The cooling equipment, in an ideal case, must remove heat energy from the space's air at a rate equal to the cooling load. In this way, the space air temperature will remain constant. However, this is seldom true. Therefore, a transfer function has been devised to describe the process. The room air transfer function is
where p;, g; = transfer function coefficients (ASHRAE, 1992).
qx = heat extraction rate (W).
qc = cooling load at various times (W).
t; = room temperature used for cooling load calculations (°C).
tr = actual room temperature at various times (°C).
All g coefficients refer to unit floor area. The coefficients g0 and g; depend also on the average heat conductance to the surroundings (UA) and the infiltration and ventilation rate to the space. The p coefficients are dimensionless. The characteristic of the terminal unit usually is of the form qxfi = W + 5 X trfi (6.18)
where W and S are parameters that characterize the equipment at time 9.
The equipment being modeled is actually the cooling coil and the associated control system (thermostat) that matches the coil load to the space load.
The cooling coil can extract heat energy from the space air from some minimum to some maximum value.
Equations (6.17) and (6.18) may be combined and solved for qx,e:
where
Ge = ti ^gi - ^gi(iy,e-i6) + ^Pi(qc,e-i6) - ^Pi(4x,e-n) (6.20) i = 0 i=1 i=0 i=0
When the value of qx,e computed by Eq. (6.19) is greater than qxmax, it is taken to be equal to qx,max; when it is less than qxmin, it is made equal to qx,m;n. Finally, Eqs. (6.18) and (6.19) can be combined and solved for tr,e:
It should be noted that, although it is possible to perform thermal load estimation manually with both the heat balance and the transfer function methods, these are better suited for computerized calculation, due to the large number of operations that need to be performed.
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