I I 51 21 *p1 • CO I Contact factor
A psychrometric definition of this was given in section 3.4. Such a definition is not always useful—for example, in a cooler coil for sensible cooling only—and so it is worth considering another approach, in terms of the heat transfer involved, that is in some respects more informative though not precise.
Coils used for dehumidification as well as for cooling remove latent heat as well as sensible heat from the airstream. This introduces the idea of the ratio S, defined by the expression:
Fig. 10.5 The psychrometric relationship between sensible and total cooling load.
_ sensible heat removed by the coil total heat removed by the coil
In terms of Figure 10.5 this becomes
If the total rate of heat removal is Qt when a mass of dry air ma in kg s 1 is flowing over the cooler coil, then the sensible heat ratio S, can also be written as
Mac(ti — t2)
Where c is the humid specific heat of the airstream.
The approximate expression for sensible heat exchange given by equation (6.7) allows equation (10.2) to be re-written as
Qt = 1.25 x v x (?, — t2)/S
Sensible heat transfer, Qs, can also be considered in terms of the outside surface air film resistance of the coil, Ra:
Qs = (lmtdaiR*
Where At is the total external surface of the coil and LMTDas is the logarithmic mean temperature difference between the airstream and the mean coil surface temperature, /sm.
Ln[(/|- ?sm)/(r2 — 4m)] = (At//?a)/(1.25 X V)
Since v equals Af x vf, where Af and vf are the face area and face velocity, respectively, equation (10.7) becomes
Ln[(r, — tsm)/(t2 — tsJ] = (At/A[)/(R. d x 1.25 x vf) = k
K is a constant for a given coil and face velocity but it takes no account of heat transfer through the inside of the tubes. We can now write
(^2 ~ tsm)/(ti — tsm) — exp(— k)
Reference to Figure 10.5 shows that this is the approximate definition of the by-pass factor (see equation (3.4)) and hence equals (1 — P) where (3 is the contact factor. If r is the number of rows and Ar is the total external surface area per row, At = Arxr and k becomes (ArMf)(r)/(Ra1.25vf). An approximate expression for the contact factor now emerges:
Note that the contact factor is independent of the psychrometric state and the coolant temperature, provided that the mass flow ratio of air to water (usually about unity) remains fairly constant.
A four-row coil with a face velocity of 2.5 m s_I has a contact factor of 0.85. Calculate the contact factor for the following cases: (a) 3.0 m s_I and four rows, (b) 2.0 m s-1 and four rows, (c) 2.5 m s_1 and six rows, (d) 2.5 m s“1 and two rows, (e) 2.5 m s_1 and eight rows. Assume that changes in the face velocity do not significantly alter Ra.
By equation (10.8) we can calculate that
0.85 1 exp| Af i.25 x Rax 2.5
0.15 = expl -1.28 x
In 0.15 = (-1.28 x
AfRa -1.28 1-482
This constant can now be used to answer the questions:
(a) |3 = 1 — exp[-1.482 x 4/(1.25 x 3.0)] = 0.79
(b) P = 1 — exp[-1.482 x 4/(1.25 x 2.0)] = 0.91
(c) P = 1 — exp[-1.482 x 6/(1.25 x 2.5)] = 0.94
(d) P = 1 — exp[-1.482 x 2/(1.25 X 2.5)] = 0.61
(e) P = 1 — exp[-1.482 x 8/(1.25 x 2.5)] = 0.98
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