GATE Papers >> Mechanical >> 2019 >> Question No 156

Question No. 156 Mechanical | GATE 2019

Hot and cold fluids enter a parallel flow double tube heat exchanger at 100 °C and 15 °C, respectively. The heat capacity rates of hot and cold fluids are Ch = 2000 W/K and Cc = 1200 W/K, respectively. If the outlet temperature of the cold fluid is 45 °C, the log mean temperature difference (LMTD) of the heat exchanger is _________ K (round off to two decimal places).


Answer : 57.00 to 58.00


Solution of Question No 156 of GATE 2019 Mechanical Paper

Ch = 2000 W/K

Cc = 1200 W/K

By energy equation,

$ \begin{array}{l}{\mathrm C}_{\mathrm h}\left(\triangle{\mathrm T}_{\mathrm h}\right)={\mathrm C}_{\mathrm c}\left(\triangle{\mathrm T}_{\mathrm c}\right)\\2000\left(100-{\mathrm T}_{\mathrm{ho}}\right)=1200\left(30\right)\\{\mathrm T}_{\mathrm{ho}}=82^\circ\mathrm C\\\mathrm{LMTD}=\frac{\left(\left(100-15\right)-82-45\right)}{\ln\left({\displaystyle\frac{100-15}{82-45}}\right)}=57.71^\circ\mathrm C\end{array} $

Since LMTD is temperature difference so the answer will be 57.71 K

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