Page 130 - Analysis and Design of Energy Geostructures

102 Analysis and Design of Energy Geostructures

where n i is the normal to the surface at the point H. The special case where
λ @T ðH;tÞ 5 0 is called the homogeneous boundary condition of the second kind. It
@n i
refers to a perfectly insulated surface across which no heat flux can occur.
For an energy wall considered as a one-dimensional system (cf. Fig. 3.15), the
boundary condition may consist of assuming a fixed (e.g. constant) heat flux at the
surface

5 _q :
x50 s
2 λ @T=@x

3.8.4 Convection boundary condition
The so-called Cauchy’s boundary condition, mixed Neumann’s boundary condition
or boundary condition of the third kind allows prescribing a convection boundary
condition. In many problems the heat flux across a bounding surface may be taken as
being proportional to the difference between the surface temperature, TðH; tÞ, and
the known temperature, T N , of the surrounding medium. In this case Eq. (3.25) takes
the form

Figure 3.15 Example of an initial and a Neumann’s boundary condition for an energy wall.