A simple insulated concentric tube heat exchanger is used to cool hot water by transferring heat to cool air. Hot water enters the center tube at 200oF, and a mass flow rate of 6.5 lbm/s. The water exits the heat exchanger at 100°F. Air flows through the annulus surrounding the central tube. The air enters at 50°F.
(a) If the air exits at 95°F, determine the mass flow rate of the air.
(b) Using your heat exchanger model to acquire the data, plot the required mass flow rate of the air for air exit temperatures ranging from 55°F to 100°F.
(c) Consider that the maximum allowed exit temperature of the air is 90°F. Plot the maximum exit water temperature as a function of the mass flow rate of the air for air mass flow rates varying between 5 lbm/s and 70 lbm/s. Consider the specific heat of the air to be 0.240 Btu/lbm-R, and the specific heat of the liquid water to be 1.00 Btu/lbm-R.
Consider State 1 to be the water inlet and State 2 to be the water outlet. Consider State 3 to be the air inlet and State 4 to be the air outlet.
Given: T1 = 200°F; m? w = 6.5 lbm/s; T2 = 100°F T3 = 50°F, T4 = 95°F
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?
(a) The First Law for Open systems will reduce to
m? w(h1 ? h2) = m? air(h4 ? h3)
We will assume that the water behaves as incompressible substances with constant specific heats: cw = 1.00 Btu/lbm-R: Then ?hw = cw ?Tw
Assume the air behaves as an ideal gas with constant specific heats: cp,air = 0.240 Btu/lbm-R, and then ?hair = cp,air ?Tair
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