Library / Heat transfer and thermal systems / HTS-41
Heat transfer and thermal systems
Parallel-flow exchanger effectiveness
Effectiveness of a parallel-flow exchanger with both fluids entering at the same end, from the number of transfer units N = UA/Cmin and the capacity ratio Cr = Cmin/Cmax.
- Ref
- HTS-41
- Rev
- v1
- Field
- Heat transfer and thermal systems
- Result
- ε
In a parallel-flow exchanger both fluids enter at the same end and move together, so the outlet temperatures converge towards a common value but can never cross. The effectiveness is ε = [1 − exp(−NTU(1 + Cr))]/(1 + Cr), which cannot exceed 1/(1 + Cr), however large the NTU. NTU = UA/Cmin and Cr = Cmin/Cmax.
Effectiveness of a parallel-flow exchanger with both fluids entering at the same end, from the number of transfer units N = UA/Cmin and the capacity ratio Cr = Cmin/Cmax.
Calculator
- Limit at large NTU, 1/(1 + Cr)0.6667
- Shortfall against the limit0.1488
- Counterflow effectiveness at the same NTU and Cr0.5647
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The exchanger recovers 51.79 % of the maximum possible heat transfer, and cannot exceed 66.67 % however large it is made.
- A counterflow unit of the same size would reach 56.47 %, which is why counterflow is preferred when high effectiveness is needed.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| NTU Number of transfer units UA/Cmin | 0 to 20 | 0 | 0.6667 | 0.6667 | +10% | +4 % |
| Cr Capacity ratio Cmin/Cmax | 0 to 1 | 0.4323 | 0.6321 | 0.1998 | +10% | −1.87 % |
Sweep of Number of transfer units UA/Cmin
| Number of transfer units UA/Cmin | Effectiveness |
|---|---|
| 0 | 0 |
| 2.5 | 0.651 |
| 5 | 0.6663 |
| 7.5 | 0.6667 |
| 10 | 0.6667 |
| 12.5 | 0.6667 |
| 15 | 0.6667 |
| 17.5 | 0.6667 |
| 20 | 0.6667 |
Sweep one variable
Variables and how each one contributes
Effectiveness
What the equation gives you. Everything else feeds it.
Number of transfer units UA/Cmin
The number of transfer units, UA/Cmin. Raises the effectiveness, with falling returns towards the limit 1/(1 + Cr). Raising it by 10 % (to 1.1) moves the result by +4 %, from 0.5179 to 0.5386.
Capacity ratio Cmin/Cmax
The capacity ratio Cmin/Cmax, between 0 and 1. A larger ratio lowers the effectiveness and its limit. Raising it by 10 % (to 0.55) moves the result by −1.87 %, from 0.5179 to 0.5082.
Worked example with the values above
- Exponent: NTU(1 + Cr) = 1 × 1.5 = 1.5; 1 − exp(−that) = 0.77687.
- Divide by 1 + Cr = 1.5.
- ε = 0.51791.
Assumptions and limits
- Steady operation with constant properties and overall coefficient, and an insulated exterior.
- The flow arrangement matches the formula exactly, including which fluid is mixed.
Common mistakes
- Using the wrong stream as Cmin when forming the capacity ratio.
- Mixing up NTU with UA.
- Using a counterflow formula for a parallel or crossflow unit.
Statistics and uncertainty
Effectiveness formulas are exact for their ideal arrangements, but real exchangers have bypass, leakage and non-uniform flow, which lower performance by a few per cent to 10 %. Fouling allowances are largely judgement.
Where it is used
- Rating exchangers from known UA and flow rates.
- Estimating the effect of fouling on duty.
Maths you need
- Capacity rate: C = ṁcp, in W/K
- NTU: UA divided by Cmin
- Effectiveness: actual heat transfer over the thermodynamic maximum