.BuildingSystems.HAM.HeatConduction.HeatConduction3D

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 = Q̇_x1 + Q̇_x2 + Q̇_y1 + Q̇_y2 + Q̇_z1 + Q̇_z2 + Q̇_heatsource,

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

Q̇_x1/x2; = k_x (T_x1/x2 - T).

Q̇_y1/y2; = k_y (T_y1/y2 - T).

Q̇_z1/z2; = k_z (T_z1/z2 - T).

Here k_x, k_Y and k_z are the thermal conductances in the x-, y- and z-dimension

k_x = 2 λ ⁄ dx dy dz.

k_y = 2 λ ⁄ dy dx dz.

k_z = 2 λ ⁄ dz dy dx.

c is the specific heat capacity, ρ the density, λ the heat conductivity, Q̇_heatsource an optional heat source within the body. T_x1/x2, T_y1/y2 and T_z1/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.