382 THERMAL SPREADING AND CONTACT RESISTANCES1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [382],122 Lines
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[381],(121)
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N number ofsides in a polygon, dimensionless
number ofdiscrete sources, dimensionless number ofmicrocontacts, dimensionless
N(k) numerator function, dimensionless
n counter, dimensionless
Hertz elastic parameter, dimensionless combination parameter, dimensionless contact spot density, 1/m2
pressure, N/m2or Pa
P g,∞ reference gas pressure, N/m2or Pa
P m mean contact area pressure, N/m2or Pa
Pr Prandtl number, dimensionless
Q heat transfer rate, W
Q g gap heat transfer rate, W
R thermal resistance, K/W
R g thermal resistance ofgap, K/W
Rmac macroscopic thermal resistance ofgap, K/W
Rmic microscopic thermal resistance ofgap, K/W
R r radiation resistance, K/W
R∗ combination ofterms, dimensionless
R∗ combination ofterms, dimensionless
R∗
j combination ofterms, dimensionless
R∗
r combination ofterms, dimensionless
r radial coordinate, m
S f material yield or flow stress, N/m2
s side dimension, m
T g gas molecule temperature, K
T g,∞ reference temperature, K
∆T temperature drop or difference, K
∆T j joint temperature drop, K
T area-averaged temperature, K
T1 temperature, K
T2 temperature, K
t layer thickness, m
thickness ofelastic layer, m time, s
t1 layer 1 thickness, m
thickness ofisotropic plate, m
t2 layer 2 (substrate) thickness, m
u local gap thickness, dimensionless
position, dimensionless
w(x,y) total local displacement, m
Trang 2382 THERMAL SPREADING AND CONTACT RESISTANCES
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[382],(122)
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w o approach ofcontacting bodies due to loading, m
X c coordinate ofcenter ofeccentric rectangular area, m
x length coordinate, m
Y mean plane separation, m
Y c coordinate ofcenter ofeccentric rectangular area, m
length coordinate, m
z length coordinate, m
Greek Letter Symbols
α ratio ofsemimajor axes, dimensionless
thermal diffusivity, m2/s thermal conductivity ratio, dimensionless accommodation parameter or coefficient, dimensionless
α1 accommodation coefficient, dimensionless
α2 accommodation coefficient, dimensionless
β combination ofterms, dimensionless
fluid property parameter, dimensionless
βm,n eigenvalue, dimensionless
Γ(x) gamma function of argumentx, dimensionless
γ aspect ratio parameter, dimensionless
ratio ofspecific heats, dimensionless
γT combination ofterms, dimensionless
∆ change in, dimensionless
physical parameter, m2/N
δ local gap thickness, m
δ0 local gap thickness under zero-load conditions, m
δm eigenvalue, dimensionless
δn eigenvalues ofJ n (x), dimensionless
radius ratio, dimensionless ellipse aspect ratio, dimensionless emissivity ofhemisphere, dimensionless emissivity ofdisk, dimensionless relative contact spot size, dimensionless
c contact strain, dimensionless
ζ ellipsoidal coordinate, m
dummy variable, dimensionless
θ temperature excess, K
θ area averaged temperature rise, K
θ(r,z) temperature excess field, K
θ(τ) ellipsoidal temperature rise, K
θo centroid temperature rise, K
θs temperature rise due to spreading, K
κ parameter, dimensionless
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[383],(123)
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thermal conductivity ratio, dimensionless
Λ mean free path length of gas molecules, m
Λg molecular mean free path length at reference temperature, m
Λo reference value of mean free path length, m
λ dummy variable, dimensions vary
relative mean free path length, dimensionless
λ1 combination ofterms, dimensionless
λ2 combination ofterms, dimensionless
λn eigenvalue, dimensionless
µ dynamic viscosity, N· s2/m
positive root ofan equation, dimensionless molecular weight ratio, dimensionless
ν arbitrary order ofBessel function, dimensionless
Poisson’s ratio, dimensionless
ξ length ratio, dimensionless
ρ radius ofcurvature, m
radius ofelastic hemisphere, m
ρn,e boundary condition parameter, dimensionless
1 rectangular aspect ratio, dimensionless
combination ofterms, dimensionless
σ Stefan–Boltzmann constant, 5.67 × 10−8W/m2· K4
effective surface roughness, m or microns
τ thickness, dimensionless
τ1 thickness, dimensionless
τ2 thickness, dimensionless
τ∗ combination ofterms, dimensionless
combination ofterms, dimensionless
φn combination ofterms, dimensionless
ϕ combination ofterms, dimensionless
ϕ+ layer parameter, dimensionless
ϕ− layer parameter, dimensionless
ψ combination ofterms, dimensionless
spreading resistance, dimensionless spreading–constriction parameter, dimensionless amplitude angle, rad
ψmac macroscopic spreading–constriction parameter, dimensionless
ψmic microscopic spreading–constriction parameter, dimensionless
ψo combination ofterms, dimensionless
ψn combination ofterms, dimensionless
ψe,i combination ofterms, dimensionless
ψ∗ thermal elasto constriction parameter, dimensionless
ψ12 dimensional spreading resistance in layer–substrate
∇2 Laplacian operator, 1/m2
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Subscripts
active area contact
circle circle
e elastic contact radius
ei layer thickness parameter
ep elastic–plastic radius ellipse ellipse
g, ∞ gas conductivity under continuum conditions
1 layer one layer
2 layer two layers
mean
counter
n, e combination ofterms
p plastic contact radius
polymer
q layer thickness parameter
r radiation or radiative
thin layer source area source source
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o value at centroid ofarea
Superscripts
i identifies ith source parameter
q isoflux boundary condition
T isothermal boundary condition
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