# ACIMA

## Hello, world!

1. 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:

• ${T}_{i}$ is inside temperature in K (or °C);
• ${T}_{e}$ is environment temperature in K (or °C); and
• $R$ is thermal resistance in K·m²/W.
2. The total power to heat the space in W is given by:

$P=u·a$ .

Where:

• $P$ is the total heat flux in W; and
• $a$ is the area in m².
3. 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:

${T}_{i}-{T}_{e}=R·u$ .

4. 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

$U=\frac{1}{R}$ , $R=\frac{1}{U}$ , $R=\underset{i=1}{\overset{n}{\Sigma }}{R}_{i}$ , $U=\frac{1}{a}·\underset{j=1}{\overset{m}{\Sigma }}{a}_{j}·{U}_{j}$ , $a=\underset{j=1}{\overset{m}{\Sigma }}{a}_{j}$ , $U=\frac{1}{s}·\underset{0}{\overset{s}{\int }}U\left(x\right)·dx$ , $\frac{\partial u}{\partial t}=k{\nabla }^{2}u$ (heat is not really superluminal).

Each .html may be generated by a corresponding .md file. The markdown format is given in daringfireball.net and manpage. See source, eqnguide, eqn2e and the Makefile. Note that MathML is now broken in Chrome. See the MathJax or Math Anywhere Chrome extensions.