Question

In the heat transfer relation \(\dot{Q}=U A_{s} F \Delta T_{\mathrm{lm}}\) for a heat exchanger, what is the quantity \(F\) called? What does it represent? Can \(F\) be greater than 1?

Short answer

Answer: In the heat exchanger relation, the correction factor (F) accounts for deviations from the ideal counter-current flow and adjusts the heat transfer equation accordingly. Its value is always between 0 and 1 (0<F≤1), meaning it can never be greater than 1.

Step-by-step solution

Identify the heat transfer relation

The given relation for heat transfer in a heat exchanger is \(\dot{Q}=U A_{s} F \Delta T_{\mathrm{lm}}\). In this relation, various symbols represent: - \(\dot{Q}\): rate of heat transfer - \(U\): overall heat transfer coefficient - \(A_s\): surface area for heat transfer - \(F\): correction factor - \(\Delta T_{\mathrm{lm}}\): logarithmic mean temperature difference

Understand the purpose of the Correction Factor (F)

The correction factor, \(F\), is used to account for any deviation from the ideal counter-current flow in a heat exchanger. In ideal conditions, the heat exchanger has pure counter-current flow, which means the hot fluid flows in the opposite direction of the cold fluid. However, in real-world heat exchangers, the flow is not always purely counter-current, which reduces the efficiency of the heat transfer process. Therefore, the correction factor is introduced to adjust the heat transfer equation for these deviations from the ideal counter-current flow.

Determine if F can be greater than 1

As mentioned earlier, the correction factor \(F\) accounts for deviations from the ideal counter-current flow. Since an ideal counter-current flow has the maximum possible efficiency, any deviation from it would reduce the efficiency of the heat exchanger. Therefore, the correction factor \(F\) is introduced to decrease the heat transfer rate in such cases. Hence, the value of \(F\) is always between 0 and 1, i.e., \(0<F\leq 1\). This means that the correction factor can never be greater than 1.