# 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

1. a b Lutz, Jenisch, Klopfer, Freymuth, Krampf: Textbook of building physics. Stuttgart 1989, p. 147ff.
2. 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