Shock waves as generalized solutions of thermoelastodynamics equations. On the uniqueness of boundary value problems solutions

Alipova, Bakhyt; Alexeyeva, L. A.; Dadayeva, A.N.

doi:10.1063/1.4972595

Cited by 5 publications

(3 citation statements)

References 9 publications

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“…The dimensionless heat transfer parameter Ω = 4Nu/Pe² is related to the Nusselt number Nu=αdₒ/λg and the Peclet number Pe=Vbdₒ/ae, which are determined for the channel of height dₒ (here α is the heat transfer coefficient; λg is the thermal conductivity of the gas). The boundary conditions for equations (1) far from the flame have the following form:…”

Section: Flame Attenuation Mathematical Modelingmentioning

confidence: 99%

See 1 more Smart Citation

Flame Distribution and Attenuation in Narrow Channels Using Mathematical Software

Sapargaliyeva¹,

Naukenova²,

Alipova³

et al. 2019

Adv. sci. technol. eng. syst. j.

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The article of given research presents the mathematical and computer modeling of flame attenuation in narrow channels for different fire extinguishing and explosion suppression compositions. Such kind of flame distribution and attenuation could be considered for different media and channels but in this case it was considered for narrow channels. The effect on the combustion reaction is possible with gas mixture components concentration reducing, cooling the combustion zone and slowing down of chain reactions with the help of a phlegmatizing or inhibiting substances, of which the most universal and perspective are powder materials. Therefore, a necessary condition for solving the problems of developing effective flame arresters is to find common indicators and properties of substances that can become criteria for their phlegmatizing ability. The computer model in MatLab was created for methane allowing the choice of diameter and length of channel and velocity of explosion suppression composition, showing the dependence of temperature on length of channel.

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Section: Flame Attenuation Mathematical Modelingmentioning

confidence: 99%

“…As result it would assimilated the principal concepts and laws governing the kinematics and dynamics of deformable media. In addition, this research should understand the application of this theory to the cases (i) of infinitesimal Thermo-Elasticity, and (ii) of Newtonian and perfect Fluid Mechanics [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Flame Distribution and Attenuation in Narrow Channels Using Mathematical Software

Sapargaliyeva¹,

Naukenova²,

Alipova³

et al. 2019

Adv. sci. technol. eng. syst. j.

View full text Add to dashboard Cite

show abstract

“…They are connected with the gradient of temperature in the first hyperbolic equation and divergence of velocities in the second parabolic one. It leads to presence of singular solutions -shock thermoelastic waves with jumps in stresses and velocities at their fronts (Alipova et al, 2017). To construct solutions of such systems for different external forces and heat sources, the fundamental solution -Green tensor is used.…”

Section: Introductionmentioning

confidence: 99%

Green tensor and regular solutions of equations of rods thermodynamics and their properties

Alexeyeva¹,

Dadayeva²,

Ainakeyeva³

2021

Journal of Theoretical and Applied Mechanics

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In the present paper, solutions of the equations of uncoupled thermoelastodynamics of thermoelastic rods are constructed for power and thermal effects. Based on the Fourier transform, the Green tensor and generalized solutions of the thermoelasticity equations are constructed in the original space-time using the apparatus of generalized functions theory. Analytical formulas for definitions of the thermal stress-strain state of the rods taking into account its thermoelastic parameters are obtained. Shock thermoelastic waves are considered and conditions on their fronts are obtained. The results of numerical calculations of Green tensor are presented.

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Simulation of wave dynamics of thermoelastic medium with crack

Alexeyeva

Alipova

2018

AIP Conference Proceedings

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Shock waves as generalized solutions of thermoelastodynamics equations. On the uniqueness of boundary value problems solutions

Cited by 5 publications

References 9 publications

Flame Distribution and Attenuation in Narrow Channels Using Mathematical Software

Flame Distribution and Attenuation in Narrow Channels Using Mathematical Software

Green tensor and regular solutions of equations of rods thermodynamics and their properties

Simulation of wave dynamics of thermoelastic medium with crack

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