# Thermodynamics shell-and-tube heat exchanger

A shell-and-tube heat exchanger is used to cool a flow of steam using a stream of cooling water cooling water. The steam enters the heat exchanger at $0.1 ~bar$ and a quality of $91$% , and exits as a saturated liquid at the same pressure. The mass flow rate of the steam is $2.6 ⋅ 10^5 \frac{kg}{hour}$. The cooling water enters the heat exchanger at $5 ~MPa$ and $15^ \circ{C}$ and exits at $38^ \circ{C}$at the same pressure.

Neglect stray heat transfer and neglect kinetic and potential energy effects. As well, assume the system is operating under steady-state conditions. Draw a schematic of the system and locate the state points on a T-v diagram. Determine the mass flow rate of cooling water in kg/s and determine the rate of heat transfer between the steam and the cooling water in MW.

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I know by neglecting PE and KE and rearranging we have,

$$m_3 = m_1 ⋅ \frac{h_1-h_2}{h_4-h_3}$$

which i solved for using some table values for enthalpy to get $m_3 = 1634.44 \dfrac{kg}{s}$

now how do I determine the rate of heat transfer between the steam and the cooling water? and if someone could show me the T-v diagram, would be awesome!

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google mean log temperature difference for the HX sizing. –  mart Oct 14 '13 at 13:38