Thermal resistance

The thermal resistance R (formerly ) is the resistance that a homogeneous component or, in the case of multi-layer components, a homogeneous component layer opposes the heat flow at a temperature difference of 1 Kelvin on an area of 1 m² between its surfaces. It is the reciprocal of the heat transfer coefficient (heat transfer coefficient) . ${\ displaystyle 1 / \ Lambda}$

definition

The thermal resistance characterizes the ratio of the thickness to the thermal conductivity of a component and is defined as the reciprocal of the thermal conductivity coefficient. The higher the thermal resistance, the better the thermal insulation properties of the component or a layer.

calculation

The thermal resistance is calculated from the quotient of the thickness d and the thermal conductivity ( coefficient of thermal conductivity) of the material of a homogeneous component. In the case of components made up of several homogeneous layers, their individual resistances add up. ${\ displaystyle \ lambda}$

{\ displaystyle R = {\ frac {d} {\ lambda}}}

or.

{\ displaystyle R = {\ frac {d_ {1}} {\ lambda _ {1}}} + {\ frac {d_ {2}} {\ lambda _ {2}}} + \ ldots + {\ frac { d_ {n}} {\ lambda _ {n}}} = \ sum \ left ({\ frac {d} {\ lambda}} \ right)}

The unit of measurement for this is (m² · K) / W

For inhomogeneous components, an approximation method (averaging from an upper and a lower limit value) is used at the level of thermal resistance . This takes into account the heat conduction at the building material boundaries and enables a sufficiently precise determination of the thermal resistance established over the entire component. The calculation method is standardized in ISO 6946: 2005-06 Section 6.2

application

In the DIN 4108 standard and legislation on thermal protection, requirements regarding the thermal resistance for individual components are specified on the one hand; on the other hand, it is included in the calculation of the U-value (formerly: k-value) of the building envelope , with which the energy requirement of a building can be calculated.

Thermal transmittance

The heat transfer resistance is the reciprocal of the heat transfer coefficient, also the heat transfer coefficient , (according to DIN 4108-1:, today without a symbol). The heat transfer coefficient results from the material-related thermal conductivity which is divided by the corresponding layer thickness d of the material. ${\ displaystyle \ Lambda}$ ${\ displaystyle \ lambda}$

{\ displaystyle \ Lambda = {\ frac {1} {R}} = {\ frac {\ lambda} {d}}}

The unit of measurement for this is W / (m² · K)

The heat transfer coefficient indicates the amount of heat in joules per second (J / s) - that is the heat output in watts - which passes through 1 m² of a material with a certain thickness ( d ) if the temperature difference between the two surfaces is 1 Kelvin. The higher the thermal transmittance, the worse the thermal insulation properties of the layer.

Derivation of the heat transfer coefficient

The heat transfer coefficient can be determined by integrating the differential equations of the heat flux density ${\ displaystyle q}$

{\ displaystyle q = - \ lambda {\ frac {\ mathrm {d} \ theta} {\ mathrm {d} x}} \ quad {\ text {and}} \ quad {\ frac {\ mathrm {d} ^ {2} \ theta} {\ mathrm {d} x ^ {2}}} = 0}

to ( here is a constant of integration) ${\ displaystyle q \ cdot x = - \ lambda \ cdot \ theta + C}$ ${\ displaystyle C}$

and continue to

{\ displaystyle q = {\ frac {\ lambda} {d}} \ left (\ theta _ {1} - \ theta _ {2} \ right)}

With

{\ displaystyle \ Delta \ theta = 1}

can be derived. The heat transfer coefficient is equal to the heat flow density q for a temperature difference of 1k between the component surfaces and thus a measure of the passage of heat through a homogeneous material layer of a certain thickness if both sides have a temperature difference of 1 Kelvin. The heat transfer coefficient in W / (m² · K) is a specific parameter of a material of a certain thickness d .

Forward resistance and volume resistance

The addition of the total thermal resistance of the material layers of a component and the thermal resistance ( both outer sides) results in the thermal resistance (total resistance of the thermal migration from one side to the other).

Heat gangs resistance = heat let resistors + heat transition resistances.

swell

↑ ^a ^b Lutz, Jenisch, Klopfer, Freymuth, Krampf: Textbook of building physics. Stuttgart 1989, p. 147ff.

↑ WM Willems, K. Schild, S. Dinter: Handbuch der Bauphysik part 1. Wiesbaden 2006, S. 2.17f

Norms

EN ISO 6946 Building components - Thermal resistance and thermal transmittance - Calculation method
EN ISO 7345 , as DIN: 1996-01 Thermal protection - physical quantities and definitions
EN ISO 9346 Thermal insulation - Mass transfer - Physical quantities and definitions

Web links

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: 10/1999. ( Web document , PDF 168 KB)

[Teubner-1] Lutz, Jenisch, Klopfer, Freymuth, Krampf: Textbook of building physics. Stuttgart 1989, p. 147ff.