A simple insulated concentric tube heat exchanger is used to cool hot oil by transferring heat to water. Hot oil enters the center tube at 120°C, and a mass flow rate of 5.0 kg/s. The oil exits the heat exchanger at 80°C. Liquid water flows through the annulus surrounding the central tube. The water enters at 10°C.

Question

(a) If the water exits at 50°C, determine the mass flow rate of the water.
(b) Using your heat exchanger model to acquire the data, plot the required mass flow rate of the water for water exit temperatures ranging from 15°C to 75°C. Consider the specific heat of the oil to be 1.90 kJ/kg-K, and the specific heat of the liquid water to be 4.18 kJ/kg-K.
Consider State 1 to be the oil inlet and State 2 to be the oil outlet.
Consider State 3 to be the water inlet and State 4 to be the water outlet.
Given: T1 = 120°C; m?oil = 5.0 kg/s; T2 = 80°C
T3 = 10°C, T4 = 50°C
Assume: Q?=0 (insulated). Also, given no other information regarding the heat exchanger, make the following common heat exchanger assumptions: W?=?KE=?PE=0
Also, assume the heat exchanger is a multiple-inlet, multiple-outlet, steady-state, steady-flow device.
What will be an ideal response?

Answer 1

(a) Solution: The First Law for Open systems will reduce to m?oil(h1?h2)=m?w(h4?h3)

We will assume that the oil and water both behave as incompressible substances with constant specific heats: coil = 1.90 kJ/kg-K; cw = 4.18 kJ/kg-K: Then ?h = c?T

So m?w=m?oilcoil(T1?T2)/cw(T4?T3) = (5.0kg/s)(1.90 kJ/kg?K)(120?80)C/(4.18 kJ/kg?K)(50?10)C = 2.27 kg/s

(b) For the given range of exit temperatures, the mass flow rate of the water is