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?

First, we will calculate the effectiveness of the heat exchanger at the initial NTU value of 4. We will use the effectiveness formula, which is: Effectiveness \((ε_1)\) = \( (1- e^{-NTU_1(1-C_r)})/(1-C_r e^{-NTU_1(1-C_r)}) \) Plug the NTU_1 value (4) into the equation to find ε_1.

Next, we will calculate the effectiveness of the proposed heat exchanger at NTU_2 of 8. We will use the same effectiveness formula: Effectiveness \((ε_2)\) = \( (1- e^{-NTU_2(1-C_r)})/(1-C_r e^{-NTU_2(1-C_r)}) \) Plug the NTU2 value (8) into the equation to find ε2.

Now, we will compare the values of ε1 and ε2. If ε2 is significantly greater than ε1, the increase in effectiveness might lead to energy savings, and we can support the proposal. However, if there is only a marginal difference, the proposal might not bring significant energy savings.

Based on the comparison in Step 3, if the increase in effectiveness justifies the extra cost of doubling the size of the heat exchanger, we can support the proposal. Otherwise, we should not support the proposal. (Note: This solution assumes that doubling the size of the heat exchanger will indeed double the NTU value in practice. And it should be noted that this simplification does not factor in potential energy-saving differences for various heat exchanger types, i.e., countercurrent flow, parallel flow, or heat exchanger efficiency values. There are also additional practical considerations, such as available installation space and maintenance requirements, that should be taken into account when deciding on a proposal.)