January 2025
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19 Reads
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1 Citation
International Journal of Heat and Mass Transfer
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January 2025
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19 Reads
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1 Citation
International Journal of Heat and Mass Transfer
November 2024
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52 Reads
Fast and accurate predictions of the spatiotemporal distributions of temperature are crucial to the multi-scale thermal management and safe operation of microelectronic devices. To realize it, an efficient semi-implicit Lax-Wendroff kinetic scheme is developed for numerically solving the transient phonon Boltzmann transport equation (BTE) from the ballistic to diffusive regime. The phonon BTE at the cell center is discretized under the framework of finite volume method, where the trapezoidal and midpoint rules are used to deal with the temporal integration of phonon scattering and convection terms, respectively. For the reconstruction of the interfacial distribution function, the phonon BTE at the cell interface is discretized in the form of finite difference method and solved numerically, where second-order upwind and central scheme are used to deal with the spatial interpolation and gradient of interfacial distribution function, respectively. The macroscopic governing equations are invoked for the evolution of macroscopic fields at both the cell center and interface, where the macroscopic flux is obtained by taking the moment of the interfacial distribution function. Numerical results show that the present scheme could accurately predict the steady/unsteady heat conduction in solid materials from the ballistic to diffusive regime, and its time and cell size are not limited by the relaxation time and phonon mean free path. The present work could provide a useful tool for the efficient predictions of the macroscopic spatiotemporal distributions in the multi-scale thermal engineering.
August 2024
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113 Reads
Efficiently capturing the three-dimensional spatiotemporal distributions of temperature is of great significance for alleviating hotspot issues in 3D FinFETs. However, most previous thermal simulations mainly focused on the steady-state problem with continuous heating. Few studies are conducted for the transient thermal conduction in 3D FinFETs with non-continuous heating, which is actually closer to the reality. To investigate the effects of heating strategies on the transient micro/nano scale thermal conduction in 3D FinFETs, three heating strategies are considered, including `Continuous', `Intermittent' and `Alternating' heating. A comparison is made between the phonon BTE solutions and the data predicted by the macroscopic diffusion equation, where the effect of boundary scattering on phonon transport is added into the effective thermal conductivity. Numerical results show that it is not easy to accurately capture the heat conduction in 3D FinFETs by the macroscopic diffusion equation, especially near the hotspot areas where ballistic phonon transport dominates and the temperature diffusion is no longer valid. Different heating strategies have great influence on the peak temperature rise and transient thermal dissipation process. Compared to `Intermittent' or `Continuous' heating, the temperature variance of `Alternating' heating is smaller.
January 2024
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206 Reads
A synthetic iterative scheme is developed for thermal applications in hotspot systems with large temperature variance. Different from previous work with linearized equilibrium state and small temperature difference assumption, the phonon equilibrium distribution shows a nonlinear relationship with temperature and mean free path changes with the spatial temperature when the temperature difference of system is large, so that the same phonon mode may suffer different transport processes in different geometric regions. In order to efficiently capture nonlinear and multiscale thermal behaviors, the Newton method is used and a macroscopic iteration is introduced for preprocessing based on the iterative solutions of the stationary phonon BTE. Macroscopic and mesoscopic physical evolution processes are connected by the heat flux, which is no longer calculated by classical Fourier's law but obtained by taking the moment of phonon distribution function. These two processes exchange information from different scales, such that the present scheme could efficiently deal with heat conduction problems from ballistic to diffusive regime. Numerical tests show that the present scheme could efficiently capture the multiscale heat conduction in hotspot systems with large temperature variances. In addition, a comparison is made between the solutions of the present scheme and effective Fourier's law by several heat dissipations problems under different sizes or selective phonon excitation. Numerical results show that compared to the classical Fourier's law, the results of the effective Fourier's law could be closer to the BTE solutions by adjusting effective coefficients. However, it is still difficult to capture some local nonlinear phenomena in complex geometries.
October 2022
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19 Reads
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3 Citations
Frontiers of Physics
In this paper, we numerically studied the late-time evolutional mechanism of three-dimensional (3D) single-mode immiscible Rayleigh—Taylor instability (RTI) by using an improved lattice Boltzmann multiphase method implemented on graphics processing units. The influences of extensive dimensionless Reynolds numbers and Atwood numbers on phase interfacial dynamics, spike and bubble growth were investigated in details. The longtime numerical experiments indicate that the development of 3D singlemode RTI with a high Reynolds number can be summarized into four different stages: linear growth stage, saturated velocity growth stage, reacceleration stage and turbulent mixing stage. A series of complex interfacial structures with large topological changes can be observed at the turbulent mixing stage, which always preserve the symmetries with respect to the middle axis for a low Atwood number, and the lines of symmetry within spike and bubble are broken as the Atwood number is increased. Five statistical methods for computing the spike and bubble growth rates were then analyzed to reveal the growth law of 3D single-mode RTI in turbulent mixing stage. It is found that the spike late-time growth rate shows an overall increase with the Atwood number, while the bubble growth rate experiences a slight decrease with the Atwood number at first and then basically maintains a steady value of around 0.1. When the Reynolds number decreases, the later stages cannot be reached gradually and the evolution of phase interface presents a laminar flow state. [Figure not available: see fulltext.].
January 2022
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90 Reads
Rayleigh-Taylor instability (RTI) as a multi-scale, strongly nonlinear physical phenomenon which plays an important role in the engineering applications and scientific research. In this paper, the mesoscopic lattice Boltzmann method is used to numerically study the late-time evolutional mechanism of three-dimensional (3D) single-mode RTI and the influences of extensive dimensionless Reynolds number and Atwood number on phase interfacial dynamics, spike and bubble growth are investigated in details. For a high Reynolds number, it is reported that the development of 3D single-mode RTI would undergo four different stages: linear growth stage, saturated velocity growth stage, reacceleration stage and turbulent mixing stage. A series of complex interfacial structures with large topological changes can be observed at the turbulent mixing stage, which always preserve the symmetries with respect to the middle axis at a low Atwood number, and the lines of symmetry within spike and bubble are broken as the Atwood number is increased. Five statistical methods for computing the spike and bubble growth rates are then analyzed to reveal the growth law of 3D single-mode RTI in turbulent mixing stage. It is found that the spike late-time growth rate shows an overall increase with the Atwood number, while the bubble growth rate seems to be independence of the Atwood number, approaching a constant of around 0.1. When the Reynolds number decreases, the later stages cannot be reached gradually and the evolution of phase interface presents a laminar flow state.
December 2021
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35 Reads
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8 Citations
International Journal of Thermal Sciences
In this paper, the saturated pool boiling heat transfer from a heated circular surface is investigated numerically based on the popular lattice Boltzmann phase-change method. The crucial interfacial phenomena, including the bubble growth, departure, coalescence, and rising under different wall superheats, wettabilities, and heater sizes are studied, and the corresponding heat transfer characteristics within these bubble dynamics are also revealed. The numerical experiments indicate that at low wall superheats the bubble nucleation occurs only at the top of the heated circle. With the increase in the wall superheat, the sides and the bottom of the heated circle also become nucleate sites. As the wall superheats continue to increase, more and more nucleate sites are activated so that the heated circle is wrapped by the vapor film early in the boiling process. And the average heat flux varies periodically with time corresponding to bubble dynamics in nucleation boiling regime. It reaches a steady state of film boiling regime after the stable vapor film is generated from the heated circular. It is also found that hydrophobic surface is conducive to the onset of boiling. However, it leads to a low critical heat flux and incurs film boiling at a lower wall superheat, which is also observed in both experimental and numerical studies. On the other hand, the boiling regimes can undergo the transition from nucleate boiling regime to film boiling regime at the same wall superheat with the increase in the heater size. In addition, under various wall superheats and wettabilities, the bubble departure diameters from the circular surface are smaller than those from the flat surface, while the bubble departure periods from the circular surface are less than those from the flat surface one. Finally, the saturated boiling curves from the circular surface for different wall wettabilities, heater sizes, liquid–vapor density ratios, and heating modes are also achieved.
July 2020
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73 Reads
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21 Citations
Communications in Nonlinear Science and Numerical Simulation
Fractional phase field models have been reported to suitably describe the anomalous two-phase transport in heterogeneous porous media, evolution of structural damage, and image inpainting process. It is commonly different to derive their analytical solutions, and the numerical solution to these fractional models is an attractive work. As one of the popular fractional phase-field models, in this paper we propose a fresh lattice Boltzmann (LB) method for the fractional Cahn-Hilliard equation. To this end, we first transform the fractional Cahn-Hilliard equation into the standard one based on the Caputo derivative. Then the modified equilibrium distribution function and proper source term are incorporated into the LB method in order to recover the targeting equation. Several numerical experiments, including the circular disk, quadrate interface, droplet coalescence and spinodal decomposition, are carried out to validate the present LB method. It is shown that the numerical results at different fractional orders agree well with the analytical solution or some available results. Besides, it is found that increasing the fractional order promotes a faster evolution of phase interface in accordance with its physical definition, and also the system energy predicted by the present LB method conforms to the energy dissipation law.
June 2020
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71 Reads
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8 Citations
Entropy
Time evolution features of kinetic and thermal entropy generation rates in turbulent Rayleigh-Bénard (RB) convection with mixed insulating and conducting boundary conditions at Ra = 109 are numerically investigated using the lattice Boltzmann method. The state of flow gradually develops from laminar flow to full turbulent thermal convection motion, and further evolves from full turbulent thermal convection to dissipation flow in the process of turbulent energy transfer. It was seen that the viscous, thermal, and total entropy generation rates gradually increase in wide range of t/τ < 32 with temporal evolution. However, the viscous, thermal, and total entropy generation rates evidently decrease at time t/τ = 64 compared to that of early time. The probability density function distributions, spatial-temporal features of the viscous, thermal, and total entropy generation rates in the closed system provide significant physical insight into the process of the energy injection, the kinetic energy, the kinetic energy transfer, the thermal energy transfer, the viscous dissipated flow and thermal dissipation.
... A mainstream engineering treatment method is to adopt a 3D heat diffusion equation with an effective thermal conductivity which takes into account the size effect [14,15,17,12,18,19,20]. This method is widely used in many industrial softwares such as TCAD, ANSYS and COMOSL. ...
January 2025
International Journal of Heat and Mass Transfer
... Under the condition of small Atwood number, Wei et al. employed the lattice Boltzmann model to study the effect of rotation effect on the small-scale characteristics and scaling rules of three-dimensional (3D) turbulent RT instability mixing region [29]. Using an improved lattice Boltzmann polyphase method implemented on graphics processing units, Liu et al. numerically studied the late evolution mechanism of 3D single-mode immiscible RT instability, the effects of a wide range of Reynolds number and Atwood number on phase interface dynamics, spikes and bubble growth were investigated [30]. ...
October 2022
Frontiers of Physics
... In addition to the extensive investigation of planar heaters in pool boiling systems, dedicated research focused specifically on heated wires has also been conducted [28][29][30][31][32][33][34]. Hu et al. [28] experimentally investigated the heat transfer phenomenon of a heated wire during the pool boiling process and showed that the application of a self-rewetting fluid as an operating fluid achieves a 2.52-time improvement in the CHF value compared to that obtained when using water. ...
December 2021
International Journal of Thermal Sciences
... Lee et al. [27] proposed an LB method for incompressible binary fluids, modeling contact line dynamics on partially wetting surfaces. Liang et al. [28] enhanced numerical stability with a multiple-relaxation-time LB method for incompressible multiphase flows, and Liang et al. [29] proposed an LB method for solving the fractional CH equation, integrating modified equilibrium distribution functions and appropriate source terms to simplify and effectively model complex systems with fractional derivatives. Although these works have demonstrated the potential of phase-field-based LB method in multiphase flow simulations, they have primarily focused on classical models. ...
July 2020
Communications in Nonlinear Science and Numerical Simulation
... where f i is the velocity distribution function, f eq i is the equilibrium distribution function, F i is the discrete force term, c i is the discrete velocity vector, x is the position of a particle, d t is a discrete time step, and s � is the relaxation time of f i : The equilibrium distribution function f eq i can be expressed as [22]: ...
June 2020
Entropy