# How are heat transfer and temperature related?

 Building physics formula collection warmth

Chapter 1

Thermal insulation terms

1.1 temperature

Temperature is one of the few basic quantities in physics that cannot be derived from other types of quantities.

As a starting point for temperature scales, fixed temperature points are set that are set during certain well-defined physical processes. For the Celsius scale, fixed points at a pressure of 1.01325 bar are defined as the melting point of water at 0 ° C and the evaporation point of water at 100 ° C. Celsius temperature J and thermodynamic temperature T are related as follows:

J = T-T0with T0 = 273.15K

Temperature differences are always given in Kelvin.

1.2 amount of heat

 in J (where 1 J = 1 Nm = 1 Ws)

The thermal energy stored in the building material is

 in J

Here, V is the building material volume, DJ is the temperature difference and S is the heat storage number, or the volume-related heat capacity. The direct dependence of the heat storage capacity on the weight of the component becomes clear. "Heavy" components store more thermal energy than "light" components.

The area-related heat storage capacity is through

characterized. Here d is the thickness of the component layer in m and m 'the mass per unit area in kg / m2. The heat storage capacity W indicates the amount of heat stored in 1 m² of a component layer of thickness d in J / (m2K) at an excess temperature of 1 K.

1.3 heat flow

Under the heat flow one understands the amount of heat Q that flows in the time unit t from a place of high temperature to a place of low temperature.

 in W

1.4 heat flux density

The heat flow density q is the heat flow related to a unit area.

 in W / m²

The following applies for heat conduction under steady-state conditions (q = const., I.e., )
:

 in W / m²

 in W / m²

With the thermal resistances Rj it is heat transfer / heat transfer and / or heat transfer resistances. The term stationary conditions presupposes that the energy transfer across the system boundary is constant over time, i.e. all processes proceed under steadiness. No heat storage occurs within the treated area.

1.5 Heat transport processes

Three mechanisms - heat conduction, convection and radiation exchange - are involved in heat transport. In the solid body, heat conduction dominates, while convection and radiation are dominant in the gas space.

1.5.1 Thermal conduction

When it comes to heat conduction, a distinction is made between serial and parallel conduction. In the case of a multi-layer wall structure, the amount of heat Q is transported through all layers one after the other (in series). With a modular structure, the amount of heat Q is distributed to the individual modules (in parallel). The following calculation approaches apply to the amount of heat Q transported by heat conduction under stationary, level conditions:

 single-layer components multilayer components

"Flat" denotes the fact that the heat flow is perpendicular to the penetrated material. There is no curvature.

 Table 6: Calculated values ​​for thermal conductivity and guide values ​​for water vapor diffusion resistance figures
 Bulk density or bulk density classes kg / m³ Calculated value of thermal conductivity lR. in W / (mK) Guide value for water vapor diffusion resistance m 1. Plasters, screeds and other layers of mortar Lime mortar, lime cement mortar, mortar made from hydraul. lime Cement mortar Cement screed 2. Large format components Normal concrete Lightweight concrete Steam-hardened aerated concrete 5/10 Lightweight concrete with an upright structure according to DIN 4232 with non-porous aggregates according to DIN 4226 with porous aggregates according to DIN 4226 part 2 without addition of quartz sand Asbestos cement panels 2000 0,58 20/50 Aerated concrete building panels, unreinforced DIN4166 with normal joint thickness and masonry mortar according to DIN 1053 part 1 700 0,27 5/10 laid with thin joints 700 0,24 5/10 Wall panels made of lightweight concrete according to DIN18162 1000 0,37 5/10 Plasterboard according to DIN 18180 900 0,21 8 made of bricks according to DIN 105 T.1 to T.4 Full clinker, vertical hole clinker 2000 0,96 50/100 Solid brick, vertically perforated brick 1600 0,68 5/10 Made of sand-lime brick according to DIN 106 T.1 and T.2 1600 0,79 15/25 Masonry made of concrete blocks 3K bricks £ 300mm 900 0,44 5/10 3-component stones, width = 365 mm 900 0,55 5/10 5. Thermal insulation materials Wood wool lightweight panels according to DIN1101 panel thickness greater than 25mm 400 0,093 2/5 Foam plastics according to DIN18159 T.1 and T.2 Polyurethane (PUR) on-site foam according to DIN18159 T.1 greater than or equal to 37 0,030 30/100 Cork insulation materials Cork boards according to DIN 18161 T.1 Thermal conductivity group 050 80-500 0,050 5/10 Foam plastics according to DIN 18164 T.1 Polystyrene rigid foam thermal conductivity group 030 0,30 Foam glass according to DIN 18174 thermal conductivity group 020 100-150 0,050 6. Wood and wood-based materials Spruce, pine, fir 600 0,13 40 Plywood according to DIN 68705 part 2 to part 4 800 0,15 50/400 Chipboard 700 0,13 50/100 7. Coverings, sealants, waterproofing membranes Cork linoleum flooring 700 0,081 Bitumen sealants 110 0,17 Plastic roofing membrane 40000/175000 PVC films 20000/50000 8. Other common substances Tiles 2000 1,00 Glass 2500 0,80 Natural stones 2800 3,5 steel 60 copper 380 aluminum 200 Rubber (compact) 1000 0,20

1.5.1.1 Thermal transmittance

The heat transfer coefficient L indicates the amount of heat Q in J that flows through 1 m² of a building material layer of thickness d in 1 second if there is a temperature difference of 1 K between the surfaces. It depends on the thermal conductivity and the layer thickness of the material.

1.5.1.2 Thermal resistance

The reciprocal value of the thermal transmittance L is referred to as the thermal resistance R.

The following applies to single-layer components:

 in m²K / W

The following applies to multi-layer components:

 in m²K / W

1.5.1.3 Heat transfer coefficient and heat transfer resistance

The heat transfer is determined by the heat transfer coefficient h or the heat transfer resistances R.si, Rse described. The heat transfer coefficient h corresponds to the amount of heat in J, which is exchanged by a 1 m2 area in 1 second if the temperature difference between the wall surface and the air is 1 K. The heat transfer coefficient h includes the convective, radiation-related and conduction-related components. The following applies:

1.5.1.4 Heat transfer coefficient

The heat transfer coefficient U (short: U-value) is the most important parameter for describing and assessing the energetic behavior of a component. It indicates the heat flow in W that flows through an area of ​​1 m² at a temperature difference of 1 K between indoor and outdoor air. Poorly insulated components have a high, well-insulated components have a low heat transfer coefficient U.

 in W / m²K

By rearranging the equation one obtains:

 in W / m²

The heat transfer coefficient is calculated as follows:

 in W / m²K

The addition of heat transfer coefficients U is not permitted. Only thermal resistances Rsi, Rse, R, 1 / U can be added.

1.5.2 Convection

The transfer of heat by entrainment in moving media, currents (gases, air, liquids) is called heat convection.

 in W

Below the specific heat capacity cp constant pressure p is the amount of heat (amount of energy) required to heat 1 kg of a substance by 1 K.

1.5.3 Radiation exchange

The electromagnetic radiation that a body emits as a result of its temperature is called thermal radiation. Every body emits thermal radiation (emission) and absorbs thermal radiation from its surroundings (absorption).

1.5.3.1 Spectrum of electromagnetic waves

The radiation is divided into different spectral ranges.

Table 7: Wavelength ranges

 Wavelength l in m Wave type > 400 . 10-6 Microwaves, radio waves 400 . 10-6 ... 0,78 . 10-6 Infrared, also ultrared 0,78 . 10-6 ... 0,38 . 10-6 visible light 0,38 . 10-6 ... 0,01 . 10-6 Ultraviolet < 0,01 . 10-6 X-rays, g-rays

1.5.3.2 Radiation amount, radiant energy

The radiation energy Qr is the energy that a heat source emits into the room through radiation.

 in J

1.5.3.3 Radiated power

The radiation power Pr is the quotient of the radiation energy, or the amount of radiation Qr, and the time t. It is the power that a radiation source radiates into the room.

 in W

1.5.3.4 Specific charisma

The specific radiation Mr is the quotient of the radiation power dPr emitted by a surface element dAr into the front half-space and the area dAr.

 in W / m²

1.5.3.5 Spectral specific radiation

The specific emission Mr, l is the spectral density of the specific emission Mr.

1.5.3.6 Black body radiation

A body that emits the highest possible amount of energy at temperature T is called a black body. The spectral specific emission Mr, l of a black body depends on the absolute temperature. The Planck's law of radiation describes this connection.

 in W / m³

The total emission increases sharply with increasing temperature. The area under the curve is a measure of the total emission.

The wavelength of the radiation maximum is temperature-dependent. It shifts to shorter wavelengths with increasing temperature. The product is () constant. It is true Wien's displacement law.

 in mK

An integration of the emitted energy over all wavelengths delivers this Law of Stefan / Boltzmann:

 in W / m²

The specific radiation or the heat flux density as a result of radiation qr, S of the black body is proportional to the fourth power of the absolute temperature of the black body.

1.5.3.7 Emission of any body

A gray body is understood to be a body whose emission behavior is in a constant ratio to the emission behavior of the black body. The ratio is called the emissivity e.

 in W / m²

1.5.3.8 Absorption, reflection, transmission

Every body radiates energy and absorbs radiant energy. It is the absorbed radiation, the reflected radiation, the transmitted radiation and q the incident radiation in W / m2. A non-transparent body reflects part of the radiation, a transparent body also lets part of the radiation through.

- Non-transparent components

A distinction must be made between the following borderline cases:

- Transparent components

r, aS, depend on the material and the wavelength of the radiation.

1.5.3.8.1 Absorption and Emission

The degree of absorption ar, kw is - depending on the wavelength and the temperature - equal to the emissivity e for all bodies (Kirchhoff's law).

 -

Areas with a low degree of radiation absorption (e.g. bare metallic surfaces) radiate little, while those with a high degree of radiation absorption (e.g. non-metallic surfaces) also emit a correspondingly large amount of energy.

1.5.3.8.2 Radiation exchange between parallel surfaces

Surfaces oriented towards one another exchange heat through radiation. For the special case that the surfaces are equally large, plane-parallel surfaces, the following applies:

Please note that the distance between the two surfaces should be small compared to the surface. It is the heat flux density radiated from the surface 1 (T1, e1), and the heat flux density radiated from surface 2 (T2, e2). Furthermore, T1 should be> T2. The resulting heat flow is given by:

If you set and also for , , and one, it results:

and with the introduction of the radiation exchange constant C12

 in W

The radiation exchange constant C12 is only dependent on the emissivity e or the radiation constant C of the surfaces. It is calculated as follows:

 in W / m²K4

Special cases apply to areas that are not parallel or whose size is small compared to the distance.

The following applies to the radiation current density qr:

 in W / m²

It applies to the radiation exchange coefficient hr:

 in W / m²K

For T1 - T2 <200 K, according to [X], with approximately:

 in K³

It is important in this context:

1. In the case of long-wave radiation (e.g. thermal radiation) it is irrelevant what color the surface is. In the case of long-wave radiation exchange, a clear distinction must be made between bare metallic surfaces (e »0.05) and non-metallic surfaces (e» 0.90 - 0.98).

2. In the case of short-wave radiation (e.g. solar radiation), the color of the surface plays a decisive role in contrast to long-wave radiation (thermal radiation, IR). Dark surfaces absorb short-wave radiation more strongly and therefore also heat up more strongly than light surfaces.

3. Glass is for the most part permeable to short-wave radiation (sunlight), but not to long-wave radiation (thermal radiation, IR). When exposed to sunlight, this leads to the heating of rooms (greenhouse effect).