# Answer to Question #83902 in Mechanical Engineering for GOPAL JHA

The *NTU* (number of transfer units) is given by

@$NTU=\frac{UA}{C_{min}},@$

where *U* is the overall heat transfer coefficient,

*A* is the heat transfer area,

*C*_{min}* *is the smaller heat capacity of the two fluids
.

Since the flow rates of the fluids remain the same in both cases, the overall heat transfer coefficient *U* is the same too. The area of the heat exchanger and the smaller heat capacity of the fluids remain the same. Thus, the *NTU* the same for both cases too.

The figure above shows the dependencies of the effectiveness from *NTU* and *C*_{min}/*C*_{max}* *ratio for the paralle-flow and counter-flow double pipe heat exchangers. In our case the maximum to minimum thermal capacity ratio is 0.5. Thus, from the plot (*b*) we can define *NTU *= 0.8 for the counter-flow. Now, from the plot (*a*) we can define the effectiveness of the parallel-flow heat exchanger as @$\varepsilon=48\%@$.

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