I. The Awkwardness of the LMTD Method
The previous article designed with Q = K·A·LMTD, but when checking, the outlet temperature is unknown and LMTD cannot be calculated, requiring repeated trial calculation. The ε-NTU method bypasses this, directly using area and capacity ratio to find effectiveness.
II. Three Core Quantities
- Heat capacity flow rate C = m·cp (how much heat can be carried per unit time);
- Heat capacity ratio Cr = C_min / C_max (0~1; Cr→0 when one side has phase change);
- Number of transfer units NTU = K·A / C_min, representing "how strong the heat transfer capacity is relative to the heat capacity flow rate."
Effectiveness ε = actual heat transfer / maximum possible heat transfer, where the maximum possible = C_min·(T_hot_in − T_cold_in).
III. ε Formulas for Typical Flow Patterns
| Flow Pattern | ε Expression (schematic) |
|---|---|
| Counter flow | ε = (1 − exp(−NTU(1−Cr))) / (1 − Cr·exp(−NTU(1−Cr))) |
| Parallel flow | ε = (1 − exp(−NTU(1+Cr))) / (1 + Cr) |
| One-side phase change (Cr=0) | ε = 1 − exp(−NTU) |
In engineering, one directly consults the ε-NTU chart or table without hand-calculating the exponential.
IV. When to Use It
- Check existing equipment: Given K, A, and flow rates, find how much heat can be transferred and the outlet temperature in one step;
- Reverse selection: Set the target ε and Cr, look up the required NTU, then obtain K·A;
- Compare flow patterns: At the same NTU and Cr, counter flow has the highest ε and parallel flow the lowest, again confirming the counter-flow advantage.
Remember the division of labor: LMTD suits "known temperature difference, find area"; ε-NTU suits "known area, find capacity."