Modeling and Design of Net ZEBs as Integrated Energy Systems - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 86

Fig. 2.24 Schematic of the fluid control volume
For discretization with fine mesh (i.e., small grid spacing), the mean fluid
temperature inside one control volume can also be approximated using
upwind differencing scheme ( Eq. (2.51) ) (Chen, Athienitis, and Galal, 2012;
Patankar, 1980).
(2.51)
where is the temperature of the fluid in the previous control volume.
is conductance between the surface and the fluid.
Detailed models reflecting the actual heat transfer process, such as two- or
three-dimensional spatial discretization, can provide more accurate results;
however, they require more computational effort. Simple
lumped-parameter finite difference models with acceptable accuracy are
needed for long-period simulations, especially for implementation into
whole building simulations and model-based control. Studies presented in
literature have shown that a one-dimensional (normal to the room-side
surface of the BITES) thermal model can approximate the thermal behavior
of active BITES systems well in cases of practical interest (Barton, Beggs,
andSleigh,2002;Chen,Galal,andAthienitis,2010b;RenandWright,1998;
Strand, 1995).
Transfer Function Methods
Since active BITES systems usually involve large thermal capacitance (e.g.,
concrete slab), transient thermal behavior needs to be modeled. Transfer
function methods are computationally efficient for the calculation of the
transient thermal response of a thermal system. The z -transfer function
method has been discussed in Section 2.1.3, and more general applications
are discussed in Chapter 6 .