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International Journal of Thermophysics

, Volume 27, Issue 1, pp 171–183 | Cite as

Estimation of Thermal Contact Resistance Using Ultrasonic Waves

  • P. Z. Cong
  • X. Zhang
  • M. Fujii
Article

Abstract

In this paper, numerical simulations of both the three-dimensional heat conduction and two-dimensional elastic wave propagation at the interface of contact solids have been carried out. Numerical results of heat conduction simulations show that both the true contact area and thermal contact conductance increase linearly with an increase in the contact pressure. Numerical results of the ultrasonic wave propagation show that the intensity of a transmitted wave is very weak but depends clearly on the contact pressure. On the other hand, the intensity of reflected wave amounts to more than 99% of the standard reflected wave that results from the case of one cylindrical specimen without contact. However, the intensity of the modified reflected wave defined by the difference between the reflected wave and standard reflected wave shows the same tendency as that of the transmitted wave. The intensities of both transmitted and modified reflected waves could be expressed by the same power function of the contact pressure. By comparing the results of heat conduction with those of ultrasonic propagation calculations, a power functional correlation between the thermal contact conductance and transmitted or modified reflected intensity has been obtained. Using this correlation, it will be possible to estimate the thermal contact conductance between two solids through measuring the intensity of either reflected or transmitted ultrasonic waves.

Keywords

nondestructive measurement numerical simulation thermal contact conductance thermal contact resistance ltrasonic wave 

Nomenclature

A

dimensionless true contact area

B

dimensionless scale factor

D

diameter of specimen (m)

E

Young’s modulus (Pa)

\(\overline e_{zz}\)

dimensionless area averaged strain in Z-direction

H

height of specimen (m)

Hm

dimensionless thermal contact conductance

k

thermal conductivity of specimen

Li

dimensionless wavelength of surface roughness

li

wavelength of surface roughness (m)

M

grid number in radial direction

N

grid number in peripheral direction

n

upper limit number of superposed waves

P

dimensionless mean nominal contact pressure

p

mean nominal contact pressure (Pa)

Ps

dimensionless amplitude of source function

q

heat flux (W·m−2)

R

dimensionless radius in cylindrical coordinates

r

radius in cylindrical coordinates (m)

R0

dimensionless radius of specimen

Ra

mean roughness (m)

RND

random number

Rmax

maximum roughness (m)

t

time (s)

Tc

temperature at the top surface (K)

tp

duration of pulse (s)

U

dimensionless displacement in R-direction

u

displacement in r-direction (m)

W

dimensionless displacement in Z-direction

w

displacement in z-direction (m)

Z

dimensionless axis in cylindrical coordinates

z

axis in cylindrical coordinates

Zs(R,θ)

dimensionless height of surface roughness

αi

orientation

Δ

difference between the strain of reflected wave and SRW

Er,Et

ratios of intensities of transmitted and modified reflected to the intensity of SRW

θ

angle in cylindrical coordinates

Λ, M

dimensionless lamé constants

λ, μ

Lamé constants (Pa)

σrr

normal stress in the r-direction

σrz

shearing stress in the r-direction

σz,r

shearing stress in the z-direction

σz,z

normal stress in the z-direction

τ

dimensionless time

ρ

density of specimens (kg·m−3)

Φ

dimensionless density of specimen

φi

initial phase

Subscripts

 

0

standard reflected wave

I

specimen I

II

specimen II

i

number

min

minimum

max

maximum

r

reflected wave

t

transmitted wave

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References

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Interdisciplinary Graduate School of Engineering SciencesKyushu UniversityKasugaJapan
  2. 2.Institute for Materials Chemistry and EngineeringKyushu UniversityKasugaJapan

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