# Heat transfer coefficient

Physical size
Surname Heat transfer coefficient
Formula symbol ${\ displaystyle \ alpha, \, h}$
Size and
unit system
unit dimension
SI W / ( m 2  ·  K ) M · T −3 · Θ −1

The heat transfer coefficient (engl. H for heat transfer coefficient ), and coefficient of heat transfer or heat transfer coefficient called, is a proportionality factor , which the intensity of heat transfer at an interface determined. The heat transfer coefficient in W / (m² · K) is a specific figure for a configuration of materials or from a material to an environment in the form of a fluid . ${\ displaystyle \ alpha}$

Individual disciplines, including building physics , have been using the English formula symbol h since July 1999 due to internationally adapted standards . This fact is taken into account in the corresponding sections. ${\ displaystyle \ alpha}$

## Definition and meaning

The heat transfer coefficient describes the ability of a gas or a liquid to dissipate energy from the surface of a substance or to give it off to the surface. It depends, among other things, on the specific heat capacity , the density and the coefficient of thermal conductivity of the heat- dissipating and heat- supplying medium. The coefficient for thermal conduction is usually calculated using the temperature difference between the media involved.

In contrast to thermal conductivity, the heat transfer coefficient is not a material constant , but - in the case of an environment - strongly dependent on

In the construction industry, heat transfer coefficients are often assumed or specified as a constant. Strictly speaking, this is incorrect because of its dependence on the flow velocity, but it is relatively harmless, because in construction the main thermal resistance is not in the heat transfer, but in the heat transfer through an insulated wall.

## Calculation for heat transfer

{\ displaystyle {\ begin {alignedat} {2} Q & = \ alpha \ times A \ times (T_ {1} -T_ {2}) \ times \ Delta t \ quad \ Leftrightarrow \ quad {\ dot {Q}} & = \ alpha \ cdot A \ cdot (T_ {1} -T_ {2}) \\\ Leftrightarrow \ alpha & = {\ frac {Q} {A \ cdot (T_ {1} -T_ {2}) \ cdot \ Delta t}} & \ alpha = {\ frac {\ dot {Q}} {A \ cdot (T_ {1} -T_ {2})}} \ end {alignedat}}}

With

• Q : amount of heat transferred
• A : considered contact area / wetted surface
• T 1 , T 2 : temperatures of the media involved
• Δt : considered time interval
• ${\ displaystyle {\ dot {Q}}}$: Heat flow

The derived dimension of the heat transfer coefficient in SI units is . ${\ displaystyle {\ frac {\ mathrm {W}} {\ mathrm {m ^ {2} \ cdot K}}} = {\ frac {\ mathrm {kg}} {\ mathrm {s ^ {3} \ cdot K}}}}$

Depending on the direction of heat transfer, Δ Q will assume a positive or negative value.

For boundary layers between solid materials or fluids at rest, the thermal resistance can be specified as an absolute value - in the sense of a material constant independent of the area : ${\ displaystyle R_ {th}}$

${\ displaystyle R_ {th} = {\ frac {1} {\ alpha \ cdot A}} = {\ frac {(T_ {1} -T_ {2}) \ cdot \ Delta t} {Q}}}$in (with - Kelvin , - Watt ).${\ displaystyle \ mathrm {\ frac {K} {W}}}$${\ displaystyle \ mathrm {K}}$${\ displaystyle \ mathrm {W}}$

## Thermodynamic calculations

### Local heat transfer coefficient

Local values ​​of the heat transfer coefficient are important for computer simulations and theoretical considerations. In a thin boundary layer on the wall surface, the flow is laminar and the heat is transported predominantly by conduction . In this case, the local heat transfer coefficient results in ${\ displaystyle \ alpha (x)}$

${\ displaystyle \ alpha _ {\ mathrm {GS}} = {\ frac {\ lambda} {\ delta _ {\ mathrm {T}}}}}$

With

• the thermal conductivity of the fluid at the mean temperature${\ displaystyle \ lambda}$${\ displaystyle T _ {\ mathrm {m}} = {\ frac {T _ {\ mathrm {F}} + T _ {\ mathrm {S}}} {2}}}$
• the fluid temperature in the turbulent mixed area, d. H. outside the laminar boundary layer${\ displaystyle T _ {\ mathrm {F}}}$
• the local surface temperature of the wall (S = solid , solid or surface ).${\ displaystyle T _ {\ mathrm {S}}}$
• the thickness of the thermal boundary layer . In the case of gases it is approximately the same size as the thickness of the flow boundary layer . The boundary layer ratio is a pure function of the Prandtl number and is therefore characteristic of the fluid. As a good approximation (deviation less than 3%):${\ displaystyle \ delta _ {T}}$${\ displaystyle \ delta _ {\ mathrm {T}}}$${\ displaystyle \ delta}$
${\ displaystyle {\ frac {\ delta _ {\ mathrm {T}}} {\ delta}} = {\ frac {1} {\ sqrt [{3}] {Pr}}}}$

The local heat flux density through the boundary layer results from ${\ displaystyle {\ dot {q}} _ {\ mathrm {GS}}}$

${\ displaystyle \ Rightarrow {\ dot {q}} _ {\ mathrm {GS}} = {\ frac {{\ dot {Q}} _ {\ mathrm {GS}}} {A}} = \ alpha _ { \ mathrm {GS}} \ cdot (T _ {\ mathrm {F}} -T _ {\ mathrm {S}}).}$

### Mean heat transfer coefficient

For technical calculations, mean heat transfer coefficients are usually used, which are defined for a given geometry ( assembly ) with the difference between the fluid temperature at the inlet and the mean wall temperature.

The mean heat transfer coefficient is proportional to the dimensionless Nusselt number , which for a given geometry is a pure function of the Reynolds and Prandtl numbers : ${\ displaystyle \ mathrm {Nu}}$

${\ displaystyle \ alpha _ {m} = {\ frac {\ lambda} {L}} \ cdot \ mathrm {Nu} (\ mathrm {Re}, \ mathrm {Pr})}$

With

• the thermal conductivity of the fluid${\ displaystyle \ lambda}$
• the characteristic length (e.g. the diameter of a nozzle )${\ displaystyle L}$
• the dimensionless Reynolds number ${\ displaystyle \ mathrm {Re} = {\ frac {v \ cdot L \ cdot \ rho} {\ eta}}}$
• the characteristic flow velocity of the fluid (e.g. the mean exit velocity from a nozzle)${\ displaystyle v}$
• the density at the arithmetically averaged temperature of the fluid (see above)${\ displaystyle \ rho}$
• the dynamic viscosity ${\ displaystyle \ eta}$
• the dimensionless Prandtl number ${\ displaystyle \ mathrm {Pr} = {\ frac {\ eta \ cdot c_ {p}} {\ lambda}}}$

The representation of the mean heat transfer coefficient by the Nusselt number represents a law of similars in which the respective definition of the characteristic length and the characteristic speed must always be given.

### Free convection

If the flow is due to free convection , the heat transfer coefficient and the Nusselt number depend on the Grashof number .

In this case, the heat transfer coefficient can be approximately determined using the following numerical equations :

• Medium air: ${\ displaystyle \ alpha = 12 \ cdot {\ sqrt {v}} + 2}$
• Medium water: ${\ displaystyle \ alpha = 2100 \ cdot {\ sqrt {v}} + 580,}$

each with the flow speed of the medium in meters per second. ${\ displaystyle v}$

The calculation of the heat transfer coefficient through thermal radiation is much more difficult than in the case of convection.

The following applies to the heat transfer coefficient due to radiation from a black body :

Temperature in ° C −10 0 10 20th 30th
${\ displaystyle h _ {\ mathrm {s0}}}$ in W / (m² K) 4.1 4.6 5.1 5.7 6.3
${\ displaystyle R _ {\ mathrm {se}} = 1 / h _ {\ mathrm {s0}}}$ 0.24 0.22 0.20 0.18 0.16

## Heat transfer coefficient and resistance in construction

English symbolism was introduced in construction some time ago. This is why building physics formulas and calculations have since used the designation h, which differs from the usual spelling .

h is defined as the amount of heat that is transferred over an area of ​​1 m² within 1 second with still air and a temperature difference of 1 Kelvin (between air and component surface). It is added from a convective h c and a radiation component h r ; the proportion from conduction is neglected due to the low thermal conductivity of the air.

${\ displaystyle h = h_ {r} + h_ {c} \}$

A simplified calculation method for determining h r and h c can be found in EN ISO 6946, Appendix A. h r is calculated there according to the Stefan-Boltzmann law from the heat transfer coefficient due to black body radiation and the emissivity of the respective surface material; h c depends on the spatial orientation of the heat flow and, in the case of external surfaces, on the wind speed. Binding values ​​both for h c and for the correction values ​​for different wind speeds are given as constants in Appendix A of the standard - without specifying the derivation. A greatly simplified correction procedure for non-flat surfaces is also specified in the standard.

The reciprocal value 1 / h (previously: 1 / α) is here (deviating from the dimensionless use commonly used in physics as a material constant) according to the standard, the heat transfer resistance R s in (m² · K) / W.

### Heat transfer coefficient for thermally active room enclosures

In the case of thermal component activation - be it as stationary heating / cooling surfaces or as non-stationary working solid storage bodies integrated in the room enclosures (ceilings, floors and / or walls) - the total heat transfer coefficient (convection plus radiation) is due to the relatively small temperature differences between surface and Space for the heat flux density is very meaningful. The complexity of mixed convection ( free and forced convection ), the superimposition of heat transport through radiation and the presence of locally different air and radiation temperatures in the room in relation to the thermally active component surfaces lead to difficulties in determining the overall heat transfer coefficient and to different interpretations of results. In practice, it is advantageous to work with the so-called basic characteristics , as introduced for example in the standardized performance calculation for underfloor heating and also used for the practical cooling ceiling design, since only the room temperature is used as a reference value. The basic characteristic shows the heat flow density of the heating / cooling surface depending on the position of the surface in the room. In the journal “ Gesundheitsingenieur” a general connection between the total heat transfer coefficient and the basic characteristic curves was established.

## Norms

• EN ISO 6946 , as DIN: 2018-03 Components - Thermal resistance and thermal transmittance - Calculation method
• EN ISO 7345 , as DIN: 2018-07 Thermal behavior of buildings and construction materials - physical quantities and definitions
• EN ISO 9346 , as DIN: 2008-02 Heat and humidity behavior of buildings and building materials - Physical parameters for the transport of substances - Terms

## literature

• O. Krischer, W. Kast: The scientific foundations of drying technology . Springer-Verlag, ISBN 3-540-08280-8 .
• H. Martin: Advances in Heat Transfer. Vol. 13. academic Press, New York / San Francisco / London 1977, pp. 1-60.
• S. Polat: Drying Technology. 11, No. 6, 1993, pp. 1147-1176.
• R. Viskanta: Experimental Thermal and Fluid Science. 6, 1993, pp. 111-134.
• B. Glück: Heat transfer coefficients on thermally active component surfaces and the transition to basic characteristics for the heat flow density. In: Health Engineer. Issue 1, 2007, pp. 1–10 (A short version can be found in the free partial report Innovative Heat Transfer and Heat Storage of the PTJ-supervised research network complex LowEx, Report_LowEx, 2008, page 18 ff .; go to the website ).

EN ISO 6946:

• M. Reick, S. Palecki: Extract from the tables and formulas of DIN EN ISO 6946 . Institute for Building Physics and Materials Science. University of Essen. Status: October 1999 ( web document , PDF ; 168 KB).
• G. Bittersmann: Heat transfer through components (k-value) according to ÖNORM EN ISO 6946 . In: LandesEnergieVerein Steiermark LEV (Ed.): Heat balances and key energy figures July 2000 . Graz July 2000, heat transfer resistances, p. 2 f . ( pdf , lev.at [accessed on January 21, 2010]).

## Individual evidence

1. ^ W. Kosler: Manuscript for E DIN 4108-3: 1998-10. German Institute for Standardization, October 28, 1998.
2. a b c d EN ISO 6946; see standards and literature
3. B. Glück: Heat transfer coefficients on thermally active component surfaces and the transition to basic characteristics for the heat flow density. In: Health Engineer. Issue 1, 2007, pp. 1–10 (A short version can be found in the free partial report Innovative Heat Transfer and Heat Storage of the PTJ-supervised research network complex LowEx, Report_LowEx, 2008; go to the website ).