Page 129 - Analysis and Design of Energy Geostructures

Heat and mass transfers in the context of energy geostructures 101

where H is a point on the considered surface and f ðH;tÞ is a prescribed function.
The special case where T H;tÞ 5 0 is called homogeneous boundary condition of the
ð
first kind.
For an energy wall considered as a one-dimensional system (cf. Fig. 3.14), heat
transfer may be assumed to occur in the positive x-direction with the temperature dis-
tribution and to depend on time as Tðx; tÞ. For this wall the initial temperature may
be assumed to be equal to T 0 . The boundary condition may consist of assuming an
instantaneous increase of the temperature of the wall surface that would evolve over
time according to the prescribed function T H;tÞ 5 f H;tÞ 5 T s .
ð
ð

3.8.3 Prescribed heat input
The so-called Neumann’s boundary condition or boundary condition of the second
kind allows the fixing of a heat input. Based on Fourier’s law this boundary condition
takes the form

2 λ @T ðH;tÞ 5 _qðH; tÞ ð3:25Þ

@n i

Figure 3.14 Example of an initial and a Dirichlet’s boundary condition for an energy wall.