For a heat exchanger with hot fluid inlet/outlet $(T_{h,in}, T_{h,out})$ and cold fluid inlet/outlet $(T_{c,in}, T_{c,out})$, which of the following statements are TRUE?
Options:
(A) For identical terminal temperatures and flow rates, the LMTD for counter-current flow is always greater than or equal to that for co-current (parallel) flow
(B) In counter-current flow, the outlet temperature of the cold fluid can exceed the outlet temperature of the hot fluid
(C) In co-current flow, the cold fluid outlet temperature cannot exceed the hot fluid outlet temperature
(D) When the heat capacity rates are balanced ($C_h = C_c$), the counter-flow temperature profile has parallel lines and $\text{LMTD} = \Delta T_1 = \Delta T_2$
Answer Key:
A, B, C, D
Step-by-Step Solution & Explanation
All four statements are core heat exchanger principles:
1. $\text{LMTD}_{counter} \ge \text{LMTD}_{parallel}$, meaning counter-flow requires less heat transfer area for the same heat duty. (Statement A True)
2. In counter-flow, $T_{c,out}$ can approach $T_{h,in}$, thus exceeding $T_{h,out}$. (Statement B True)
3. In parallel flow, the two streams approach a common thermal equilibrium temperature; $T_{c,out}$ cannot exceed $T_{h,out}$. (Statement C True)
4. When $C_h = C_c$, $\Delta T_1 = \Delta T_2 = \Delta T$. The indeterminate form $\frac{\Delta T - \Delta T}{\ln(\Delta T / \Delta T)} = \frac{0}{0}$ evaluates via L'Hôpital's rule to $\Delta T$. (Statement D True)