Problems of dynamic thermoelasticity on the basis of an analytical solution of the hyperbolic heat conduction equation

Кудинов, И. В.; Кудинов, В. А.

doi:10.1134/s0018151x15030116

Cited by 11 publications

(6 citation statements)

References 1 publication

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“…As applied to the determination of pressure during a hydraulic shock, an exact analytical solution of the boundary value problem was obtained in [17], which differs from problem (10) - (15) only by the absence of the term , the need for which in problem ( 10) -( 15) is associated with taking into account the delay of the hydraulic resistance (taking into account the nonstationarity of the friction force). In this connection, we will compare the results of calculations by formula (24) with the results obtained in [17], taking into account the complete analogy of the boundary value problems presented in dimensionless form for pressure and velocity during hydraulic shock, as well as with the exact analytical solution and with the results of a full-scale experiment given in [18].…”

Section: Resultsmentioning

confidence: 99%

“…, the relation ( 16) satisfies the boundary conditions ( 14), (15). Substituting ( 16) into (10), we obtain…”

Section: Accurate Analytical Solutionmentioning

confidence: 95%

“…The relation (24) satisfies the boundary conditions ( 14), (15), and the equation ( 10), but does not satisfy the initial conditions ( 11) -( 13), from the fulfillment of which the constants of integration are found k C 1 , k C 2 , k C 3 . Substituting (24) into (13), we obtain…”

Section: Accurate Analytical Solutionmentioning

confidence: 99%

“…In this work, to take into account the nonstationarity of changes in pressure, velocity, density, and shear stresses, a direction is chosen that is associated with taking into account relaxation phenomena, which makes it possible to take into account the prehistory of their change. This approach was applied earlier for the problems of thermal conductivity and thermoelasticity [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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Nonlocal model of velocity vibrations compressed fluid under conditions hydraulic impact

Stefanyuk

Gavrilova

Uglanov

et al. 2022

J. Phys.: Conf. Ser.

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Taking into account the relaxation properties of the fluid, a hyperbolic equation of motion is obtained that describes the change in velocity under conditions of nonlocal equilibrium, that is, taking into account the effect of unsteadiness of the flow on the magnitude of the friction force. Studies of its exact analytical solution have shown that taking into account the nonstationarity of tangential stresses leads to results that differ significantly from the solutions of the classical hyperbolic equation obtained by using the values of velocity, density, tangential stresses, and pressure averaged over the flow cross section (the hypothesis of quasi-stationarity). Comparison of the obtained solution with experimental data, as well as with the results of theoretical studies of other authors (I.A. Charny), obtained from the solution of the Navier - Stokes equations (equations for local quantities), showed their satisfactory agreement. Consequently, studies based on the theory of quasi-stationarity can be used only after comparing them with the results obtained taking into account the nonstationarity of tangential stresses (friction force) or with experimental data, that is, only after determining the range of the degree of nonstationarity in which it can be used.

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Section: Resultsmentioning

confidence: 99%

“…, the relation ( 16) satisfies the boundary conditions ( 14), (15). Substituting ( 16) into (10), we obtain…”

Section: Accurate Analytical Solutionmentioning

confidence: 95%

Section: Accurate Analytical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlocal model of velocity vibrations compressed fluid under conditions hydraulic impact

Stefanyuk

Gavrilova

Uglanov

et al. 2022

J. Phys.: Conf. Ser.

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“…By substituting (5) in heat balance equation (3), considering three members of the right and left part of relation (5), the heat transfer equation in the non-dimensional form will be as follows [9,10] (12) is reduced to a classic parabolic heat conductivity equation.…”

Section: Heat Conductivity Mathematical Models Considering Spatimentioning

confidence: 99%

Mathematical Modelling of Strongly Non-Equilibrium Transfer Processes at Nanoscopic Scale

Кудинов

Еремин²,

Tkachev³

et al. 2017

Proceedings of the International Conference "Actual Issues of Mechanical Engineering" 2017 (AIME 2017)

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Abstract-Based on the concepts of local non-equilibrium thermodynamics, mathematical models for heat, mass and momentum transfer have been developed with space-time nonlocality taken into consideration. Derivation of transfer differential equations is based on taking into account both specific flows (of heat, mass and momentum) and gradients of corresponding values in diffusion laws by Fourier, Fick and Newton. The research of accurate analytical solutions of the derived models enabled us to find new change patterns of the required parameters for small and ultra small values of time and space variables, as well as for high-speed processes, the change time of which is comparable to relaxation time. Particularly, from the investigation of an accurate analytical solution, it has been found that there is a time delay for Derichlet's boundary condition acceptance, which demonstrates that due to body's resistance to heat penetration, its instant heat-up is impossible, irrespective of any heat exchange with the environment. Therefore, wall heat exchange factor depends not only on heatexchange conditions (medium speed, viscosity, etc.), but also on the body's physical properties. So, firstly, it is a time-variant and, secondly, it can not exceed a certain limit value, established for each particular case. The conducted research of the rod oscillations with relaxation phenomena, taken into consideration, discovered bifurcation oscillations (beat) appearing under the external harmonic load in cases when the difference between the frequency of eigen-oscillations of the rod and constrained load oscillations is insufficient.

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Mathematical modelling of thermal dynamic stresses on the basis of a dual – Phase lag model

Кудинов

Gavrilova

2019

International Journal of Heat and Mass Transfer

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Problems of dynamic thermoelasticity on the basis of an analytical solution of the hyperbolic heat conduction equation

Cited by 11 publications

References 1 publication

Nonlocal model of velocity vibrations compressed fluid under conditions hydraulic impact

Nonlocal model of velocity vibrations compressed fluid under conditions hydraulic impact

Mathematical Modelling of Strongly Non-Equilibrium Transfer Processes at Nanoscopic Scale

Mathematical modelling of thermal dynamic stresses on the basis of a dual – Phase lag model

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