Rock wool board as an insulation material, its specifications have multiple densities, such as 60KG per cubic meter, 100KG per cubic meter, etc. Different densities also have a certain relationship with thermal conductivity. Below, we will use the thermal conductivity of objects to give a general explanation.
Thermal conductivity (usually expressed as k, λ or κ) is a property of thermally conductive materials. It is mainly evaluated according to Fourier's law for heat conduction. The modeling of thermal conductivity is very complex because there are many factors that affect it, and what is more complex is that in a complete model, thermal conductivity must be regarded as a tensor, because there may be different values in different directions.
However, you can find experiments that relate thermal conductivity to density. However, there are still several more direct factors that affect thermal conductivity:
Temperature
For metals and non-metals, the effect of temperature on thermal conductivity is different. In metals, thermal conductivity is mainly due to free electrons. Following the Wiedemann-Franz law, the thermal conductivity of metals is approximately proportional to the absolute temperature (in Kelvin) multiplied by the electrical conductivity. In pure metals, electrical conductivity decreases with increasing temperature, so the product of the two (thermal conductivity) remains approximately constant. However, as the temperature approaches absolute zero, thermal conductivity drops sharply.
In alloys, the change in electrical conductivity is usually small, so thermal conductivity increases with temperature, usually proportional to temperature. On the other hand, the thermal conductivity of non-metals is mainly due to lattice vibrations (phonons). Except for high-quality crystals at low temperatures, the phonon mean free path does not decrease significantly at high temperatures. Therefore, the thermal conductivity of non-metals is approximately constant at high temperatures. At low temperatures far below the Debye temperature, thermal conductivity decreases due to carrier scattering, and heat capacity also decreases from defects at very low temperatures.
Chemical phase
When a material undergoes a phase transition from solid to liquid or from liquid to gas, thermal conductivity may change. An example of this is the change in thermal conductivity that occurs when ice (thermal conductivity of 2.18 W/(m·K) at 0°C) melts to form liquid water (thermal conductivity of 0.56 W/(m·K) at 0°C).
Thermal anisotropy
Some substances, such as non-cubic crystals, can exhibit different thermal conductivities along different crystal axes due to differences in phonon coupling along a given crystal axis. Sapphire is a notable example of variable thermal conductivity based on direction and temperature, 35 W/(m·K) along the C axis and 32 W/(m·K) along the A axis. Wood usually conducts better along the grain than across it. Other examples of materials with thermal conductivity that varies with direction are heavily cold-pressed metals, laminated materials, cables, materials for space shuttle thermal protection systems, and fiber-reinforced composite material structures. When anisotropy exists, the direction of heat flow may not be exactly the same as the direction of the thermal gradient.
Electrical conductivity
In metals, according to the Wiedemann-Franz law, thermal conductivity approximately tracks electrical conductivity, as freely moving valence electrons can transfer not only electric current but also thermal energy. However, due to the increased importance of phonons, the general correlation between electrical conductivity and thermal conductivity does not apply to other non-metallic heat carriers. Highly conductive silver has lower thermal conductivity than diamond, which is an electrical insulator, but conducts heat through phonons due to its ordered atomic arrangement.
Convection
Exhaust system components with low thermal conductivity ceramic coatings can reduce heat generation in nearby sensitive components. In the absence of convection, air and other gases are usually good insulators. Therefore, many insulation materials work simply by having a large number of air-filled pockets that prevent large-scale convection. Examples of these include expanded and extruded polystyrene (commonly known as "styrofoam") and silica aerogel, as well as warm clothing. Natural biological insulators such as fur and feathers achieve similar effects by significantly suppressing convection of air or water near the animal's skin.
Light gases, such as hydrogen and helium, usually have high thermal conductivity. Dense gases such as xenon and dichlorodifluoromethane have low thermal conductivity. An exception, sulfur hexafluoride, a dense gas, has relatively high thermal conductivity due to its high heat capacity. Argon, a gas denser than air, is commonly used in insulating glass (double-glazed windows) to improve its insulation properties.
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