It can be shown that these observations are true for comparing a parallelflow exchan-

ger to an exchanger with any other flow arrangement for specified NTU, C*, and inlet

temperatures.

As expected, the parallelflow exchanger provides lower heat transfer rate

ð78% ¼ 122:7 kW " 100=157:4 kWÞ than that of a counterflow exchanger. However, if

the exchanger is designed for the effectiveness lower than 40%, there is not a significant

difference in the exchanger effectiveness and heat transfer rate between parallelflow and

counterflow exchangers at equal NTU and inlet temperatures. This is an industrially

important conclusion for low effectiveness waste heat recovery from exhaust gases

having SO2 as one of the constituents. The sulfuric acid condensation in a heat exchanger

can be prevented at atmospheric pressure if the minimum wall temperature is maintained

above about 1508C. For this case, the parallelflow exchanger becomes an attractive

solution since its lowest wall temperature is higher than that of any other exchanger

flow arrangement.

Example 3.3 One important design point for a radiator design is to cool the engine at

50 km/h on a 7% grade road. Your responsibility as a design engineer is to make sure that

the coolant (50% water–50% glycol) at the radiator inlet (top tank) does not exceed

1208C temperature at 100 kPa gauge radiator cap pressure. Determine the radiator top

tank temperature for the following conditions: engine heat rejection rate q ¼ 35 kW,

airflow rate 0.75 kg/s, air inlet temperature 538C, and water–glycol flow rate 1.4 kg/s.

For this radiator, UA ¼ 1180W/K. The specific heats for the air and the water–glycol

mixture are 1009 and 3664 J/kg $ K respectively. What will be the outlet temperature of

the water–glycol mixture? Consider the radiator with both fluids unmixed.

SOLUTION

Problem Data and Schematic: Fluid flow rates, inlet temperature of the cold fluid, heat

transfer rate, and the total thermal conductance are given (see Fig. E3.3).

Determine: The inlet temperature of the hot fluid (water–glycol mixture).

EFFECTIVENESS–NUMBER OF TRANSFER UNIT RELATIONSHIPS 137

FIGURE E3.3

Assumptions: The fluid properties and UA are constant, and the maximum inlet

temperature for the hot fluid is 1208C at 100 kPa, beyond which it will boil in the engine.

Analysis:We could find the NTU from the information given. But first, we have to find

C* and Cmin:

Cair ¼ Cc ¼ ð _mmcpÞair ¼ 0:75 kg=s# 1009 J=kg $K ¼ 756:75W=K ¼ Cmin

Cliquid ¼ Ch ¼ ð _mmcpÞliquid ¼ 1:4 kg=s# 3664 J=kg $K ¼ 5129:6W=K

C* ¼Cair

Cliquid¼756:75W=K

5129:6W=K¼ 0:148

NTU ¼UA

Cmin¼

1180W=K

756:75W=K¼ 1:559

From Fig. 3.9 or the Table 3.3 formula for an unmixed–unmixed crossflow exchanger, we

get

" ¼ 0:769

Hence, Th;i from Eq. (3.35) is given by

Th;i ¼ Tc;i þq

"Cmin¼ 538Cþ

35 kW# 1000W=kW

0:769# 756:75W=K¼ 113:18C Ans:

Since this is less than 1208C, the design is safe. If we would have determined Th;i > 1208C,

we would have changed the radiator design (such as increasing A and hence UA and

NTU) so that Th;i & 1208C.

Using the energy balance equation (3.5), we could find the water–glycol mixture outlet

temperature as follows:

Th;o ¼ Th;i 'q

Ch¼ 113:18C'

35 kW# 1000W=kW

5129:6W=K¼ 106:38C Ans:

Discussion and Comments: As we discussed in Section 2.1.2.1, the two most important

heat exchanger design problems are the rating and sizing problems. However, based

on Eq. (3.7), the six independent variables of the problem for the specified flow arrange-

ment yields a total of 21 different problems, summarized later in Table 3.11. The

problem above is one example beyond the simple sizing problems (numbers 2 and 4 in

Table 3.11).

In reality, one needs to design/size a radiator (i.e.,UA or NTU to be determined) such

that the top tank temperature does not exceed the boiling temperature of the water–

glycol mixture at the worst design point (7% grade with air-conditioning on at the

highest blower speed for airflow in a desert summer condition); and at the same time,

it requires ‘‘low’’ fan power to reduce the total cost of the radiator and fan as well as to

reduce a negative impact on the fuel economy. However, to simplify the present problem,

the UA and airflow rate were given as part of the input data.

138 BASIC THERMAL DESIGN THEORY FOR RECUPERATORS