Answer to Question #83902 in Mechanical Engineering for GOPAL JHA

Question

A double pipe heat exchanger has an effectiveness of 0.5 when the flow is counter- current and the thermal capacity of one fluid is twice that of the Other fluid. Calculate the effectiveness of the heat exchanger if the direction is of flow of one of the Fluids is reversed with the same mass flow rates as before?

Answer 1

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

$$\varepsilon=48\%$$

.