# Parallel and contra-flow

Consider a four-row coil in stylised form, as shown in Figure 10.3(a). Air enters the first row at state 0. Water enters at a temperature fwa and, its temperature rising as it absorbs heat from the airstream, leaves at a higher value. Denote the mean surface temperature of the first row by fwl. If the first row had a contact factor of unity, the air would be conditioned to saturation at a state 1′, as shown in Figure 10.3(b). In fact, the contact factor (3 is less than unity and the air leaves at a state denoted by 1. This is now the entry state for the second row, the mean surface temperature of which is fw2. In a similar way, the exit state from the second row is 2, rather than 2′. This reasoning is applied to the succeeding rows, from which the leaving states of the airstream are denoted by 3 and 4. A line joining the state points 0, 1, 2, 3 and 4 is a concave curve and represents the change of state of the air as it flows past the rows under parallel-flow conditions. A straight line joining the points 0 and 4 indicates the actual overall performance of the coil. This condition line, replacing the condition curve, cuts the saturation curve at a point A when produced. By the reasoning adopted when flow through a single row was considered, one may regard the temperature of A as the mean coil surface temperature for the whole coil. It is denoted by fsm.

Similar considerations apply when contra-flow is dealt with, but the result is different. A convex condition curve is obtained by joining the points 0, 1, 2, 3 and 4. Referring to Figure 10.4 it can be seen that, this time, air entering the first row encounters a mean coil surface temperature for the row of twl and that this is higher than the mean surface temperatures of any of the succeeding rows. As air flow through the four rows occurs, progressively lower surface temperatures are met. The tendency of the state of the air is to approach the apparatus dew points, Y, 2′, 3′ and 4′, each at a lower value than the point preceding it, as it passes through the rows. The condition curve thus follows a downward trend as flow proceeds.

The result of this is that, by comparison with the case of a parallel flow, a lower leaving air temperature is achieved, greater heat transfer occurs, and the coil is more efficient, if it is piped for contra-flow operation.

The above analysis refers to what happens along the centre-line of the cooler coil. For any given row, the heat transfer is cross-flow and a different picture would emerge if any other section of the four-row coil, in the direction of airflow, were considered. The same argument could be adopted but the curve of the process line would not have the smooth

(a) Fig. 10.3 Parallel flow. The points 0, 4 and A are in a straight line and A lies on the 100 per cent saturation curve. A is the apparatus dew point and its temperature, ;sm, is the mean coil surface temperature for the whole four rows of the coil. The temperatures? wl, rw2, fw3 and tw4 in figure (b) are the mean surface temperatures of the 1st, 2nd, 3rd and 4th rows in figure (a). |

Shape shown in Figures 10.3(6) and 10.4(6). There would also be some lateral variation in the psychrometric state of the air after each row. Since, for air conditioning purposes, one is only interested in the mean state of the air entering and leaving the coil it is common sense to show the condition line as a straight line joining the entering and leaving states, which must cut the saturation curve at the apparatus dew point when extended. The temperature of the apparatus dew point can still be regarded as the mean coil surface temperature.

(a) Fig. 10.4 Contra-flow. The points 0, 4 and A are in a straight line. A is the apparatus dew point and its temperature is the mean coil surface temperature, tsm. |

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