Modeling and Design of Net ZEBs as Integrated Energy Systems - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 46

2.1.5 Building Transient Response Analysis
Transient thermal analysis of walls or zones may be performed with the
following objectives:
1. Peak heating/cooling load calculations to size heating and cooling
systems.
2. Calculation of dynamic temperature variation within walls, including
solar effects, room temperature swings and condensation on wall
interior surfaces; two-dimensional steady-state temperature profiles in
walls (e.g., for investigation of thermal bridge effects).
For a multilayered assembly (wall or slab), an energy balance is applied at
eachnodeatregulartimeintervalstoobtainthetemperatureofthenodesas
a function of time. These equations may be solved with the implicit method
as a set of simultaneous equations or with the explicit method in which we
march forward in time from a set of initial conditions. Mixed differencing
schemes are also often used in building simulation.
Here we consider the finite-difference thermal network approach . In this
approach, each assembly layer is discretized (divided) into a number of
sublayers (control volumes). Each control volume is represented by a node
and is assumed to be isothermal. Each node ( i ) has a thermal capacitance
( C i ) associated with it and resistances connecting it to adjacent nodes.
Transient thermal response analysis with finite difference techniques may
generally provide a more accurate estimation of temperatures and heat
flowsduetothecapabilitytomodelnonlineareffectssuchasconvectionand
radiation. However, the initial conditions are usually unknown. Thus the
simulation is repeated until a steady periodic response is obtained.
In the transient one-dimensional finite difference case we represent each
assembly layer by one or more sub-layers (control volumes). Each control
volume is represented by a central node with a thermal capacitance C
connected to two thermal resistances, each equal to half the R- value of the
layer. The energy balance for the thermal network is given by