Question

Oil is cooled by water in a counter flow heat exchanger. The oil flow rate is 2000 kg/h, entering at ${107}^{o}C$ and leaving at ${30}^{o}C$. Its mean specific heat is 2.51 kJ/kg.K. Water enters at ${15}^{o}C$ and its exit temperature is not to exceed ${80}^{o}C$. The heat transfer coefficient is expected to be $1.5kW/m^{2}K$

The surface area required for the heat exchanger is

• A. $350m^2$
• B. $0.35m^2$
• C. $35m^2$
• D. $3.5m^2$

Answer 1

The correct option is D $3.5m^2$


$U=1500W/m^2.K,$

$\dot{m_o}=2000kg/hr=0.555kg/s$

$C_{po}=2510J/kg-K$

${\theta }_m=LMTD=\frac{{\theta }_1-{\theta }_2}{ln\left(\frac{{\theta }_1}{{\theta }_2}\right)}=\frac{27-15}{ln\left(\frac{27}{15}\right)}={20.41}^{o}C$

$\text{Net heat transfer}=\dot{m_0}.C_{po}(T_{hi}-T_{he})$

$U.A{\theta }_m=\dot{m_0}.C_{po}(T_{hi}-T_{he})$

$1500\times A\times 20.41=0.5556\times 2510\times (107-30)$

$\Rightarrow A=3.5m^2$