Problem 4.051 SI Oil enters a counterflow heat exchanger at 525 K with a mass fl

Question

Problem 4.051 SI Oil enters a counterflow heat exchanger at 525 K with a mass flow rate of 10 kg/s and exits at 350 K. A separate stream of liquid water enters at 20°C, 5 bar. Each stream experiences no significant change in pressure. Stray heat transfer with the surroundings of the heat exchanger and kinetic and potential energy effects can be ignored. The specific heat of the oil is constant, c-2 kJ/kg K. If the designer wants to ensure no water vapor is present in the exiting water stream, what is the minimum mass flow rate for the water, in kg/s? kg/s the tolerance is +/-290

Explanation / Answer

For hot fluid
Thi = 525 K
Tho = 350 K
mh = 10 kg/s
Ch = 2 kj/kg-K

For cold fluid
Tci = 293 K
Tco = 373 K    (since, the designer doesn't want water vapour in exit stream, so the temperature shouldn't increase 373 K, which is boiling point)
mc = 10 kg/s
Cc = 4.186 kj/kg-K

As heat is trasfered from hot fluid to cold fluid only and not to atmosphere,

(Thi - Tho) * mh * Ch = (Tci - Tco) * mc * Cc

(525 - 350) * 10 * 2 = (373 - 293) * mc * 4.186

mc = 10.452 kg/s

Therefore, mass flow rate of water is 10.452 kg/s

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