Question

The hot gases enters a parallel flow heat exchanger at ${425}^{o}C$ and leaves at ${260}^{o}C$, heating 25kg/s of water from ${32}^{o}C$ to ${82}^{o}C$. For a surface area of $370m^2$, what is the overall heat transfer coefficient in $\left(W/m^{2}K\right)$

• A. 521.4
• B. 13.03
• C. 52.14
• D. 26.07

Answer 1

The correct option is C 52.14


Heat transfered by the heat exchanger = Heat gained by the cold water

$UA\left(LMTD\right)=\dot{m_c}C{p}_c(\Delta T{)}_e$

$U=\frac{\dot{m}{C}_p\left(\Delta T\right)}{A\left(LMTD\right)}$

$LMTD=\frac{(\Delta T{)}_i-(\Delta T{)}_e}{ln\left(\frac{(\Delta T{)}_i}{(\Delta T{)}_e}\right)}$

From equation (1)

$U=\frac{25\times 4200(82-32)}{370\times \frac{(393-178)}{ln\left(\frac{393}{178}\right)}}$

$U=52.27W/m^2-K$