planning:thermal_protection:thermal_protection_works:thermal_protection_vs._thermal_storage

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planning:thermal_protection:thermal_protection_works:thermal_protection_vs._thermal_storage [2022/01/18 15:27] yaling.hsiao@passiv.de [Literature] |
planning:thermal_protection:thermal_protection_works:thermal_protection_vs._thermal_storage [2022/02/15 19:57] (current) admin |
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<WRAP center 60%> | <WRAP center 60%> | ||

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$$\rho c \dfrac{\delta T}{\delta t} = - div\,(- \Lambda\, | $$\rho c \dfrac{\delta T}{\delta t} = - div\,(- \Lambda\, | ||

- | </ | ||

</ | </ | ||

The heat equation in general formulation describes the time variation of a temperature field T(x,y,z) in fixed matter (e.g. in a solid body). | The heat equation in general formulation describes the time variation of a temperature field T(x,y,z) in fixed matter (e.g. in a solid body). | ||

- | * Differences in the temperature (gradient //grad//, on the right) propel a heat flux which increases proportional to the relevant component of the thermal conductivity tensor <\Lambda </. ((The most general formulation with which the thermal conductivity can vary for different spatial directions (e.g. in a perforated brick) is represented here. If the thermal conductivity is invariant with respect to direction (isotropic),<\lambda </applies instead of the tensor <\Lambda </. The specific heat capacity <\rho c</and thermal conductivity <\Lambda</can depend on the location, without significantly changing the character of the equation. If the coefficients also depend on the temperature (e.g. gases), the equation becomes non-linear – however, even then the numerical solution can still provide useable results under certain conditions.)) (<q = -\Lambda \,</is the heat flux). | + | * Differences in the temperature (gradient //grad//, on the right) propel a heat flux which increases proportional to the relevant component of the thermal conductivity tensor $\Lambda$. ((The most general formulation with which the thermal conductivity can vary for different spatial directions (e.g. in a perforated brick) is represented here. If the thermal conductivity is invariant with respect to direction (isotropic),$\lambda$ applies instead of the tensor $\Lambda$. The specific heat capacity $\rho c$ and thermal conductivity $\Lambda$ can depend on the location, without significantly changing the character of the equation. If the coefficients also depend on the temperature (e.g. gases), the equation becomes non-linear – however, even then the numerical solution can still provide useable results under certain conditions.)) ($q = -\Lambda \,grad\,T$ is the heat flux). |

* The negative divergence of the heat flow is the change of the heat content in the infinitesimal volume element. | * The negative divergence of the heat flow is the change of the heat content in the infinitesimal volume element. | ||

- | * This is the same as the temporal change in temperature <\frac{\partial T}{\partial t}\)</multiplied by the heat capacity <\rho c</(left side of equation). | + | * This is the same as the temporal change in temperature $\frac{\partial T}{\partial t}$ multiplied by the heat capacity $\rho c$(left side of equation). |

This equation has proved to be consistently effective in physics and technology. Such different things like heat transfer in stars, in semi-conductor devices, brake pads and many others can be calculated in good correlation with measurements. This equation also applies in building physics – and the calculations made using it correspond just as well with building physical measurements as shown in [[planning: | This equation has proved to be consistently effective in physics and technology. Such different things like heat transfer in stars, in semi-conductor devices, brake pads and many others can be calculated in good correlation with measurements. This equation also applies in building physics – and the calculations made using it correspond just as well with building physical measurements as shown in [[planning: | ||

planning/thermal_protection/thermal_protection_works/thermal_protection_vs._thermal_storage.txt · Last modified: 2022/02/15 19:57 by admin