Question

What is the physical significance of the number of transfer units \(\mathrm{NTU}=h A_{s} / \dot{m} c_{p}\) ? What do small and large NTU values tell us about a heat transfer system?

Short answer

Answer: The NTU in a heat transfer system can be affected by factors such as heat transfer surface area, heat transfer coefficient, and mass flow rate. Small heat transfer surface area, poor heat transfer coefficient, and high mass flow rate can result in a lower NTU, indicating a less effective heat transfer system. On the other hand, large heat transfer surface area, high heat transfer coefficient, and low mass flow rate can lead to a higher NTU, indicating a highly effective heat transfer system.

Step-by-step solution

Defining the terms in the NTU formula

The NTU formula is given as \(\mathrm{NTU}=h A_{s} / \dot{m} c_{p}\), where: - \(NTU\): Number of Transfer Units, a dimensionless number - \(h\): Heat transfer coefficient (W/m²K) - \(A_s\): Heat transfer surface area (m²) - \(\dot{m}\): Mass flow rate (kg/s) - \(c_p\): Specific heat capacity of the fluid at constant pressure (J/kgK) The NTU (Number of Transfer Units) quantifies how effective a heat exchanger is in transferring heat between two fluids.

Significance of NTU

The NTU is a measure of the "thermal size" of a heat exchanger, which accounts for its ability to transfer heat from one fluid to another. A high NTU indicates that the exchanger is highly effective in transferring heat between the two fluids, while a low NTU means that the exchanger is less effective in transferring heat.

Small NTU values

Small NTU values indicate that the heat exchanger is relatively ineffective in transferring heat between the two fluids. This could be due to a variety of factors, such as: - Low heat transfer surface area: A smaller heat transfer surface area reduces the potential for heat to transfer between the fluids, resulting in a lower NTU value. - Poor heat transfer coefficient: A low heat transfer coefficient indicates that the heat transfer process is not as effective, likely due to a lower thermal conductivity of the materials involved or impeded heat transfer due to dirt, fouling, or other factors. - High mass flow rate: A high mass flow rate means the fluid is moving quickly through the system, which can limit the amount of time the fluid spends in the heat exchanger, reducing the opportunity for heat transfer to take place.

Large NTU values

Large NTU values indicate that the heat transfer system is highly effective in transferring heat between the fluids, which can be due to a variety of factors, such as: - Large heat transfer surface area: The larger the heat transfer surface area, the greater the potential for heat exchange between the fluids, leading to a higher NTU value. - High heat transfer coefficient: A high heat transfer coefficient indicates that the heat transfer process is more effective, which can be due to increased thermal conductivity for both the heat exchanger materials and the fluids themselves. - Low mass flow rate: If the mass flow rate is low, the fluid spends more time in the heat exchanger, allowing for more thorough heat exchange and thus increasing the NTU value. In conclusion, the Number of Transfer Units (NTU) is a significant parameter to characterize the performance of heat transfer systems. Small NTU values indicate less effective heat transfer systems, whereas large NTU values indicate highly effective heat transfer systems. By understanding the impact of the heat transfer surface area, heat transfer coefficient, and mass flow rate on NTU, we can design more efficient heat exchangers and optimize heat transfer system performance.