Question

In a double pipe cocurrent heat exchanger, operating at steady state, oil (specific heat capacity = \(2100\ \mathrm{J\,kg^{-1}\,^\circ C^{-1}}\)) entering at \(7\ \mathrm{kg\,s^{-1}}\) at \(100^\circ\mathrm{C}\) is used to heat water (specific heat capacity = \(4200\ \mathrm{J\,kg^{-1}\,^\circ C^{-1}}\)) flowing at \(3.5\ \mathrm{kg\,s^{-1}}\) from \(20^\circ\mathrm{C}\) to \(50^\circ\mathrm{C}\). If the overall heat transfer coefficient is \(291\ \mathrm{W\,m^{-2}\,^\circ C^{-1}}\), the required heat transfer area (in \(\mathrm{m^2}\)) is ______ (rounded off to one decimal place).

Hint:

First find the oil outlet temperature from an energy balance, then compute the cocurrent LMTD from the inlet-end and outlet-end temperature differences, and use \(Q=UA\Delta T_{lm}\).

Answer 1

Correct Answer: 35

Both streams have equal heat capacity rates (14700 W/C), so both change by 30C. Oil outlet is 70C. LMTD=43.28C. $A=441000/(291\times43.28)\approx35.0\ \mathrm{m^2}$.