Two Temperature

Three-Dimensional Thermoelastic Problem Under Two-Temperature Theory

2017 ◽  
Vol 14 (03) ◽  
pp. 1750030 ◽  
Author(s):  
Abhik Sur ◽  
M. Kanoria
Keyword(s):  
Thermal Loading ◽  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Thermodynamic Temperature ◽  
Mode Analysis ◽  
Phase Lag ◽  
Field Equations ◽  
Conductive Temperature ◽  
Lag Model ◽  
Two Temperature

The present paper deals with the problem of thermoelastic interactions in a homogeneous, isotropic three-dimensional medium whose surface suffers a time dependent thermal loading. The problem is treated on the basis of three-phase-lag model and dual-phase-lag model with two temperatures. The medium is assumed to be unstressed initially and has uniform temperature. Normal mode analysis technique is employed onto the non-dimensional field equations to derive the exact expressions for displacement component, conductive temperature, thermodynamic temperature, stress and strain. The problem is illustrated by computing the numerical values of the field variables for a copper material. Finally, all the physical fields are represented graphically to analyze the difference between the two models. The effect of the two temperature parameter is also discussed.

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