Project ForgeTwo countercurrent heat exchanger designs heat a cold stream from tin to tout using a hot stream available at Tin, with identical inlet conditions and overall heat transfer coefficients. Design I is a simple exchanger; Design II includes an internal recycle loop. If heat losses are neglected and both designs are feasible, which statement holds?
- AA_HX^I > A_HX^II, T_out^I < T_out^II
- BA_HX^I = A_HX^II, T_out^I = T_out^II
- CA_HX^I < A_HX^II, T_out^I > T_out^II
- A_HX^I < A_HX^II, T_out^I = T_out^II
Explanation
Since the inlet flow rates, inlet temperatures, and the fixed target tin→tout duty are identical between the two designs, an overall energy balance (Q=Ḟin·Cp·(tout−tin)=ḟin·Cp·(Tin−Tout)) forces Tout to be IDENTICAL in both cases regardless of the exchanger's internal configuration. Design II's internal recycle reduces the effective driving force (akin to partial back-mixing), requiring MORE area for the same duty: A_HX^I < A_HX^II.
Source: GATE CH 2019 (2019)
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