Deformation due to time harmonic sources in micropolar thermoelastic medium possessing cubic symmetry with two relaxation times

We compare the Lattice BGK, the Multiple Relaxation Times and the Entropic Lattice Boltzmann Methods for time harmonic flows. We measure the stability, speed and accuracy of the three models for Reynolds and Womersley numbers that are representative for human arteries. The Lattice BGK shows predictable stability and is the fastest method in terms of lattice node updates per second. The Multiple Relaxation Times LBM shows erratic stability which depends strongly on the relaxation times set chosen and is slightly slower. The Entropic LBM gives the best stability at the price of fewer lattice node updates per second. A parameter constraint optimization technique is used to determine which is the fastest model given a certain preset accuracy. It is found that the Lattice BGK performs best at most arterial flows, except for the high Reynolds number flow in the aorta, where the Entropic LBM is the fastest method due to its better stability. However we also conclude that the Entropic LBM with velocity/pressure inlet/outlet conditions shows much worse performance.

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Three-Dimensional Interaction in Thermoelastic Medium with Two Relaxation Times Due to Thermal Source

Journal of Molecular and Engineering Materials ◽

10.1142/s2251237315500033 ◽

2015 ◽

Vol 03 (03n04) ◽

pp. 1550003 ◽

Cited By ~ 1

Author(s):

Ibrahim A. Abbas ◽

Rajneesh Kumar ◽

A. Lahiri

Keyword(s):

Normal Mode Analysis ◽

Relaxation Times ◽

Three Dimensional ◽

Specific Model ◽

Mode Analysis ◽

Thermal Source ◽

Thermoelastic Medium ◽

Coupled Equations ◽

Dimensional Interaction ◽

Element Technique

The present study is concerned with the interaction in thermoelastic medium with two relaxation times due to thermal source. The finite element technique under normal mode analysis is used to solve the resulting nondimensional coupled equations. As an application of the approach, the particular type of thermal source has been considered. The components of displacement, stress and temperature change are computed numerically. The numerical stimulated results are depicted graphically for a specific model. The effect of rotation has been shown on the resulting quantities. Effect of relaxation times is shown on the resulting quantities by a comparison between the absence and presence of relaxation times.

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Temperature-Rate-Dependent Thermoelasticity Theory With Memory-Dependent Derivative: Energy, Uniqueness Theorems, and Variational Principle

Journal of Heat Transfer ◽

10.1115/1.4047510 ◽

2020 ◽

Vol 142 (10) ◽

Cited By ~ 3

Author(s):

Biswajit Singh ◽

Indranil Sarkar ◽

Smita Pal (Sarkar)

Keyword(s):

Variational Principle ◽

Relaxation Times ◽

Thermoelastic Medium ◽

Rate Dependent ◽

Thermoelasticity Theory ◽

Laplace Transform Technique ◽

The Laplace Transform ◽

Temperature Rate ◽

With Memory ◽

Coupled Theory

Abstract This article is focused on developing a new mathematical model on the temperature-rate-dependent thermoelasticity theory (Green–Lindsay), using the methodology of memory-dependent derivative (MDD). First, the energy theorem of this model associated with two relaxation times in the context of MDD is derived for homogeneous, isotropic thermoelastic medium. Second, a uniqueness theorem for this model is proved using the Laplace transform technique. A variational principle for this model is also established. Finally, the results for Green–Lindsay model without MDD and coupled theory are obtained from the considered model.

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