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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 Both sides previous revision Previous revision 2022/02/15 19:57 admin 2022/01/18 15:27 yaling.hsiao@passiv.de [Literature] 2022/01/18 15:17 yaling.hsiao@passiv.de [Literature] 2021/02/09 13:48 jgrovesmith 2019/02/21 10:18 cblagojevic 2018/11/22 12:11 cblagojevic 2015/01/02 14:56 wolfgangfeist@googlemail.com 2014/09/18 18:19 external edit2014/04/14 16:02 twessel 2012/04/20 13:04 sarah 2012/04/20 13:02 sarah 2010/10/25 09:23 aespenberger 2010/10/25 09:12 aespenberger 2010/10/25 09:07 aespenberger 2010/10/25 09:06 aespenberger 2010/10/25 09:03 aespenberger 2010/10/22 16:22 beatrice 2010/10/22 16:21 beatrice 2010/10/22 16:21 beatrice 2010/10/22 16:19 beatrice 2010/10/22 16:19 beatrice 2010/10/22 16:18 beatrice 2010/10/22 16:17 beatrice 2010/10/22 16:17 beatrice 2010/10/22 16:16 beatrice 2010/10/22 16:14 beatrice 2010/10/22 16:13 beatrice 2022/02/15 19:57 admin 2022/01/18 15:27 yaling.hsiao@passiv.de [Literature] 2022/01/18 15:17 yaling.hsiao@passiv.de [Literature] 2021/02/09 13:48 jgrovesmith 2019/02/21 10:18 cblagojevic 2018/11/22 12:11 cblagojevic 2015/01/02 14:56 wolfgangfeist@googlemail.com 2014/09/18 18:19 external edit2014/04/14 16:02 twessel 2012/04/20 13:04 sarah 2012/04/20 13:02 sarah 2010/10/25 09:23 aespenberger 2010/10/25 09:12 aespenberger 2010/10/25 09:07 aespenberger 2010/10/25 09:06 aespenberger 2010/10/25 09:03 aespenberger 2010/10/22 16:22 beatrice 2010/10/22 16:21 beatrice 2010/10/22 16:21 beatrice 2010/10/22 16:19 beatrice 2010/10/22 16:19 beatrice 2010/10/22 16:18 beatrice 2010/10/22 16:17 beatrice 2010/10/22 16:17 beatrice 2010/10/22 16:16 beatrice 2010/10/22 16:14 beatrice 2010/10/22 16:13 beatrice 2010/10/22 16:12 beatrice 2010/10/22 16:09 beatrice 2010/10/22 16:08 beatrice 2010/10/22 16:04 beatrice 2010/10/22 15:58 beatrice 2010/10/22 15:49 beatrice 2010/10/22 15:49 beatrice 2010/10/22 15:48 beatrice 2010/10/22 15:46 beatrice 2010/10/22 15:46 beatrice 2010/10/22 15:42 beatrice 2010/10/22 15:40 beatrice 2010/10/22 15:39 beatrice 2010/10/22 15:38 beatrice 2010/10/22 15:36 beatrice 2010/10/22 15:35 beatrice 2010/10/22 15:35 beatrice 2010/10/22 15:35 beatrice 2010/10/22 15:34 beatrice 2010/10/22 15:33 beatrice 2010/10/22 15:33 beatrice 2010/10/22 15:28 beatrice 2010/10/22 15:27 beatrice 2010/10/22 15:25 beatrice Line 55: Line 55: - $$\rho c \dfrac{\delta T}{\delta t} = - div\,(- \Lambda\,grad\,T )$$ $$\rho c \dfrac{\delta T}{\delta t} = - div\,(- \Lambda\,grad\,T )$$ - 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), the scalar value of the conductivity  \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). + * 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 $\lambda$ 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: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]].