Mathematical Simulation of the Locally Nonequilibrium Heat Transfer in a Body with Account for its Nonlocality in Space and Time

Кудинов, И. В.; Кудинов, В. А.

doi:10.1007/s10891-015-1206-6

Cited by 27 publications

(5 citation statements)

References 8 publications

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“…For deriving the differential heat ignition equation, considering local not-equilibrium, let us represent the Fourier law formula in the form of [8]:…”

Section: Mathematical Task Settingmentioning

confidence: 99%

Study of Fast Relaxing Excitations Caused by Ultrashort Laser Pulses in Nanoscale Domain

Еремин¹,

Trubitsyn²,

Кудинов³

et al. 2017

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

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Abstract-By using the heat balance equation and a modified Fourier law's formula considering the relaxation of heat flow and temperature gradient, a model of the local non-equilibrium process of plate heating with ultrashort laser pulses, modelled by heat flow of time-variable second-class boundary conditions, step (discontinuous) time function, was developed. The research showed that consideration of non-locality results in the delayed plate heatup irrespective of the laser radiation flow intensity. This fact is explained by the resistance caused by the medium to the process of change of its temperature condition, which increases as the relaxation factor grows. It was also shown that in consideration of the relaxation phenomena, the boundary conditions (first-, second-and third-class) may not be fulfilled immediately -they may be set only within a definite range of the initial time section. Therefore, the immediate implementation of the boundary condition is impossible since the value of the heat transfer factor has a definite limit, depending on the relaxation properties of the medium, which may not be exceeded under any conditions of heat exchange with the medium. The relations are given which allow establishing such laser radiation flow change patterns at which the wall surface temperature would remain set and constant over time.

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“…For deriving the differential heat ignition equation, considering local not-equilibrium, let us represent the Fourier law formula in the form of [8]:…”

Section: Mathematical Task Settingmentioning

confidence: 99%

Study of Fast Relaxing Excitations Caused by Ultrashort Laser Pulses in Nanoscale Domain

Еремин¹,

Trubitsyn²,

Кудинов³

et al. 2017

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

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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%

“…Considering relation (9), a differential equation was obtained in work [9] with formulating the boundary problem describing pressure variation in elastic fluid under the hydraulic impact conditions. The mathematical problem definition in this case is as follows: …”

Section: Mathematical Model For Pressure Variation In Incompressimentioning

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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“…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%

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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Mathematical Simulation of the Locally Nonequilibrium Heat Transfer in a Body with Account for its Nonlocality in Space and Time

Cited by 27 publications

References 8 publications

Study of Fast Relaxing Excitations Caused by Ultrashort Laser Pulses in Nanoscale Domain

Study of Fast Relaxing Excitations Caused by Ultrashort Laser Pulses in Nanoscale Domain

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

Nonlocal model of velocity vibrations compressed fluid under conditions hydraulic impact

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