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Consider the two countercurrent heat exchanger designs for heating a cold stream from $t_{in}$ to $t_{out}$ as shown in figure. The hot process stream is available at $T_{in}$. The inlet stream conditions and overall heat transfer coefficients are identical in both the designs. The heat transfer area in Design $I$ and Design $II$ are respectively $A_{HX}^{I}$ and $A_{HX}^{II}$

If heat losses are neglected, and if both the designs are feasible, which of the following statements holds true:

  1. $A_{HX}^{I}> A_{HX}^{II}\:\:\:\:T_{out}^{I}< T_{out}^{II}$
  2. $A_{HX}^{I}= A_{HX}^{II}\:\:\:\:T_{out}^{I}=T_{out}^{II}$
  3. $A_{HX}^{I}<  A_{HX}^{II}\:\:\:\:T_{out}^{I}> T_{out}^{II}$
  4. $A_{HX}^{I}< A_{HX}^{II}\:\:\:\:T_{out}^{I}= T_{out}^{II}$
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