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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%>
-<latex>  
 $$\rho c \dfrac{\delta T}{\delta t} = - div\,(- \Lambda\,grad\,T )$$ $$\rho c \dfrac{\delta T}{\delta t} = - div\,(- \Lambda\,grad\,T )$$
-</latex> 
 </WRAP> </WRAP>
 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 <latex> \Lambda </latex>. ((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), the scalar value of the conductivity <latex> \lambda </latex> applies instead of the tensor <latex> \Lambda </latex>. The specific heat capacity <latex>\rho c</latex> and thermal conductivity <latex>\Lambda</latex> 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.)) (<latex> q = -\Lambda \,grad\,</latex> 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), the scalar value of the conductivity $\lambdaapplies instead of the tensor $\Lambda$. The specific heat capacity $\rho cand thermal conductivity $\Lambdacan depend on the location, without significantly changing the character of the equation. If the coefficients also depend on the temperature (e.g. gases), the equation becomes non-linear – however, even then the numerical solution can still provide useable results under certain conditions.)) ($q = -\Lambda \,grad\,Tis 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 <latex>\(\frac{\partial T}{\partial t}\)</latex> multiplied by the heat capacity   <latex>\rho c</latex>(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:thermal_protection:thermal_protection_works:Thermal protection vs. thermal storage#Theory and practice (measurement)|the following example]]. 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:thermal_protection:thermal_protection_works:Thermal protection vs. thermal storage#Theory and practice (measurement)|the following example]].
  
planning/thermal_protection/thermal_protection_works/thermal_protection_vs._thermal_storage.txt · Last modified: 2022/02/15 19:57 by admin