Page 131 - Analysis and Design of Energy Geostructures

Heat and mass transfers in the context of energy geostructures 103

2 λ @T ð H;tÞ 5 h c ½T N 2 T H; tފ ð3:26Þ
ð
@n i
The special case where TðH; tÞ 5 0 and thus λ @T ð H;tÞ 5 h c T N is called the homo-
@n i
geneous boundary condition of the third kind. It represents convection for a medium
at zero temperature.
For an energy wall considered as a one-dimensional system (cf. Fig. 3.16), the
boundary condition may consist of assuming a fixed (e.g. constant) convection heat
flux at the surface

2 λ @T 5 h c ½T N 2 T 0; tފ:
ð
x50
@x

3.8.5 Radiation boundary condition
The Cauchy’s boundary condition also allows prescribing a radiation boundary condi-
tion for conduction problems. If the surface of a body is exposed to a high-
temperature source, it will receive heat by radiation according to Eq. (3.10). In this
case Eq. (3.25) takes the form

2 λ @T ð H;tÞ 5 Eσ SB ðT ðtÞ 2 T ðH; tÞÞ ð3:27Þ
4
4
N
@n i

Figure 3.16 Example of an initial and a mixed Neumann’s boundary condition for an energy wall.