phenomenon

thermal boundary resistance

Resistance to heat flow at interfaces between materials, often measured at microscopic scales.
17 related articles · 3 formulas

Description

Thermal boundary resistance, also known as Kapitza resistance, is the resistance to heat flow that occurs at the interface between two different materials. Even when two surfaces are in perfect contact, the difference in their atomic vibrations (phonons) and electronic properties makes it difficult for heat to pass directly across the boundary. This effect becomes especially significant at microscopic scales, where interfaces dominate the overall thermal behavior of a system.

History

The effect was first characterized by Peter Kapitza in 1941 while studying heat transfer between liquid helium and solid copper, and it is sometimes called Kapitza resistance.

How it works

Heat is carried through solids primarily by phonons (quantized lattice vibrations) and electrons. At an interface, a phonon arriving from one material must either transmit into the other material or reflect back. Because the two materials have different vibrational spectra and acoustic impedances, many phonons are reflected, creating a temperature drop at the boundary. The resistance is quantified as the ratio of this temperature discontinuity to the heat flux across the interface.

In practice

Thermal boundary resistance is a critical factor in cooling microelectronics, such as computer chips, where heat must pass through many material interfaces; it also affects the design of thermal interface materials, thermoelectric devices, and cryogenic systems.

Fun fact

In some cases, thermal boundary resistance can be reduced by adding a thin intermediate layer with intermediate properties, acting like a 'bridge' for phonons.

Concept graph →

Formulas

$$K = -V rac{dP}{dV}$$
Bulk modulus measures resistance to uniform compression.
What is in the formula
Kvariablebulk modulus of the material — bulk modulus pascal
Vvariablevolume of the material — volume cubic metre
Pvariablepressure applied to the material — pressure pascal
dP/dVoperatorinstantaneous rate of change of pressure as volume changes — derivative
k_v=\frac{1}{9}(c_{11}+c_{22}+c_{33}+2(c_{12}+c_{13}+c_{23})) · 2606.25275
$$k_J = \sqrt{\frac{4\pi G \rho}{c_s^2}}$$
Scale where thermal pressure supports against collapse.
What is in the formula
k_JvariableJeans wavenumber — wavenumber reciprocal metre
\rhovariableMass density — mass density kilogram per cubic metre
c_svariableSound speed — speed of sound metre per second
GconstantUniversal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
k_j=\sqrt{\frac{8πgρ_0}{v_t^2}} · 2607.04893
$$\limsup_{n\to\infty} \left| \frac{a_{n+1}}{a_n} \right|$$
The ratio test limit determines series convergence.
What is in the formula
a_nvariablen-th term of the sequence — sequence term
a_{n+1}variable(n+1)-th term of the sequence — sequence term
nvariableindex of the term — index
limsupoperatorlimit superior (largest accumulation point) — limit superior
| |operatorabsolute value (magnitude) — absolute value
\limsup_{n\to\infty}\frac{t_n}{t_{n+1}}\le2 · 2607.00123

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