BuildingSystems.HAM.HeatConduction.HeatConduction3D

# .BuildingSystems.HAM.HeatConduction.HeatConduction3D

Model for 3D heat conduction

## Information

This is a model which describes the three-dimensional heat conduction in x-, y- and z-direction within a cuboid shaped body width the edge length `dx`, `dy` and `dz`

c ρ dx dy dz dT ⁄ dt = Q̇x1 + Q̇x2 + Q̇y1 + Q̇y2 + Q̇z1 + Q̇z2 + Q̇heatsource,

with the heat flow rates to the borders `x1/y2`, `y1/y2` and `z1/z2`

Q̇x1/x2; = kx (Tx1/x2 - T).

Q̇y1/y2; = ky (Ty1/y2 - T).

Q̇z1/z2; = kz (Tz1/z2 - T).

Here kx, kY and kz are the thermal conductances in the x-, y- and z-dimension

kx = 2 λ ⁄ dx dy dz.

ky = 2 λ ⁄ dy dx dz.

kz = 2 λ ⁄ dz dy dx.

c is the specific heat capacity, ρ the density, λ the heat conductivity, Q̇heatsource an optional heat source within the body. Tx1/x2, Ty1/y2 and Tz1/z2 are the temperatures on the borders `x1/x2`, `y1/y2` and `z1/z2` with the areas `dy dz`, `dx dz` and `dy dx`.

#### Notes

For problems with 1 dimensional heat conduction, the simplified model BuildingSystems.HAM.HeatConduction.HeatConduction1D can be used and combined with other models from the `BuildingSystems` library.

## Revisions

- April 24, 2019 by Christoph Nytsch-Geusen:
  Adaptation to flexible geometries.
- May 23, 2016 by Christoph Nytsch-Geusen:
  First implementation.

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