Thermal conductivity

"K value" redirects here. For the force constant of a spring, see Hooke's law. In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the

In physics, thermal conductivity, $k$ , is the property of a material that indicates its ability to conduct heat. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. A Materials property is an intensive, often Quantitative property of a material usually with a unit that may be used as a metric In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature It appears primarily in Fourier's Law for heat conduction. Heat conduction or thermal conduction is the spontaneous transfer of thermal energy through matter from a region of higher Temperature to a region of lower Heat conduction or thermal conduction is the spontaneous transfer of thermal energy through matter from a region of higher Temperature to a region of lower

First, we define heat conduction by the formula:

$H=\frac{\Delta Q}{\Delta t}=k\times A\times\frac{\Delta T}{x}$

where $\frac{\Delta Q}{\Delta t}$ is the rate of heat flow, k is the thermal conductivity, A is the total surface area of conducting surface, ΔT is temperature difference and x is the thickness of conducting surface separating the 2 temperatures. Heat conduction or thermal conduction is the spontaneous transfer of thermal energy through matter from a region of higher Temperature to a region of lower

Thus, rearranging the equation gives thermal conductivity,

$k=\frac{\Delta Q}{\Delta t}\times\frac{1}{A}\times\frac{x}{\Delta T}$

(Note: $\frac{\Delta T}{x}$ is the temperature gradient)

In other words, it is defined as the quantity of heat, ΔQ, transmitted during time Δt through a thickness x, in a direction normal to a surface of area A, due to a temperature difference ΔT, under steady state conditions and when the heat transfer is dependent only on the temperature gradient.

Alternately, it can be thought of as a flux of heat (energy per unit area per unit time) divided by a temperature gradient (temperature difference per unit length)

$k=\frac{\Delta Q}{A\times{} \Delta t}\times\frac{x}{\Delta T}$

Typical units are SI: W/(m·K) and English units: Btu·ft/(h·ft²·°F). In the various subfields of Physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks English unit is the American name for a unit in one of a number of systems of Units of measurement, some obsolete and some still in use in present-day USA, the To convert between the two, use the relation 1 Btu·ft/(h·ft²·°F) = 1. 730735 W/(m·K). [Perry's Chemical Engineers' Handbook, 7th Edition, Table 1-4]

1 Examples
2 List of thermal conductivities
3 Measurement
- 3.1 Standard Measurement Techniques
4 Difference between US and European notation
5 Related terms
6 Textile industry
7 Origins
8 See also
9 External links
10 References

Examples

In metals, thermal conductivity approximately tracks electrical conductivity according to the Wiedemann-Franz law, as freely moving valence electrons transfer not only electric current but also heat energy. The M acro E xpansion T emplate A ttribute L anguage complements TAL, providing macros which allow the reuse of code across Electrical conductivity or specific conductivity is a measure of a material's ability to conduct an Electric current. In Physics, the Wiedemann-Franz law states that the ratio of the Thermal conductivity ( K) to the Electrical conductivity ( &sigma) In chemistry valence electrons are the Electrons contained in the outermost or valence, Electron shell of an Atom. However, the general correlation between electrical and thermal conductance does not hold for other materials, due to the increased importance of phonon carriers for heat in non-metals. In Physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the Atomic lattice of a Solid As shown in the table below, highly electrically conductive silver is less thermally conductive than diamond, which is an electrical insulator. Silver (ˈsɪlvɚ is a Chemical element with the symbol " Ag " (argentum from the Ancient Greek: ἀργήντος - argēntos gen In Mineralogy, diamond is the allotrope of carbon where the carbon atoms are arranged in An insulator, also called a Dielectric, is a material that resists the flow of Electric current.

Thermal conductivity depends on many properties of a material, notably its structure and temperature. For instance, pure crystalline substances exhibit very different thermal conductivities along different crystal axes, due to differences in phonon coupling along a given crystal axis. In Materials science, a crystal is a Solid in which the constituent Atoms Molecules or Ions are packed in a regularly ordered repeating Sapphire is a notable example of variable thermal conductivity based on orientation and temperature, for which the CRC Handbook reports a thermal conductivity of 2. Sapphire (antique greek hyacinthos refers to gem varieties of the mineral Corundum, an Aluminium oxide (Al2O3 when it is a color other than 6 W/(m·K) perpendicular to the c-axis at 373 K, but 6000 W/(m·K) at 36 degrees from the c-axis and 35 K (possible typo?).

Air and other gases are generally good insulators, in the absence of convection. Convection in the most general terms refers to the movement of molecules within Fluids (i Therefore, many insulating materials function simply by having a large number of gas-filled pockets which prevent large-scale convection. Examples of these include expanded and extruded polystyrene (popularly referred to as "styrofoam") and silica aerogel. Polystyrene ˌpɒliˈstaɪriːn ( IUPAC Polyphenylethene is an aromatic Polymer made from the aromatic Monomer Styrene Aerogel is a low-density solid-state material derived from Gel in which the liquid component of the gel has been replaced with gas Natural, biological insulators such as fur and feathers achieve similar effects by dramatically inhibiting convection of air or water near an animal's skin. Feathers are one of the epidermal growths that form the distinctive outer covering or Plumage, on Birds They are considered the most complex integumentary structures

Thermal conductivity is important in building insulation and related fields. Building insulation refers broadly to any object in a building used as Insulation for any purpose However, materials used in such trades are rarely subjected to chemical purity standards. Several construction materials' k values are listed below. These should be considered approximate due to the uncertainties related to material definitions.

The following table is meant as a small sample of data to illustrate the thermal conductivity of various types of substances. For more complete listings of measured k-values, see the references.

List of thermal conductivities

Main article: List of thermal conductivities

This is a list of approximate values of thermal conductivity, k, for some common materials. In Physics, thermal conductivity, k is the Intensive property of a material that indicates its ability to conduct Heat. Please consult the list of thermal conductivities for more accurate values, references and detailed information. In Physics, thermal conductivity, k is the Intensive property of a material that indicates its ability to conduct Heat.

Material	Thermal conductivity W/(m·K)
Cement, portland ^[1]	0. Materials are physical Substances used as inputs to production or Manufacturing. The watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic In the most general sense of the word a cement is a binder a substance which sets and hardens independently and can bind other materials together 29
Concrete, stone ^[1]	1. Concrete is a construction material composed of Cement (commonly Portland cement) as well as other cementitious materials such as Fly ash and Slag 7
Air	0. Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five 025
Wood	0. Wood is hard fibrous lignified structural tissue produced as secondary Xylem in the stems of Woody plants notably trees but also shrubs 04 - 0. 4
Alcohols and oils	0. In Chemistry, an alcohol is any Organic compound in which a Hydroxyl group ( - O[[hydrogen H]]) is bound to a Carbon An oil is a substance that is in a viscous Liquid state ( "oily") at ambient temperatures or slightly warmer and is 1 - 0. 21
Silica Aerogel	0. Aerogel is a low-density solid-state material derived from Gel in which the liquid component of the gel has been replaced with gas 004-0. 03
Soil	1. Soil, often typeset as SOiL, is a four piece rock band from Chicago Illinois United States founded by Shaun Glass Tom Schofield Tim King and Adam Zadel 5
Rubber	0. 16
Epoxy (unfilled)	0. In Chemistry, epoxy or polyepoxide is a Thermosetting Epoxide Polymer that cures (polymerizes and crosslinks when mixed with a 19
Epoxy (silica-filled)	0. In Chemistry, epoxy or polyepoxide is a Thermosetting Epoxide Polymer that cures (polymerizes and crosslinks when mixed with a 30
Water (liquid)	0. Water is a common Chemical substance that is essential for the survival of all known forms of Life. 6
Thermal grease	0. Thermal grease (also called thermal compound, heat paste, heat transfer compound, thermal paste, or 7 - 3
Thermal epoxy	1 - 4
Glass	1. In Chemistry, epoxy or polyepoxide is a Thermosetting Epoxide Polymer that cures (polymerizes and crosslinks when mixed with a Glass in the common sense refers to a Hard, Brittle, transparent Solid, such as that used for Windows many 1
Ice	2
Sandstone	2. Ice is a Solid phase, usually crystalline, of a Non-metalic substance that is liquid or gas at Room temperature, such as Ammonia Sandstone is a Sedimentary rock composed mainly of Sand -size Mineral or rock grains. 4
Stainless steel^[2]	12. In Metallurgy, stainless steel is defined as a Steel Alloy with a minimum of 11 11 ~ 45. 0
Lead	35. Characteristics Lead has a dull luster and is a dense, Ductile, very soft highly 3
Aluminium	237
Gold	318
Copper	401
Silver	429
Diamond	900 - 2320
LPG	0. WikipediaNaming Gold (ˈɡoʊld is a Chemical element with the symbol Au (from its Latin name aurum) and Atomic number 79 Copper (ˈkɒpɚ is a Chemical element with the symbol Cu (cuprum and Atomic number 29 Silver (ˈsɪlvɚ is a Chemical element with the symbol " Ag " (argentum from the Ancient Greek: ἀργήντος - argēntos gen In Mineralogy, diamond is the allotrope of carbon where the carbon atoms are arranged in 23 - 0. 26

Measurement

Main article: Thermal conductivity measurement

Generally speaking, there are a number of possibilities to measure thermal conductivity, each of them suitable for a limited range of materials, depending on the thermal properties and the medium temperature. Two classes of methods exist to measure the thermal conductivity of a sample steady-state and non-steady-state methods There can be made a distinction between steady-state and transient techniques.

In general the steady-state techniques perform a measurement when the temperature of the material that is measured does not change with time. This makes the signal analysis straight forward (steady state implies constant signals). The disadvantage generally is that it takes a well-engineered experimental setup. The Divided Bar (various types) is the most common device used for consolidated rock samples.

The transient techniques perform a measurement during the process of heating up. The advantage is that measurements can be made relatively quickly. Transient methods are usually carried out by needle probes (inserted into samples or plunged into the ocean floor).

For good conductors of heat, Searle's bar method can be used. [1] For poor conductors of heat, Lees' disc method can be used. [2] An alternative traditional method using real thermometers is described at [3]. A brief review of new methods measuring thermal conductivity, thermal diffusivity and specific heat within a single measurement is available at [4]. In Heat transfer analysis thermal diffusivity (symbol \alpha\ but note that the symbols \kappa D and k are all commonly A thermal conductance tester, one of the instruments of gemology, determines if gems are genuine diamonds using diamond's uniquely high thermal conductivity. Gemology ( gemmology outside the United States) is the Science, Art and Profession of identifying and evaluating Gemstones A gemstone or gem, also called a precious or semi-precious stone, is a piece of attractive Mineral, which &mdash when cut and polished &mdash In Mineralogy, diamond is the allotrope of carbon where the carbon atoms are arranged in

Standard Measurement Techniques

IEEE Standard 442-1981, "IEEE guide for soil thermal resistivity measurements" see als soil_thermal_properties [5]

IEEE Standard 98-2002, "Standard for the Preparation of Test Procedures for the Thermal Evaluation of Solid Electrical Insulating Materials", ISBN 0-7381-3277-2 [6]

ASTM Standard D5470-06, "Standard Test Method for Thermal Transmission Properties of Thermally Conductive Electrical Insulation Materials" [7]

ASTM Standard E1225-04, "Standard Test Method for Thermal Conductivity of Solids by Means of the Guarded-Comparative-Longitudinal Heat Flow Technique" [8]

ASTM Standard D5930-01, "Standard Test Method for Thermal Conductivity of Plastics by Means of a Transient Line-Source Technique" [9]

ASTM Standard D2717-95, "Standard Test Method for Thermal Conductivity of Liquids" [10]

Difference between US and European notation

In Europe, the k-value of construction materials (e. The thermal properties of soil are a component of Soil physics that has found important uses in Engineering, Climatology and Agriculture. g. window glass) is called λ-value.

U-value used to be called k-value in Europe, but is now also called U-value. The R value or R-value is a measure of Thermal resistance (K·m²/W used in the building and Construction industry

K-value (with capital k) refers in Europe to the total isolation value of a building. K-value is obtained by multiplying the form factor of the building (= the total inward surface of the outward walls of the building divided by the total volume of the building) with the average U-value of the outward walls of the building. K-value is therefore expressed as (m². m^-3). (W. K^-1. m^-2) = W. K^-1. m^-3. A house with a volume of 400 m³ and a K-value of 0. 45 (the new European norm. It is commonly referred to as K45) will therefore theoretically require 180 W to maintain its interior temperature 1 degree K above exterior temperature. So, to maintain the house at 20°C when it is freezing outside (0°C), 3600 W of continuous heating is required.

Related terms

The reciprocal of thermal conductivity is thermal resistivity, measured in kelvin-metres per watt (K·m·W⁻¹). The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second.

When dealing with a known amount of material, its thermal conductance and the reciprocal property, thermal resistance, can be described. Unfortunately there are differing definitions for these terms.

First definition (general)

For general scientific use, thermal conductance is the quantity of heat that passes in unit time through a plate of particular area and thickness when its opposite faces differ in temperature by one degree. For a plate of thermal conductivity k, area A and thickness L this is kA/L, measured in W·K⁻¹ (equivalent to: W/°C). Thermal conductivity and conductance are analogous to electrical conductivity (A·m⁻¹·V⁻¹) and electrical conductance (A·V⁻¹). Analogy is both the cognitive process of transferring Information from a particular subject (the analogue or source to another particular subject (the target and Electrical conductivity or specific conductivity is a measure of a material's ability to conduct an Electric current. Electrical conductance is a measure of how easily Electricity flows along a certain path through an Electrical element.

There is also a measure known as heat transfer coefficient: the quantity of heat that passes in unit time through unit area of a plate of particular thickness when its opposite faces differ in temperature by one degree. The heat transfer coefficient, in Thermodynamics and in mechanical and Chemical engineering, is used in calculating the Heat transfer, typically The reciprocal is thermal insulance. In summary:

thermal conductance = kA/L, measured in W·K⁻¹
- thermal resistance = L/kA, measured in K·W⁻¹ (equivalent to: °C/W)
heat transfer coefficient = k/L, measured in W·K⁻¹·m⁻²
- thermal insulance = L/k, measured in K·m²·W⁻¹.

The heat transfer coefficient is also known as thermal admittance

Thermal Resistance

When thermal resistances occur in series, they are additive. So when heat flows through two components each with a resistance of 1 °C/W, the total resistance is 2 °C/W.

A common engineering design problem involves the selection of an appropriate sized heat sink for a given heat source. A heat sink (or heatsink) is an environment or object that absorbs and dissipates heat from another object using Thermal contact (either direct or radiant Working in units of thermal resistance greatly simplifies the design calculation. The following formula can be used to estimate the performance:

$R_{hs} = \frac {\Delta T}{P_{th}} - R_s$

where:

R_hs is the maximum thermal resistance of the heat sink to ambient, in °C/W
$Δ T$ is the temperature difference (temperature drop), in °C
P_th is the thermal power (heat flow), in Watts
R_s is the thermal resistance of the heat source, in °C/W

For example, if a component produces 100 W of heat, and has a thermal resistance of 0. 5 °C/W, what is the maximum thermal resistance of the heat sink? Suppose the maximum temperature is 125 °C, and the ambient temperature is 25 °C; then the $Δ T$ is 100 °C. The heat sink's thermal resistance to ambient must then be 0. 5 °C/W or less.

Second definition (buildings)

When dealing with buildings, thermal resistance or R-value means what is described above as thermal insulance, and thermal conductance means the reciprocal. The R value or R-value is a measure of Thermal resistance (K·m²/W used in the building and Construction industry For materials in series, these thermal resistances (unlike conductances) can simply be added to give a thermal resistance for the whole.

A third term, thermal transmittance, incorporates the thermal conductance of a structure along with heat transfer due to convection and radiation. Convection in the most general terms refers to the movement of molecules within Fluids (i Thermal radiation is Electromagnetic radiation emitted from the surface of an object which is due to the object's Temperature. It is measured in the same units as thermal conductance and is sometimes known as the composite thermal conductance. The term U-value is another synonym.

In summary, for a plate of thermal conductivity k (the k value ^[3]), area A and thickness L:

thermal conductance = k/L, measured in W·K⁻¹·m⁻²;
thermal resistance (R value) = L/k, measured in K·m²·W⁻¹;
thermal transmittance (U value) = 1/(Σ(L/k)) + convection + radiation, measured in W·K⁻¹·m⁻². Addition is the mathematical process of putting things together Convection in the most general terms refers to the movement of molecules within Fluids (i Thermal radiation is Electromagnetic radiation emitted from the surface of an object which is due to the object's Temperature.

Textile industry

In textiles, a tog value may be quoted as a measure of thermal resistance in place of a measure in SI units. The tog is a measure of Thermal resistance, commonly used in the Textile industry, and often seen quoted on for example Duvets The Shirley Institute

Origins

The thermal conductivity of a system is determined by how atoms comprising the system interact. There are no simple, correct expressions for thermal conductivity. There are two different approaches for calculating the thermal conductivity of a system.

The first approach employs the Green-Kubo relations. Green–Kubo relations give exact mathematical expression for transport coefficients in terms of integrals of time correlation functions Although this employs analytic expressions which in principle can be solved, in order to calculate the thermal conductivity of a dense fluid or solid using this relation requires the use of molecular dynamics computer simulation.

The second approach is based upon the relaxation time approach. Due to the anharmonicity within the crystal potential, the phonons in the system are known to scatter. In Physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the Atomic lattice of a Solid There are three main mechanisms for scattering:

Boundary scattering, a phonon hitting the boundary of a system;
Mass defect scattering, a phonon hitting an impurity within the system and scattering;
Phonon-phonon scattering, a phonon breaking into two lower energy phonons or a phonon colliding with another phonon and merging into one higher energy phonon.

Further information can be found in the publication "The Physics of Phonons" by G P Srivastava.

External links

Table with the Thermal Conductivity of the Elements
http://physics.nist.gov/Pubs/SP811/appenB9.html
http://www.npl.co.uk/thermal/faq_index.html#heat%20transfer%20property thermophysics FAQ5
http://www.ornl.gov/roofs+walls/research/detailed_papers/rastra/dynamic.htm
http://www.tak2000.com/data2.htm
http://thermophys.savba.sk
Calculation of the Thermal Conductivity of Glass Calculation of the Thermal Conductivity of Glass at Room Temperature from the Chemical Composition
http://www.mathisinstruments.com/index.asp?pathinfo=/html/content/technology/tech_glossary.asp&dbbypass=
Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air

References

Callister, William (2003). Heat conduction or thermal conduction is the spontaneous transfer of thermal energy through matter from a region of higher Temperature to a region of lower In thermal physics, heat transfer is the passage of Thermal energy from a hot to a colder body In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature The R value or R-value is a measure of Thermal resistance (K·m²/W used in the building and Construction industry Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity A thermal bridge is created when materials that are poor insulators come in contact allowing heat to flow through the path created In Physics, thermal contact conductance is the study of Heat conduction between Solid bodies in contact In Heat transfer analysis thermal diffusivity (symbol \alpha\ but note that the symbols \kappa D and k are all commonly Thermal resistance is the Temperature difference across a structure when a unit of Heat energy flows through it in unit Time. A thermistor is a type of Resistor with resistance varying according to its Temperature. In Electrical engineering and industry thermocouples are a widely used type of temperature sensor and can also be used as a means to convert thermal Potential Electrical conductivity or specific conductivity is a measure of a material's ability to conduct an Electric current. "Appendix B", Materials Science and Engineering - An Introduction. John Wiley & Sons, INC, 757. ISBN 0-471-22471-5.
Halliday, David; Resnick, Robert; & Walker, Jearl(1997). Fundamentals of Physics (5th ed. ). John Wiley and Sons, INC. , NY ISBN 0-471-10558-9.
TM 5-852-6 AFR 88-19, Volume 6 (Army Corp of Engineers publication)
Srivastava G. P (1990), "The Physics of Phonons. " Adam Hilger, IOP Publishing Ltd, Bristol.

© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
network: | |

Contents