Question

A heat exchanger is to cool ethylene glycol (cp = 2.56kJ/kg·◦C) flowing at a rate of 3.2kg/s from 80◦C to 40◦C by water (cp = 4.18kJ/kg·◦C) that enters at 20◦C and leaves at 70◦C. Determine (a) the rate of heat transfer (b) mass flow rate of water.

Answer 1

Answer:

a) $Q=327.68kW$

b) $m_{w}=1.57\frac{kg}{s}$

Explanation:

A)

Consider the energy balance just for the ethylene glycol; we can write an energy balance for this compound because it does not mix with any other.

$Q+m_{EG}*h_{in} =m_{EG}*h_{out}$

$Q=m_{EG}*Cp_{EG}*(T_{out}-T_{in)}=3.2\frac{kg}{s}*2.56\frac{kJ}{kgK}*(40-80)C=-327.68kW$

The heat is negative for this balance because the energy in heat form is going out of the ethylene glycol.

B)

Consider the same energy balance, but for water:

$Q+m_{w}*h_{in} =m_{w}*h_{out}$

$Q=m_{w}*Cp_{w}*(T_{out}-T_{in)}$

The heat that the ethylene glycol losts is the same that the water receives, so, for this equation Q is the same quantity that we found above, but with a positive sign because it is entering to the water.

$327.68kW=m_{w}*(4.18\frac{kJ}{kgK})*(70-20)C\\m_{w}=\frac{327.68kW}{(4.18\frac{kJ}{kgK})*(70-20)C} =1.57\frac{kg}{s}$