Ballistic-Diffusive Heat Conduction in Thin Films by Phonon Monte Carlo Method: Gray Medium Approximation Versus Phonon Dispersion

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Han-Ling Li ◽  
Junichiro Shiomi ◽  
Bing-Yang Cao
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Monte Carlo ◽  
Heat Conduction ◽  
Temperature Profile ◽  
Flux Distribution ◽  
Phonon Dispersion ◽  
Weighted Average ◽  
Heat Flux Distribution ◽  
Gray Medium

Abstract The gray medium approximation treating all phonons with an averaged and representative mean-free-path (MFP) is an often used method in analyzing ballistic-diffusive heat conduction at nanoscale. However, whether there exists a reasonable value of the average MFP which effectively represents the entire spectrum of modal MFPs remains unclear. In this paper, phonon Monte Carlo (MC) method is employed to study the effects of the gray medium approximation on ballistic-diffusive heat conduction in silicon films by comparing with dispersion MC simulations. Four typical ways for calculating the average MFP with gray medium approximation are investigated. Three of them are based on the weighted average of the modal MFPs, and the remaining one is based on the weighted average of the reciprocals of the modal MFPs. The first three methods are found to be good at predicting effective thermal conductivity and heat flux distribution, but have difficulties in temperature profile, while the last one performs better for temperature profile than effective thermal conductivity and heat flux distribution. Therefore, none of the average MFPs can accurately characterize all the features of ballistic-diffusive heat conduction for the gray medium approximation. Phonon dispersion has to be considered for the accurate thermal analyses and modeling of ballistic-diffusive heat transport. Our work could be helpful for further understanding of phonon dispersion and more careful use of the gray medium approximation.

Anharmonicity Dependent Heat Conduction in One-Dimensional Lattices

2013 ◽  
Vol 209 ◽  
pp. 129-132 ◽  
Author(s):  
Shreya Shah ◽  
Tejal N. Shah ◽  
P.N. Gajjar
Keyword(s):  
Thermal Conductivity ◽  
Numerical Simulation ◽  
Heat Flux ◽  
Heat Conduction ◽  
Temperature Gradient ◽  
Temperature Profile ◽  
Chain Length ◽  
Interparticle Interactions ◽  
One Dimensional ◽  
Harmonic Chain

The temperature profile, heat flux and thermal conductivity are investigated for the chain length of 67 one-dimensional (1-D) oscillators. FPU-β and FK models are used for interparticle interactions and substrate interactions, respectively. As harmonic chain does not produce temperature gradient along the chain, it is required to introduce anharmonicity in the numerical simulation. The anharmonicity dependent temperature profile, thermal conductivity and heat flux are simulated for different strength of anharmonicity β = 0, 0.1, 0.3, 0.5, 0.7, 0.9 and 1. It is concluded that heat flux obeys J = 0.3947 e0.553β with R2 = 0.9319 and thermal conductivity obeys κ = 0.0276 e0.5559β with R2 = 0.9319.

2D divertor heat flux distribution using a 3D heat conduction solver in National Spherical Torus Experiment

2013 ◽  
Vol 84 (2) ◽  
pp. 023505 ◽  
Author(s):  
K. F. Gan ◽  
J-W. Ahn ◽  
J.-W. Park ◽  
R. Maingi ◽  
A. G. McLean ◽  
...  
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Flux Distribution ◽  
Heat Flux Distribution ◽  
Spherical Torus

Determination of Outside Heating Distribution Using an Inverse Algorithm for an Industry Hydrothermal Autoclave With Three-Dimensional Flows

2004 ◽  
Author(s):  
Hongmin Li ◽  
Minel J. Braun ◽  
G.-X. Wang ◽  
Edward A. Evans
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fluid Flow ◽  
Heat Conduction ◽  
Flux Distribution ◽  
Cfd Simulation ◽  
Three Dimensional ◽  
Heat Flux Distribution ◽  
Inverse Algorithm ◽  
Small Magnitude

Hydrothermal growth is the industry method of preference to obtain high quality single crystals. Due to the high pressure and high temperature growth conditions, growth process is carried out in closed containers. During a growth run, the only flow and heat transfer that control crystal growers have is the outside heating. An inverse algorithm, used to obtain the heating distribution for an autoclave with a two-dimensional flow, is further developed and used to determine the heating distribution for an industry autoclave with three-dimensional flows. A cross-section area average temperature distribution is set as a target. With the three steps, including CFD simulation of the fluid flow, heat conduction in the metal wall, and heat conduction in the insulation layer, the heater heat flux distribution is determined. The distributions appear close to linear from the median height to the top/bottom with small magnitude deviation in the circumferential direction. Linearly distributed heaters, based on the determined heat flux distribution, are then used and heat transfer and fluid flow is numerically simulated with a conjugate model. The achieved temperature agrees well with the targeted one. The distribution and heating rates of linearly distributed heaters can be applied to industry autoclaves.

On the Analysis of Short-Pulse Laser Heating of Metals Using the Dual Phase Lag Heat Conduction Model

2009 ◽  
Vol 131 (11) ◽  
Author(s):  
K. Ramadan ◽  
W. R. Tyfour ◽  
M. A. Al-Nimr
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Laser Heating ◽  
Flux Distribution ◽  
Heat Losses ◽  
Phase Lag ◽  
Dual Phase ◽  
Heat Flux Distribution ◽  
Conduction Model ◽  
Initial Heat

Transient heat conduction in a thin metal film exposed to short-pulse laser heating is studied using the dual phase lag heat conduction model. The initial heat flux distribution in the film, resulting from the temporal distribution function of the laser pulse, together with the zero temperature gradients at the boundaries normally used in literature with the presumption that they are equivalent to negligible boundary heat losses is analyzed in detail in this paper. The analysis presented here shows that using zero temperature gradients at the boundaries within the framework of the dual phase lag heat conduction model does not guarantee negligible boundary heat losses unless the initial heat flux distribution is negligibly small. Depending on the value of the initial heat flux distribution, the presumed negligible heat losses from the boundaries can be even way larger than the heat flux at any location within the film during the picosecond laser heating process. Predictions of the reflectivity change of thin gold films due to a laser short heat pulse using the dual phase lag model with constant phase lags are found to deviate considerably from the experimental data. The dual phase lag model is found to overestimate the transient temperature in the thermalization stage of the laser heating process of metal films, although it is still superior to the parabolic and hyperbolic one-step models.

The Numerical Investigation on Optical Efficiency and Heat Flux Distribution of Conical Cavity Receiver

2011 ◽  
Vol 347-353 ◽  
pp. 1530-1536 ◽  
Author(s):  
Fu Qiang Wang ◽  
He Ping Tan ◽  
Yong Shuai
Keyword(s):  
Heat Flux ◽  
Monte Carlo ◽  
Ray Tracing ◽  
Flux Distribution ◽  
Efficiency Analysis ◽  
Heat Flux Distribution ◽  
Conical Cavity ◽  
Optical Efficiency ◽  
Slope Error ◽  
The Impact

Optical efficiency analysis of conical cavity receiver is introduced in this receiver. Monte-Carlo ray tracing codes was developed to analyze the optical efficiency and heat flux distribution of conical cavity receiver with aperture radius variation. Besides, the impact of slope error variation on the optical efficiency and heat flux distribution are also investigated. The numerical results show that inverted conical cavity receiver with optimized aperture radius has the highest optical efficiency.

Heat Flux Distribution Over a Solar Central Receiver Using an Aiming Strategy Based on a Conventional Closed Control Loop

2017 ◽  
Author(s):  
Jesús García ◽  
Yen Chean Soo Too ◽  
Ricardo Vasquez Padilla ◽  
Rodrigo Barraza Vicencio ◽  
Andrew Beath ◽  
...  
Keyword(s):  
Heat Flux ◽  
Flux Distribution ◽  
Thermal Stresses ◽  
Control Strategies ◽  
Multiple Input Multiple Output ◽  
Control Loop ◽  
Heat Flux Distribution ◽  
Input Multiple Output ◽  
Solar Receiver ◽  
Solar Field

Solar thermal towers are a maturing technology that have the potential to supply a significant part of energy requirements of the future. One of the issues that needs careful attention is the heat flux distribution over the central receiver’s surface. It is imperative to maintain receiver’s thermal stresses below the material limits. Therefore, an adequate aiming strategy for each mirror is crucial. Due to the large number of mirrors present in a solar field, most aiming strategies work using a data base that establishes an aiming point for each mirror depending on the relative position of the sun and heat flux models. This paper proposes a multiple-input multiple-output (MIMO) closed control loop based on a methodology that allows using conventional control strategies such as those based on Proportional Integral Derivative (PID) controllers. Results indicate that even this basic control loop can successfully distribute heat flux on the solar receiver.

Studies on heat flux distribution on the membrane walls in a 600 MW supercritical arch-fired boiler

2016 ◽  
Vol 103 ◽  
pp. 264-273 ◽  
Author(s):  
Dalong Zhang ◽  
Chenwei Meng ◽  
Hai Zhang ◽  
Pengyuan Liu ◽  
Zhouhang Li ◽  
...  
Keyword(s):  
Heat Flux ◽  
Flux Distribution ◽  
Heat Flux Distribution
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