Temperature Distribution through a Nanofilm by Means of a Ballistic-Diffusive Approach
Abstract
:1. Introduction
2. Methods: Constitutional Equation for Ballistic Heat Transport
3. Temperature Distribution in Nanoscaled Materials
3.1. Two-Temperature Model
3.2. Boundary and Initial Conditions
3.3. Comparison with Fourier and Cattaneo Laws
3.4. Numerical Method
4. Results
4.1. Temperature Distribution of the Two-Temperature Model
4.2. Temperature Distribution of the Fourier and Cattaneo Laws with an Effective Thermal Conductivity
5. Discussion
6. Conclusions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Symbols | |
heat capacity per unit volume [J/m3K] | |
correction factor | |
entropy flux [Wm/K] | |
wavenumber vector | |
Knudsen number | |
mean free path [m] | |
characteristic length [m] | |
heat flux [W/m2] | |
heat flux of order n [W/m2(m/s)n−1] | |
position vector | |
source term [W/m3] | |
entropy per unit volume [J/Km3] | |
temperature [K] | |
time [s] | |
dimensionless time | |
internal energy per unit volume [J/m3] | |
phonon velocity [m/s] | |
spatial coordinate [m] | |
dimensionless spatial coordinate | |
Greek symbols | |
rate of entropy production [W/K] | |
dimensionless temperature | |
thermal conductivity [W/Km] | |
relaxation time [s] | |
Subscript | |
initial state | |
ballistic | |
Cattaneo | |
diffusive | |
effective value | |
Fourier | |
Upperscript | |
Fourier transformed variable |
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Machrafi, H. Temperature Distribution through a Nanofilm by Means of a Ballistic-Diffusive Approach. Inventions 2019, 4, 2. https://doi.org/10.3390/inventions4010002
Machrafi H. Temperature Distribution through a Nanofilm by Means of a Ballistic-Diffusive Approach. Inventions. 2019; 4(1):2. https://doi.org/10.3390/inventions4010002
Chicago/Turabian StyleMachrafi, Hatim. 2019. "Temperature Distribution through a Nanofilm by Means of a Ballistic-Diffusive Approach" Inventions 4, no. 1: 2. https://doi.org/10.3390/inventions4010002
APA StyleMachrafi, H. (2019). Temperature Distribution through a Nanofilm by Means of a Ballistic-Diffusive Approach. Inventions, 4(1), 2. https://doi.org/10.3390/inventions4010002