Question

Calculate the mass flow rate of heating medium (water) required in pasteurization of 1000 kg/h milk from 45°C to 72°C. Water enters heat exchanger at 90°C and leaves at 75°C. Heat loss from the exchanger to the ambience is estimated at 1 kJ/s. Take heat capacities of water and milk as 4.2 and 3.9 kJ/kg°C, respectively.

Answer 1

Energy balance

Total energy in = total energy out

Total energy in

Energy in by water

= Cpw x Twi

= 4.2 kJ/kg-°C x 90 °C = 378 kJ/kg

Energy in by milk

= Cpm x Tmi

= 3.9 kJ/kg-°C x 45 °C

= 175.5 kJ/kg

Total energy out

Energy out by water

= Cpw x Tw, o

= 4.2 kJ/kg-°C x 75 °C = 315 kJ/kg

Energy out by milk

= Cpm x Tm, o

= 3.9 kJ/kg-°C x 72 °C

= 280.8 kJ/kg

Total energy in = total energy out

Energy in by water + energy in by milk = Energy out by water + energy out by milk + heat loss

Mass of water x 378 kJ/kg + 1000 kg/h x 175.5 kJ/kg = mass of water x 315 kJ/kg + 1000 kg/h x 280.8 kJ/kg + 1 kJ/s x 3600s/hr

Mass of water x 378 kJ/kg + 175500 kJ/h = mass of water x 315 kJ/kg + 280800 kJ/h + 3600 kJ/h

Mass of water x 378 kJ/kg - mass of water x 315 kJ/kg = 280800 kJ/h + 3600 kJ/h - 175500 kJ/h

Mass of water x 63 = 108900

Mass of water = 1728.57 kg/h