08.01.2023##### What is thermal conductivity and thermal conductivity coefficient?

##### What is heat transfer resistance R?

##### What is the heat transfer coefficient U?

##### Where to look for λ, R and U?

Let’s figure out what the thermal conductivity coefficient λ (lambda), heat transfer resistance R and heat transfer coefficient U are.

The thermal properties of building materials and structures have three most important indicators (λ, R and U), which affect the energy efficiency of buildings. To choose a construction technology that best meets modern requirements for energy saving, it is necessary to understand the differences between these indicators and what structural properties they determine.

These three parameters are closely related. In this case, the thermal conductivity coefficient λ is a characteristic of the material, while the heat transfer resistance R and the heat transfer coefficient U depend on λ and relate to the properties of building structures.

Thermal conductivity is the ability of bodies to conduct thermal energy from hotter parts to cooler parts. Thermal conductivity is determined by the amount of heat passing per unit of time through a unit of material thickness.

The thermal conductivity coefficient λ is a measure that expresses the ability of a material 1 meter thick to transmit an amount of heat in Joules per 1 second at a temperature difference on opposite surfaces of the material of 1 degree Kelvin or Celsius and is measured in W/(m∙K).

In most cases, the thermal conductivity coefficient is determined experimentally by measuring the heat flow and temperature gradient in the material under study. It depends not only on the type of material, but also on temperature, humidity, density, etc.

**Average indicators for various materials**

Material | λ, W/(m∙K) |

Reinforced concrete | 2.04 |

Ceramic brick | 0.75 |

Aerated concrete | 0.23 |

Wood | 0.14 |

Mineral wool | 0.043 |

Expanded polystyrene (styrofoam) | 0.037 |

Extruded polystyrene | 0.032 |

Polyisocyanurate foam (PIR) | 0.022 |

Materials with better thermal insulation properties have lower thermal conductivity coefficient values λ. It should be noted that there are several methods for determining λ, which allow obtaining different values under different conditions for the same material.

**Comparison of thermal conductivity coefficients for polyisocyanurate foam (PIR) obtained in a wall structure of 100 mm sandwich panels**

Thermal conductivity coefficient | λ, W/(m∙K) | R, (m^{2}∙K)/W | U, W/(m^{2}∙K) | |

1 | λ_{0 calc} | 0.0179 | 5.75 | 0.1739 |

2 | λ_{10, 0 calc} | 0.0181 | 5.68 | 0.1761 |

3 | λ_{25, 0 calc} | 0.0186 | 5.54 | 0.1805 |

4 | λ_{25, A exp} | 0.023 | 4.51 | 0.2217 |

5 | λ_{25, A eff exp} | 0.024 | 4.33 | 0.2310 |

6 | λ_{25, B exp} | 0.031 | 3.38 | 0.2959 |

7 | λ_{10, A декл} | 0.022 | 4.70 | 0.2128 |

8 | λ_{25, B calc} | 0.040 | 2.66 | 0.3759 |

**Comparison of thermal conductivity coefficients for mineral wool (W) obtained in a wall structure of 150 mm sandwich panels**

Thermal conductivity coefficient | λ, W/(m∙K) | R, (m^{2}∙K)/W | U, W/(m^{2}∙K) | |

1 | λ_{0 calc across} | 0.0317 | 4.89 | 0.2045 |

2 | λ_{10, A calc across} | 0.0337 | 4.61 | 0.2169 |

3 | λ_{25, A exp across} | 0.0370 | 4.21 | 0.2375 |

4 | λ_{25, A exp along} | 0.0380 | 4.11 | 0.2433 |

5 | λ_{25, A exp along} | 0.0390 | 4.01 | 0.2494 |

6 | λ_{10, B exp along} | 0.0406 | 3.85 | 0.2597 |

7 | λ_{10, A decl along} | 0.0430 | 3.64 | 0.2747 |

8 | λ_{25, B calc along} | 0.0490 | 3.22 | 0.3106 |

λ

_{0 calc}/ λ_{10, A calc across}– the minimum possible calculated theoretical

PIR – in a completely dry state (moisture 0%)

W – fiber orientation across the direction of heat flow propagation, operating mode A (humidity up to 0.5%)λ

_{10, 0 calc}/ λ_{10, A calc across}– for one sandwich panel, calculated at 10 °C

PIR – in a completely dry state (moisture 0%)

W – fiber orientation across the direction of heat flow propagation, operating mode A (humidity up to 0.5%)λ

_{25, 0 calc}/ λ_{25, A exp across}– for one sandwich panel at 25 °С

PIR – calculated in a completely dry state (humidity 0%)

W – experimental, fiber orientation across the direction of heat flow propagation, operating mode A (humidity up to 0.5%)λ

_{25, A exp}/ λ_{25, A exp along}– for one sandwich panel at 25 °C

PIR – operating mode A (humidity up to 2%)

W – fiber orientation in the direction of heat flow propagation, operating mode A (humidity up to 0.5%)λ

_{25, A eff exp}/ λ_{25, A eff exp along}– effective experimental, for a wall structure made of sandwich panels at 25 °С

PIR – operating mode A (humidity up to 2%)

W – fiber orientation in the direction of heat flow propagation, operating mode A (humidity up to 0.5%)λ

_{25,B exp}/ λ_{10, B exp along}– experimental, for a wall structure made of sandwich panels

PIR – at 25 °C, operating mode B (humidity up to 5%)

W – at 10 °C, fibers orientaton in the direction of heat flow propagation, operating mode B (humidity up to 1%)λ

_{10, A decl}/ λ_{10, A decl along}– declared (the worst possible result), for a wall structure made of sandwich panels at 10 °С

PIR – operating mode A (humidity up to 2%)

W – fiber orientation in the direction of heat flow propagation, operating mode A (humidity up to 0.5%)λ

_{25, B calc}/ λ_{25, B calc along}– calculated, maximum possible standard at 25 °С

PIR – operating mode B (humidity 5%)

W – fiber orientation in the direction of heat flow propagation, operating mode B (humidity 1-2.5%)

For a wall structure made of sandwich panels, the factor λ_{25, A eff exp} is decisive, therefore, in the declarations of conformity on Ruukki panels, this coefficient is always indicated. The obligatory use of λ_{25, A, eff exp} in energy efficiency calculations of building structures is due to the fact that DSTU B V.2.7-182: 2009 regulates the standard conditions for testing thermal conductivity characteristics at a temperature of 25 °C and material moisture content up to 0.5% (W) and up to 2% (PIR). At the same time, in the EU countries, it is customary to determine the characteristics of thermal conductivity at a temperature of 10 °C, therefore, in Ukraine, for products manufactured in the EU, it is necessary to additionally obtain these indicators, determined at a temperature of 25 °C.

It should be noted that for calculating the thermal resistance of an external enclosing structure, the use of indicators other than λ_{25, A, eff exp} is incorrect, therefore, in order to select the optimal thickness of sandwich panels, it is very important to understand which indicator λ is provided by the manufacturer. For example: building code DBN V.2.6-31:2021 regulates the minimum allowable values of heat transfer resistance of external enclosing structures of residential and public buildings for temperature zone I R_{qmin}=4.0 (m^{2}∙K)/W. In order to meet the requirements of this code for wall structures, if we take into account the determining λ_{25, A eff exp}, it is necessary to use Ruukki mineral wool sandwich panels with a thickness of 150 mm. At the same time, if you use a more “advertising” λ_{0 calc}, then a panel with a thickness of 120 mm is supposedly enough, but in reality this is not true. Therefore, it is important to look not only at the numerical value of λ, but also at what kind of indicator the supplier provides. Otherwise, in pursuit of savings, you can choose the wrong thickness of sandwich panels, which will lead to increased heating and air conditioning costs during the operation of the building.

Heat transfer resistance R is the ability of a structure to prevent the propagation of thermal motion of molecules. The R value shows how a structure of a certain thickness resists the transfer of heat through itself and is determined by the temperature difference in degrees Kelvin or Celsius on opposite surfaces of the structure, necessary to transfer 1 W of energy power through 1 m^{2} of the area of this structure and is measured in (m^{2}∙K)/W.

To calculate the heat transfer resistance of a multilayer thermally homogeneous enclosing structure R_{∑}, a formula is used that takes into account the various materials of this structure and the coefficients α_{I} (internal) and α_{E} (external).

To put it simply, the heat transfer resistance R is the thickness of a material in meters divided by its coefficient of thermal conductivity λ, which indicates how well it resists heat transfer at a given thickness. Therefore, the thicker the structure and the lower the thermal conductivity of its materials, the more energy efficient it is.

The reduced resistance to heat transfer R_{∑red} takes into account all actual heat losses through the enclosing structure, including in the areas of interlocks and joints, corner joints, thermal inclusions, point losses, fastening elements, etc. On the basis of experimental data from the measurement of the reduced resistance to heat transfer of a specific structure, λ_{25, A eff exp} is calculated, which is further used to calculate R_{∑red} of similar designed structures.

The calculation of R_{∑red} of a thermally inhomogeneous opaque enclosing structure is carried out according to the formula:

DSTU B V.2.6-189:2013 regulates that when designing enclosing structures, the condition R_{∑red} ≥ R_{qmin} must be fulfilled.

A structure with better thermal insulation provides the required R value at a minimum thickness and retains heat in the same way as thicker structures, while allowing more space inside the building.

The heat transfer coefficient U is the amount of heat in Joules transferred through a structure with a surface area of 1 m^{2} in 1 second with a temperature difference on opposite surfaces of 1 degree Kelvin or Celsius.

The U value is inversely proportional to the heat transfer resistance and is measured in W/(m^{2}∙K).

The heat transfer coefficient shows the ability of a structure to transfer heat from a warmer to a cooler room or between the outside and inside of a building. The lower the U value, the better the thermal insulation of the building.

There is also a more extended formula for determining U, which additionally assumes all actual heat losses through external enclosing structures, however, the results of such a calculation are identical to the calculation using the reduced formula.

Manufacturers of heat-insulating building structures must provide information on λ, R and U in the product description, posted in the public domain, or in declarations of conformity, if their presence is required by applicable law. For example, the coefficient of thermal conductivity λ, the reduced resistance to heat transfer R and the coefficient of heat transfer U for Ruukki sandwich panels are indicated in the declarations posted on the Rauta website. The declared thermal insulation characteristics of the panels must be confirmed by certification test reports, which must be available from the manufacturer. Unfortunately, in Ukraine, many suppliers of sandwich panels do not care about confirming the thermal insulation characteristics by tests and calculations, but declare fictitious values.

In addition to determining the parameters of enclosing structures during design, the indicators λ, R and U are also used to calculate the energy efficiency of buildings and control thermal parameters during operation.

In some cases, enclosing structures can have a complex configuration and therefore the thermal insulation parameters are difficult to determine. Then it is recommended to contact the material manufacturer for help in calculating the energy efficiency of the building.

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