View source for Thermal contact conductance

{{Short description|The study of heat conduction between solid bodies in thermal contact}}
In [[physics]], '''thermal contact conductance''' is the study of [[heat conduction]] between [[solid]] or liquid bodies in [[thermal contact]]. The '''thermal contact conductance coefficient''', <math>h_c</math>, is a property indicating the [[thermal conductivity]], or ability to conduct [[heat]], between two bodies in contact. The inverse of this property is termed '''thermal contact resistance'''.

==Definition==
[[Image:Contact conductance.svg|right|thumb|295px|Fig. 1: Heat flow between two solids in contact and the temperature distribution.]]

When two solid bodies come in contact, such as A and B in Figure 1, heat flows from the hotter body to the colder body. From experience, the [[temperature]] profile along the two bodies varies, approximately, as shown in the figure. A temperature drop is observed at the interface between the two surfaces in contact. This phenomenon is said to be a result of a ''thermal contact resistance'' existing between the contacting surfaces. Thermal contact resistance is defined as the ratio between this temperature drop and the average heat flow across the interface.<ref>{{cite book
  | last = Holman
  | first = J. P.
  | title = Heat Transfer, 8th Edition
  | publisher = [[McGraw-Hill]]
  | year = 1997}}</ref>

According to '''[[Fourier's law]]''', the heat flow between the bodies is found by the relation:
{{NumBlk|:|<math>q=-kA\frac{dT}{dx}</math>|{{EquationRef|1}}}}

where <math>q</math> is the heat flow, <math>k</math> is the thermal conductivity, <math>A</math> is the cross sectional area and <math>dT/dx</math> is the temperature gradient in the direction of flow.

From considerations of [[energy conservation]], the heat flow between the two bodies in contact, bodies A and B, is found as:
{{NumBlk|:|<math>q=\frac{T_1 - T_3}{X_A/(k_A A)+1/(h_c A) + X_B/(k_B A)}</math>|{{EquationRef|2}}}}

One may observe that the heat flow is directly related to the thermal conductivities of the bodies in contact, <math>k_A</math> and <math>k_B</math>, the contact area <math>A</math>, and the thermal contact resistance, <math>1/h_c</math>, which, as previously noted, is the inverse of the thermal conductance coefficient, <math>h_c</math>.

==Importance==
Most experimentally determined values of the thermal contact resistance fall between
0.000005 and 0.0005 m<sup>2</sup> K/W (the corresponding range of thermal contact
conductance is 200,000 to 2000 W/m<sup>2</sup> K). To know whether the thermal contact resistance is significant or not,  magnitudes of the thermal resistances of the layers are compared with typical values of thermal contact resistance. Thermal contact resistance is significant and may dominate for good heat conductors such as metals but can be neglected for poor heat conductors such as insulators.<ref>{{cite book|title=Introduction to Thermodynamics and Heat Transfer|author=Çengel}}</ref>
Thermal contact conductance is an important factor in a variety of applications, largely because many physical systems contain a [[mechanics|mechanical]] combination of two materials. Some of the fields where contact conductance is of importance are:<ref>{{cite journal
  | first = L. S.
  | last = Fletcher
  | title = Recent Developments in Contact Conductance Heat Transfer
  | journal = Journal of Heat Transfer
  | volume = 110
  | pages = 1059–1070
  | date = November 1988| issue = 4b
 | doi = 10.1115/1.3250610
 | bibcode = 1988ATJHT.110.1059F
  }}</ref><ref>{{cite book
  | last = Madhusudana
  | first = C. V.
  |author2=Ling, F. F.
   | title = Thermal Contact Conductance
  | publisher = [[Springer Science+Business Media|Springer]]
  | year = 1995}}</ref><ref>{{cite journal
  | last = Lambert
  | first = M. A.
  |author2=Fletcher, L. S.
   | title = Thermal Contact Conductance of Spherical Rough Metals
  | journal = Journal of Heat Transfer
  | date = November 1997| volume = 119
 | issue = 4
 | pages = 684–690
 | doi = 10.1115/1.2824172
 }}</ref>
* [[Electronics]]
** [[Electronic packaging]]
** [[Heat sink]]s
** Brackets
* Industry
** [[Nuclear reactor]] cooling
** [[Gas turbine]] cooling
** [[Internal combustion engines]]
** [[Heat exchangers]]
** [[Thermal insulation]]
** [[Press hardening]] of automotive steels
* [[Flight]]
** [[Hypersonic]] flight [[vehicles]]
** Thermal supervision for [[space]] vehicles
* [[Building science|Residential/building science]]
** Performance of [[building envelope]]s

==Factors influencing contact conductance==
[[Image:Solids in contact.svg|right|thumb|150px|Fig. 2: An enlargement of the interface between two contacting surfaces. The finish quality is exaggerated for the sake of the argument.]]
Thermal contact conductance is a complicated phenomenon, influenced by many factors. Experience shows that the most important ones are as follows:

===Contact pressure===
For thermal transport between two contacting bodies, such as particles in a granular medium, the contact [[pressure]] is the factor of most influence on overall contact conductance. As contact pressure grows, true contact area increases and contact conductance grows (contact resistance becomes smaller).<ref name="fusion">{{cite journal| last1=Gan| first1=Y| last2=Hernandez|first2=F |display-authors=etal |title=Thermal Discrete Element Analysis of EU Solid Breeder Blanket Subjected to Neutron Irradiation| journal= Fusion Science and Technology| year=2014| volume=66|issue=1| pages=83–90 | doi=10.13182/FST13-727| arxiv=1406.4199| bibcode=2014FuST...66...83G| s2cid=51903434}}</ref>

Since the contact pressure is the most important factor, most studies, [[correlation]]s and [[mathematical model]]s for measurement of contact conductance are done as a function of this factor.

The thermal contact resistance of certain sandwich kinds of materials that are manufactured by rolling under high temperatures may sometimes be ignored because the decrease in thermal conductivity between them is negligible.

===Interstitial materials===
{{main|interstitial defect}}
No truly smooth surfaces really exist, and surface imperfections are visible under a [[microscope]]. As a result, when two bodies are pressed together, contact is only performed in a [[Asperity (materials science)|finite number of points]], separated by relatively large gaps, as can be shown in Fig. 2. Since the actual contact area is reduced, another resistance for heat flow exists. The [[gas]]es/[[fluids]] filling these gaps may largely influence the total heat flow across the interface. The thermal conductivity of the interstitial material and its pressure, examined through reference to the [[Knudsen number]], are the two properties governing its influence on contact conductance, and thermal transport in heterogeneous materials in general.<ref name="fusion" />

In the absence of interstitial materials, as in a [[vacuum]], the contact resistance will be much larger, since flow through the intimate contact points is dominant.

===Surface roughness, waviness and flatness===
One can characterise a surface that has undergone certain [[surface finishing|finishing]] operations by  three main properties of: roughness, [[waviness]], and [[fractal dimension]]. Among these, roughness and fractality are of most importance, with roughness often indicated in terms of a [[root mean square|rms]] value, <math>\sigma</math> and surface fractality denoted generally by ''D<sub>f</sub>''. The effect of surface structures on thermal conductivity at interfaces is analogous to the concept of [[electrical contact resistance]], also known as [[electrical contact resistance|ECR]], involving contact patch restricted transport of [[phonons]] rather than electrons.

===Surface deformations===
When the two bodies come in contact, surface [[Deformation (engineering)|deformation]] may occur on both bodies. This deformation may either be [[Plastic deformation of solids|plastic]] or [[Deformation (engineering)#Elastic deformation|elastic]], depending on the material properties and the contact pressure. When a surface undergoes plastic deformation, contact resistance is lowered, since the deformation causes the actual contact area to increase<ref>{{cite journal
  | last = Williamson
  | first = M.
  |author2=Majumdar, A.
   | title = Effect of Surface Deformations on Contact Conductance
  | journal = Journal of Heat Transfer
  | date = November 1992| volume = 114
 | issue = 4
 | pages = 802–810
 | doi = 10.1115/1.2911886
 }}</ref><ref>{{cite journal
  | last = Heat Transfer Division
  | title = Conduction in Solids - Steady State, Imperfect Metal-to-Metal Surface Contact
  | journal = General Electric Inc.
  | date = November 1970}}</ref>

===Surface cleanliness===
The presence of [[dust]] [[wiktionary:Particle|particles]], [[acids]], etc., can also influence the contact conductance.

==Measurement of thermal contact conductance==
Going back to Formula 2, calculation of the thermal contact conductance may prove difficult, even impossible, due to the difficulty in measuring the contact area, <math>A</math> (A product of surface characteristics, as explained earlier). Because of this, contact conductance/resistance is usually found experimentally, by using a standard apparatus.<ref>ASTM D 5470 – 06 Standard Test Method for Thermal Transmission Properties of Thermally Conductive Electrical Insulation Materials</ref>

The results of such experiments are usually published in [[Engineering]] [[literature]], on [[Scientific journal|journal]]s such as ''[http://scitation.aip.org/ASMEJournals/HeatTransfer/ Journal of Heat Transfer]'', ''[http://www.elsevier.com/wps/find/journaldescription.cws_home/210/description#description International Journal of Heat and Mass Transfer]'', etc. Unfortunately, a centralized [[database]] of contact conductance coefficients does not exist, a situation which sometimes causes companies to use outdated, irrelevant data, or not taking contact conductance as a consideration at all.

''[http://sourceforge.net/projects/cocoe/ CoCoE]'' (Contact Conductance Estimator), a project founded to solve this problem and create a centralized database of contact conductance data and a computer program that uses it, was started in [[2006 in science|2006]].

==Thermal boundary conductance==

While a finite thermal contact conductance is due to voids at the interface, surface waviness, and surface roughness, etc.,  a finite conductance exists even at near ideal interfaces as well.  This conductance, known as [[Interfacial thermal resistance|thermal boundary conductance]], is due to the differences in electronic and vibrational properties between the contacting materials.  This conductance is generally much higher than thermal contact conductance, but becomes important in nanoscale material systems.

==See also==
* [[Heat transfer]]

==References==
<references/>

==External links==
* [http://sourceforge.net/projects/cocoe/ Project CoCoE] - Free software to estimate TCC

[[Category:Heat conduction]]
[[Category:Thermodynamics]]
[[Category:Physical quantities]]
[[Category:Heat transfer]]