Limits the flow of heat for a given temperature difference. Heat flow is energy which costs money. The density of heat flow rate in W/m² is given by:
$u=\frac{{T}_{i}-{T}_{e}}{R}$ .
Where:
The total power to heat the space in W is given by:
$P=u\xb7a$ .
Where:
Maintain a temperature difference for a given flow of heat and take advantage of winter sun or other heating or cooling. The temperature rise in K (or °C) is given by:
${T}_{i}-{T}_{e}=R\xb7u$ .
For steady state the building envelope can be considered as a number of elements each made up of layers. For energy saving the temperature must be allowed to vary so in dynamic case thermal capacitance may be lumped within the envelope. This would avoid the a full heat conduction solution.
i,j | 1 | 2 | ... | m | Element |
---|---|---|---|---|---|
1 | 1,1 | 1,2 | 1,. | 1,m | |
2 | 2,1 | 2,2 | 2,. | 2,m | |
: | .,1 | .,2 | .,. | .,m | |
n | n,1 | n,2 | n,. | n,m | |
Layer |
$U=\frac{1}{R}$ , $R=\frac{1}{U}$ , $R=\underset{i=1}{\overset{n}{\Sigma}}{R}_{i}$ , $U=\frac{1}{a}\xb7\underset{j=1}{\overset{m}{\Sigma}}{a}_{j}\xb7{U}_{j}$ , $a=\underset{j=1}{\overset{m}{\Sigma}}{a}_{j}$ , $U=\frac{1}{s}\xb7\underset{0}{\overset{s}{\int}}U\left(x\right)\xb7dx$ , $\frac{\partial u}{\partial t}=k{\nabla}^{2}u$ (heat is not really superluminal).
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