Question

A heat exchanger is used to condense 10 kg/s of a fluid $(h_{fg}=500kJ/kg)$ with a cooling water flowing at 60 kg/s. The log mean temperature difference for heat exchanger is 60${}^o$C and overall heat transfer coefficient is 500 W/m${}^2$K. The tubes used are 25 mm diameter and 5 m length. The velocity of cooling water is 3 m/s. What are the number of tube passes required? Assume cooling water flowing through tube and neglect pipe thickness.

• A. 41
• B. 9
• C. 8
• D. 11

Answer 1

The correct option is D 11

Given: ${\theta }_m={60}^{o}C,m_h=10kg/s,h_{fg}=500kJ/kg$

Now,
$m_h{h}_{fg}=UA{\theta }_m$

$\Rightarrow m_h{h}_{fg}=U(\pi d_{0}l\times n\times p){\theta }_m$

$\Rightarrow 10\times 500\times {10}^3=500[\pi \times 0.025\times 5\times n\times p]\times 60$

$\Rightarrow n\times p=424.41$

Let the mass flow rate of cold fluid in each pass and number of tubes in each pass and p number of tube passes be $m_c$ and $\rho$ respecitvely

$\Rightarrow m_c=[\frac{\pi }{4}{d}^2\times v\times \rho ]n$

$\Rightarrow 60=\frac{\pi }{4}\times (0.025{)}^2\times 3\times 1000\times n$

$\Rightarrow n=40.7$

Number of passes $=\frac{424.41}{41}=10.35\simeq 11$