## Example

A space is maintained at a room temperature TR = 21°C and has a (UA)l = 2500 W/°C. The ambient temperature is 1°C and the storage tank temperature is 80°C. Estimate the space load, domestic water heating load, and auxiliary energy required if the following apply:

1. Heat exchanger effectiveness = 0.7.

2. Flow rate of air side of heat exchanger = 1.1 kg/s.

4. Environmental temperature at the space where storage tank is located = 15°C.

6. Mass flow rate of domestic water = 0.2 kg/s.

7. Required domestic water temperature = 60°C.

8. Make-up water temperature = 12°C.

Solution

The space heating load, Qhl, can be estimated from Eq. (6.61):

The maximum rate of heat transferred across the load heat exchanger, Qle(max), is g^en by Eq. (6.62):

Qle(max) = (mCp)a T - Tr) = 0.7 X (1.1 X 1.05) X (80 - 21) = 47.7kW

Qls = [min(Qle(max), Qhl)]+ = min(47.7, 50)+ = 47.7kW

The storage tank losses are estimated from Eq. (5.32): Qtl = (UA)s(Ts - Tenv) = (2.5) X (80 - 15) = 162.5W = 0.16kW

The domestic water heating load, Qw, can be estimated from Eq. (6.64): Qw = (mcp)w (Tw - Tmu) = 0.2 X 4.18 X (60 - 12) = 40.1kW

The rate of auxiliary energy required to cover the domestic water heating load, Qaux,w, is given by Eq. (6.67):

16.7 kW (not considered as it is negative)

Qaux,w = (mcp)w (Tw - Ts)+ = 0.2 X 4.18 X (60 - 80)

The rate of auxiliary energy required, Qaux, to cover the domestic water heating and space loads is given by Eq. (6.66):

Qaux = (Qhl + Qaux,w - Qtl - Qls)+ = 50 + 0 - 0.16 - 47.7 = 2.14kW

It should be noted that, in all cases where a heat exchanger is used, the penalty of using this heat exchanger can be estimated according to Eq. (5.57), as indicated by the following example.

### Example 6.8

A space heating and hot water system has a collector with FRUL = 5.71 W/m2-°C and area of 16 m2. What is the ratio FR /FR if the flow rate of antifreeze is 0.012 kg/s-m2 and water is 0.018 kg/s-m2 in a collector-storage heat exchanger of effectiveness equal to 0.63, and the cp of water is 4180 J/kg-°C and of antifreeze is 3350 J/kg-°C?

Solution

First, the capacitance rates for the collector and tank sides are required, given by

Therefore, the minimum

 AfrUl (th cp )c (m cp )c £(th cp )min

643.2

643.2

643.2

0.923