Handbook of air conditioning and refrigeration / Shan K

6.14 CHAPTER SIX
Characteristics of Heat Balance Method
The heat balance method is more direct and clear in load calculation methodology. Using the heat
balance method, the assumption of linear supposition is not required, and the changing of certain
parameters, such as the surface convective heat-transfer coefficient, can be modeled as required. If
moisture transfer should be included in the cool-down period in nighttime shutdown mode in a
location where the outdoor climate is hot and humid in summer, then the heat balance method will
give comparatively more accurate results.
However, the heat balance method demands laborious work, more computing time, complicated
computer programs, and experienced users. Only expensive mainframe computers could run
computer programs adopting the heat balance methodology in the 1970s and early 1980s. The heat
balance method is generally used for research and analytical purposes.
6.5 METHODOLOGY—TRANSFER FUNCTION
Basics
The transfer function method or weighting factor method is a simplification of the laborious heat
balance method. The wide application of the TFM is due to the user-friendliness of the inputs and
outputs of the TFM software and the saving of computing time. In the transfer function method,
interior surface temperatures and the space cooling load were first calculated by the exact heat
balance method for many representative constructions. The transfer function coefficients (weighting
factors) were then calculated which convert the heat gains to cooling loads. Sometimes, transfer
function coefficients were also developed through test and experiments.
The room transfer function coefficients (weighting factors ) were originally generated based on
a typical room configuration of 15 ft � 15 ft with 10-ft (4.5 m � 4.5 m with 3-m) ceiling and one
exposure of 30 percent glass in the early 1970s . In the late 1980s, the introduction of 14 influential
parameters of zone characteristics by Sowell (1988) enabled the adopted room transfer function
coefficients to more closely match the room type to be used. Today, TFM is the most widely
adopted computer-aided load calculation method in HVAC&R consulting firms.
Transfer Function and Time Function
The transfer function K of an element or a system is the ratio of the Laplace transform of the output
Y to the Laplace transform of the input or driving force G, or
Y � KG (6.8)
When a continuous function of time f(t) is represented at regular intervals �t and its magnitudes are
f(0), f(�), f(2�),...,f(n�), the Laplace transform is given as
where � �time interval, h
z � e s�
�(z) � f (0) � f (�)z �1 � f (2�)z �2 �� � ��f (n�)z �n
(6.9a)
The preceding polynomial in z �1 is called the z transform of the continuous function f(t).
In Eq. (6.8), Y, K, and G can all be represented in the form of a z transform. Because of the
radiative component and the associated heat storage effect, the space sensible cooling load at time t
can be related to the sensible heat gains and previous cooling loads in the form of a continuous
function of time f(t), which can be expressed as a z transform.