Question

Hot oil at 150°C is used to preheat a cold fluid at 30°C in a 1:1 shell and tube heat exchanger. The exit temperature of the hot oil is 110°C. Heat capacities (product of mass flow rate and specific heat capacity) of both the streams are equal. The heat duty is 2 KW. Under co-current flow conditions, the overall heat transfer coefficient per unit area of the heat exchanger is

• A. $27.46W/m^{2}K$
• B. $72.81W/m^{2}K$
• C. $1120.26W/m^{2}K$
• D. $127.46W/m^{2}K$

Answer 1

The correct option is A $27.46W/m^{2}K$


Given:
$({\dot{m}}_h\times C_{ph})=({\dot{m}}_c\times C_{pc})$

Energy balance:
${\dot{m}}_h{C}_{ph}(T_{hi}-T_{he})={\dot{m}}_c{C}_{pc}(T_{ce}-T_{ei})$

$150-110=T_{ce}-30$

$40=T_{ce}-30$

$T_{ce}=70{}^{\circ }C$

$LMTD\left({\theta }_m\right)=\frac{{\theta }_1-{\theta }_2}{\ell n\left(\frac{{\theta }_1}{{\theta }_2}\right)}=\frac{120-40}{\ell n\left(\frac{120}{40}\right)}=72.819{}^{\circ }C$

Heat transfer = 2 kW = 2000 W

$UA{\theta }_m=2000$

$Overallheattransfercoefficientperunitarea,U=27.46W/m^2.K$