Question

Consider a heat exchanger that has an NTU of 4 . Someone proposes to double the size of the heat exchanger and thus double the NTU to 8 in order to increase the effectiveness of the heat exchanger and thus save energy. Would you support this proposal?

Short answer

Question: Evaluate the impact of doubling the size of a heat exchanger to increase its NTU from 4 to 8 on its effectiveness and energy savings, assuming a parallel-flow configuration with equal heat capacity rates for both fluids. Answer: Doubling the size of the heat exchanger from NTU 4 to 8 in a parallel-flow configuration with equal heat capacity rates for both fluids, does not result in a significant increase in its effectiveness. The effectiveness remains constant at 1 for both NTU values. Hence, it does not necessarily lead to energy savings based on this analysis. More information and analysis would be needed to support the proposal of increasing the size of the heat exchanger.

Step-by-step solution

Understand the relationship between NTU and effectiveness

The effectiveness of a heat exchanger is defined as the ratio of actual heat transfer to the maximum possible heat transfer. It can be represented as a function of NTU and the heat capacity rates of the fluids involved (C_min and C_max). For some common heat exchanger configurations, the effectiveness-NTU relationships can be found in heat transfer literature.

Determine the heat exchanger configuration

In the given exercise, the configuration of the heat exchanger is not mentioned. However, we will consider a simple parallel-flow heat exchanger configuration for our analysis. For other configurations, similar relationships can be derived and the analysis would follow the same steps.

Use the effectiveness-NTU relationship for the parallel-flow heat exchanger

For a parallel-flow heat exchanger, the effectiveness E is represented by: E = (1 - e^{(-NTU * (1 - R))}) / (1 - R * e^{(-NTU * (1 - R))}) Here R is the ratio of minimum heat capacity rate to maximum heat capacity rate (C_min/C_max). For demonstration purposes, we will assume R = 1, which means that both fluids have equal heat capacity rates.

Calculate effectiveness at NTU = 4 and NTU = 8

We substitute the given values of NTU in the effectiveness equation and calculate the effectiveness E. For NTU = 4: E = (1 - e^{(-4 * (1 - 1))}) / (1 - 1 * e^{(-4 * (1 - 1))}) E = (1 - e^0) / (1 - e^0) = 1 For NTU = 8: E = (1 - e^{(-8 * (1 - 1))}) / (1 - 1 * e^{(-8 * (1 - 1))}) E = (1 - e^0) / (1 - e^0) = 1

Evaluate the proposal

We observe that the effectiveness remains the same (equal to 1) when the NTU is increased from 4 to 8. This indicates that doubling the size of the heat exchanger will not result in a significant increase in its effectiveness (at least for the assumed configuration and parameters). Based on this analysis, increasing the NTU from 4 to 8 does not necessarily lead to energy savings for the given heat exchanger configuration and parameters. Therefore, it may not be a justified proposal, and more information and analysis would be needed to support it.