Library / Heat Transfer / HTR-17
Heat Transfer
Heat duty of an exchanger from its effectiveness
Heat transferred in an exchanger from its effectiveness, the smaller heat-capacity rate and the difference between the hot and cold inlet temperatures.
- Ref
- HTR-17
- Rev
- v1
- Field
- Heat Transfer
- Result
- Q̇ [W]
Once the effectiveness ε is known, the heat transferred is simply Q = εCmin(Th,in − Tc,in), where Cmin is the smaller heat-capacity rate (mass flow times specific heat) and the temperatures are the two inlet values. Cmin(Th,in − Tc,in) is the maximum possible heat transfer. The outlet temperatures follow from Q/C for each stream.
Heat transferred in an exchanger from its effectiveness, the smaller heat-capacity rate and the difference between the hot and cold inlet temperatures.
Calculator
- Maximum possible heat transfer, Cmin(Th,in − Tc,in)40,000 W
- Heat transferred in kW22.59 kW
- Temperature change of the stream with Cmin22.59 K
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.
- An exchanger of effectiveness 0.5647 moves 22.59 kW, 56.5 % of the maximum possible 40 kW. The stream with Cmin changes by 22.6 K, from 100 to 77.4 °C if it is the hot one.
- Because the duty scales directly with ε, any gain in effectiveness, from a bigger NTU or a more balanced flow, adds heat in proportion: an exchanger at ε = 0.8 passes 1.42 times the heat of this one.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (W) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Cmin Smaller heat-capacity rate | 10 to 100,000 W/K | 225.9 | 2,259,000 | 2,259,000 | +10% | +10 % |
| Th,in Hot inlet temperature | 20 to 600 °C | −22,590 | 304,900 | 327,500 | +10% | +25 % |
| Tc,in Cold inlet temperature | −50 to 300 °C | −112,900 | 84,700 | 197,600 | +7 °C | −17.5 % |
| ε Effectiveness | 0.05 to 1 | 2,000 | 40,000 | 38,000 | +10% | +10 % |
Sweep of Effectiveness
| Effectiveness | Heat transferred (W) |
|---|---|
| 0.05 | 2,000 |
| 0.1688 | 6,750 |
| 0.2875 | 11,500 |
| 0.4062 | 16,250 |
| 0.525 | 21,000 |
| 0.6438 | 25,750 |
| 0.7625 | 30,500 |
| 0.8812 | 35,250 |
| 1 | 40,000 |
Sweep one variable
Variables and how each one contributes
Heat transferred
What the equation gives you. Everything else feeds it.
Effectiveness
The effectiveness of the exchanger, between 0 and 1. Raises the heat duty in direct proportion. Raising it by 0.05 (to 0.6147) moves the result by +8.85 %, from 22,590 to 24,590 W.
Smaller heat-capacity rate
The smaller of the two heat-capacity rates, in W/K. Raises the heat duty in direct proportion, because a larger flow can carry more heat. Raising it by 100 W/K (to 1,100 W/K) moves the result by +10 %, from 22,590 to 24,850 W.
Hot inlet temperature
The hot-stream inlet temperature, in °C. Raises the heat duty in direct proportion to the inlet temperature difference. Raising it by 5 °C (to 105 °C) moves the result by +12.5 %, from 22,590 to 25,410 W.
Cold inlet temperature
The cold-stream inlet temperature, in °C. Lowers the heat duty: a warmer cold inlet leaves less temperature difference to exploit. Raising it by 5 °C (to 65 °C) moves the result by −12.5 %, from 22,590 to 19,760 W.
Worked example with the values above
- Inlet temperature difference: 100 − 60 = 40 K.
- Maximum heat: Cmin × ΔT = 1,000 × 40 = 40,000 W.
- Q = 0.5647 × 40,000 = 22,590 W.
Assumptions and limits
- Steady operation, with no heat loss to the surroundings and constant specific heats.
- Cmin belongs to the stream with the smaller product of flow and specific heat.
Common mistakes
- Using Cmax instead of Cmin.
- Using outlet temperatures in place of the inlet temperatures.
Statistics and uncertainty
Duty carries the combined uncertainty of ε (a few per cent from the correlation), Cmin (flow and property errors, 2 to 5 %), and the temperature difference. The three combine roughly in quadrature, giving about 5 to 7 %.
Where it is used
- Heat duty of radiators, coolers and recuperators once the effectiveness is known.
- Finding the outlet temperatures of both streams.
Maths you need
- Heat-capacity rate: mass flow times specific heat, in W/K
- Effectiveness: actual heat over maximum possible heat