comsol presentation
TRANSCRIPT
Efficient Calculation of Phonon ThermalConductivity for 2-D Nanocomposites with
Randomly Distributed Inclusions
Vidya Bachina, Gang Li
Department of Mechanical EngineeringClemson University
November 19, 2009
G. LI [email protected] ASME IMECE 2009 Nov 2009 1 / 12
Outline g
I IntroductionI Numerical Effective Medium Approximation Approach
I General modelI Modified Bulk Thermal ConductivitiesI Thermal Boundary Resistance
I Numerical Results
I Conclusion
G. LI [email protected] ASME IMECE 2009 Nov 2009 2 / 12
Introduction g
Thermal transport in nanocompositesHot Cold
Thermal transport
Modeling Challenges
I Multiscale
I Unique physics
Modeling Approaches
I Accuracy: Molecular Dynamics (MD) >Boltzmann Transport Equation (BTE) >Effective Medium Approximation (EMA)
I Computational cost: MD>BTE>EMA
G. LI [email protected] ASME IMECE 2009 Nov 2009 3 / 12
Introduction g
Effective Medium Approximation (EMA) for Nanocomposites (Minnich andChen, APL, 2007)
I Modification of a classical EMAI Good accuracy compared to the BTE/Monte Carlo solutionsI Analytical modelI Difficult when there are multiple inclusion materials with non-uniform
sizes and shapes.
G. LI [email protected] ASME IMECE 2009 Nov 2009 4 / 12
Numerical Effective Medium Approximation Approach g
I General approachmodified effective k (inclusions)
modified effective k (host)
thermal boundary resistance
G. LI [email protected] ASME IMECE 2009 Nov 2009 5 / 12
Numerical Effective Medium Approximation Approach g
Modifying the bulk thermal conductivity of inclusion materials
I Model 1 (Minnich and Chen, 2007)
k =1
3CvΛ
1
Λeff=
1
Λb+
1
d
for general shapes d = 4Ac/P, Ac : cross sectional area of theinclusion; P: perimeter of the inclusion.
I Model 2 (Xue, 2006)
keff =kb
1 + 2Rk/d
Rk : Kapitza resistance
G. LI [email protected] ASME IMECE 2009 Nov 2009 6 / 12
Numerical Effective Medium Approximation Approach g
Modifying the bulk thermal conductivity of inclusion materials
I Model 3 (Zhang, 2007)
keff
kb=
(1 +
kn
(1− 4kn)−1
)−1
kn > 5
keff
kb=
(1 +
kn
m
)−1
kn < 1
kn: Knudsen number, m: cross-sectional shape parameter
G. LI [email protected] ASME IMECE 2009 Nov 2009 7 / 12
Numerical Effective Medium Approximation Approach g
Modifying the bulk thermal conductivity of the host material (Minnich andChen, 2007)
1
Λeff=
1
Λb+
1
Λcoll(Φ)
Φ: interface density ⇐ obtained from the mesh geometry
Thermal boundary resistance
k1eff
∂T1
∂n1= k2
eff
∂T2
∂n2= β (T1 − T2)γ
G. LI [email protected] ASME IMECE 2009 Nov 2009 8 / 12
Results g
I Size effects
0 50 100 150 200 250 3005
10
15
20
25
30
35
40
45
Inclusion Size (nm)
The
rmal
Con
duct
ivity
(W
/mK
)
Model 1Model 2Model 3BTE
Si20Ge80 nanocomposite Thermal conductivity
G. LI [email protected] ASME IMECE 2009 Nov 2009 9 / 12
Results g
I Shape effects
0 50 100 150 200 250 3005
10
15
20
25
30
35
40
45
Inclusion Size (nm)
The
rmal
Con
duct
ivity
(W
/mK
)
Model 1Model 2Model 3BTE
0 50 100 150 200 250 3005
10
15
20
25
30
35
40
45
Inclusion Size (nm)
The
rmal
Con
duct
ivity
(W
/mK
)
Model 1BTE
Square cross section Circular cross section
G. LI [email protected] ASME IMECE 2009 Nov 2009 10 / 12
Conclusion g
I A numerical EMA method is developed for thermalconductivity analysis of nanocomposites
I Various bulk thermal conductivity modification models aretested and compared
I The numerical approach is more general and can account forthe shape, size and distribution effects of the inclusions.
G. LI [email protected] ASME IMECE 2009 Nov 2009 12 / 12