Velocity of Rayleigh waves with thermal relaxation in time

In this study, an effort is made to model the thermal conduction and mass diffusion phenomena in perspective of Buongiorno’s model and Cattaneo-Christov theory for 2D flow of magnetized Burgers nanofluid due to stretching cylinder. Moreover, the impacts of Joule heating and heat source are also included to investigate the heat flow mechanism. Additionally, mass diffusion process in flow of nanofluid is examined by employing the influence of chemical reaction. Mathematical modelling of momentum, heat and mass diffusion equations is carried out in mathematical formulation section of the manuscript. Homotopy analysis method (HAM) in Wolfram Mathematica is utilized to analyze the effects of physical dimensionless constants on flow, temperature and solutal distributions of Burgers nanofluid. Graphical results are depicted and physically justified in results and discussion section. At the end of the manuscript the section of closing remarks is also included to highlight the main findings of this study. It is revealed that an escalation in thermal relaxation time constant leads to ascend the temperature curves of nanofluid. Additionally, depreciation is assessed in mass diffusion process due to escalating amount of thermophoretic force constant.

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Method of first integrals and interface, surface waves

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/32/2/310 ◽

2010 ◽

Vol 32 (2) ◽

pp. 107-120

Author(s):

Pham Chi Vinh ◽

Trinh Thi Thanh Hue ◽

Dinh Van Quang ◽

Nguyen Thi Khanh Linh ◽

Nguyen Thi Nam

Keyword(s):

Rayleigh Waves ◽

Displacement Vector ◽

Attenuation Factor ◽

Electrical Potential ◽

Polarization Vector ◽

First Integrals ◽

Dispersion Equations ◽

Interface Surface ◽

Electric Induction ◽

The One

The method of first integrals (MFI) based on the equation of motion for the displacement vector, or based on the one for the traction vector was introduced recently in order to find explicit secular equations of Rayleigh waves whose characteristic equations (i.e the equations determining the attenuation factor) are fully quartic or are of higher order (then the classical approach is not applicable). In this paper it is shown that, not only to Rayleigh waves, the MFI can be applicable also to other waves by running it on the equations for mixed vectors. In particular: (i) By applying the MFI to the equations for the displacement-traction vector we get the explicit dispersion equations of Stoneley waves in twinned crystals (ii) Running the MFI on the equations for the traction-electric induction vector and the traction-electrical potential vector provides the explicit dispersion equations of SH-waves in piezoelastic materials. The obtained dispersion equations are identical with the ones previously derived using the method of polarization vector, but the procedure of driving them is more simple.

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On a technique for deriving explicit transfer matrices of orthotropic layers

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/37/4/6534 ◽

2015 ◽

Vol 37 (4) ◽

pp. 303-315 ◽

Cited By ~ 1

Author(s):

Pham Chi Vinh ◽

Nguyen Thi Khanh Linh ◽

Vu Thi Ngoc Anh

Keyword(s):

Wave Propagation ◽

Explicit Form ◽

Half Space ◽

Transfer Matrix ◽

Rayleigh Waves ◽

Secular Equation ◽

Transfer Matrices ◽

Orthotropic Layer ◽

Wave Propagation Problem ◽

Arbitrary Thickness

This paper presents a technique by which the transfer matrix in explicit form of an orthotropic layer can be easily obtained. This transfer matrix is applicable for both the wave propagation problem and the reflection/transmission problem. The obtained transfer matrix is then employed to derive the explicit secular equation of Rayleigh waves propagating in an orthotropic half-space coated by an orthotropic layer of arbitrary thickness.

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Correlating Blocking Temperatures in Single Molecule Magnets with Raman Relaxation

10.26434/chemrxiv.7067669 ◽

2018 ◽

Author(s):

Marcus J. Giansiracusa ◽

Andreas Kostopoulos ◽

George F. S. Whitehead ◽

David Collison ◽

Floriana Tuna ◽

...

Keyword(s):

Relaxation Time ◽

Single Molecule ◽

Energy Barrier ◽

Thermal Relaxation ◽

Relaxation Mechanism ◽

Blocking Temperature ◽

Single Molecule Magnets ◽

Single Molecule Magnet ◽

Key Parameter

We report a six coordinate DyIII single-molecule magnet (SMM) with an energy barrier of 1110 K for thermal relaxation of magnetization. The sample shows no retention of magnetization even at 2 K and this led us to find a good correlation between the blocking temperature and the Raman relaxation regime for SMMs. The key parameter is the relaxation time (𝜏switch) at the point where the Raman relaxation mechanism becomes more important than Orbach.

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