KEVOS® MAKEOS · Engineering
Waste Heat Recovery Limit Check (Heat Released, Exergy, Claimed Power against the Second-Law Limit)
How much heat does this waste stream give up, what is the most power any machine could make from it, and is the power claimed for a heat recovery unit believable?
Second-law limit on power recovered from a waste heat stream cooled from one temperature to another: the heat released, the exergy (the most work any reversible machine could make, integrating the Carnot efficiency over the cooling with the surroundings as the cold reservoir), the mean Carnot efficiency, the claimed power as a share of the heat and of the exergy, and the yearly value of the claimed power, against the exergy and the largest share of it you consider realistic.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Mass flow of the stream | kg/s | Mass flow of the hot water, oil or gas stream. |
| Specific heat of the stream | kJ/(kg·K) | Mean specific heat of the stream over the temperature range (water about 4.18 kJ/(kg·K)), from property data. |
| Stream temperature in | °C | Temperature of the stream entering the recovery unit. |
| Stream temperature out (after recovery) | °C | Temperature it leaves at; it cannot be below the surroundings. |
| Surroundings (cooling) temperature | °C | Temperature of the surroundings or cooling medium the machine rejects heat to. |
| Claim | ||
| Power claimed | kW | Net electrical or shaft power claimed for the recovery unit. |
| Largest realistic share of the exergy | % | Largest share of the exergy you consider achievable for this kind of machine (your own benchmark). |
| Running hours per year | h/year | Hours a year the stream is available at this condition. |
| Value of electricity (incl. GST) | AUD/kWh | Value of a kilowatt-hour of electricity to the site, including GST, or ex GST for a GST-registered business. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Mass flow of the stream
- What it is
- The mass of the hot stream passing through the recovery unit each second, such as hot water, oil or exhaust gas.
- Units and format
- Enter a number in kg/s: kg/s. The form accepts 0.000001 kg/s to 100000 kg/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 kg/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Heat released and exergy both rise in proportion.
- Get it right
- Convert volume flow to mass flow with the density at the stream temperature.
What this means: Specific heat of the stream
- What it is
- The average heat released by one kilogram of the stream per kelvin of cooling over the temperature range used.
- Units and format
- Enter a number in kJ/(kg·K): kilojoules per kilogram per kelvin. The form accepts 0.000001 kJ/(kg·K) to 100 kJ/(kg·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4.18 kJ/(kg·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Heat released and exergy both rise in proportion.
- Get it right
- Water is about 4.18 kJ/(kg·K); exhaust gas is roughly a quarter of that. Take values from property data.
What this means: Stream temperature in
- What it is
- The temperature of the waste stream as it enters the recovery unit, the hot end of the cooling.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 2000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A hotter stream releases more heat and a much larger share of it as exergy.
- Get it right
- Measure it at the recovery unit inlet, after any losses in the pipework.
What this means: Stream temperature out (after recovery)
- What it is
- The temperature the stream leaves the recovery unit at, the cold end of the cooling; it cannot be below the surroundings.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 2000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Cooling further releases more heat, though the extra heat holds little exergy.
- Get it right
- For flue gas keep it above the acid dew point; that limit is yours to set.
What this means: Surroundings (cooling) temperature
- What it is
- The temperature of the surroundings or cooling water the recovery machine rejects heat to, the cold reservoir of the Carnot limit.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 100 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A warmer surroundings temperature lowers the exergy.
- Get it right
- Use the cooling medium’s temperature at the time of the claim; summer air is warmer and lowers the limit.
Claim
What this means: Power claimed
- What it is
- The net electrical or shaft power the supplier claims the recovery unit will deliver from this stream.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0 kW to 1000000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Moves the shares of heat and exergy and the yearly value; the limit does not change.
- Get it right
- Ask whether the figure is net of the unit’s own pumps and fans; gross figures overstate it.
What this means: Largest realistic share of the exergy
- What it is
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the line between a plausible and an optimistic claim.
- Get it right
- Set it from independent test data or your own experience; this tool does not give a value.
What this means: Running hours per year
- What it is
- The number of hours a year the waste stream is available at this flow and temperature, used for the yearly value.
- Units and format
- Enter a number in h/year: h/year. The form accepts 0 h/year to 8784 h/year. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6000 h/year as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The yearly value rises in proportion.
- Get it right
- Use hours when the process actually runs at this condition, not calendar hours.
What this means: Value of electricity (incl. GST)
- What it is
- The value to the site of one kilowatt-hour of electricity generated, used for the yearly value of the claimed power.
- Units and format
- Enter a number in AUD/kWh: Australian dollars per kilowatt-hour. The form accepts 0 AUD/kWh to 100 AUD/kWh. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.25 AUD/kWh as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The yearly value rises in proportion.
- Get it right
- Use the avoided purchase price; exported power is usually worth much less. State the GST basis.
Method and formulas
- Heat released Q = ṁ c_p (T₁ − T₂).
- Each element of heat dQ at temperature T can give at most (1 − T₀ ÷ T) dQ of work (Carnot efficiency, Fermi eq 59); integrating over the cooling gives exergy E = ṁ c_p [(T₁ − T₂) − T₀ ln (T₁ ÷ T₂)], temperatures in kelvin.
- Mean Carnot efficiency = E ÷ Q; claim shares = W ÷ Q and W ÷ E; yearly value = W × hours × price.
- Example: 313.5 kW of heat holds at most 41.223 kW of power; the 15 kW claim is 36.388 % of that limit.
Limitations
- Constant specific heat and a single stream cooled steadily; phase change (condensing flue gas or steam) needs latent heat added separately.
- The exergy is a theoretical ceiling: real machines also lose to pumps, fans and parasitic loads, which the claim should already deduct.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Test a supplier’s power claim for a heat-to-power unit
- Find the most power a hot water or flue gas stream could give
- Decide whether waste heat is better used as heat than turned into power
Who it is for
- Energy managers
- Process and plant engineers
- Engineering managers assessing proposals
What you get
- Heat released
- Exergy and mean Carnot efficiency
- Claimed power as a share of heat and exergy
- Yearly value of the claimed power
Interpreting the result
- Low-temperature heat holds little exergy: water at 90 °C has a mean Carnot efficiency of only about 13 % when cooled to 40 °C against 20 °C surroundings, so using it directly as heat is often worth more.
References
- Fermi E., Thermodynamics (Dover Publications, 1956; first published by Prentice-Hall, 1937), pp. 44, 48–58. Method reference; no text, examples or tables are reproduced.
- Çengel Y. A. and Boles M. A., Thermodynamics: An Engineering Approach (McGraw-Hill): exergy of a stream.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Explains the concept · KEVOS® original book
Lost work and exergy
What it covers: Turn entropy into kilowatts: the lost-work theorem, the exergy of heat, of flowing streams and of cold, an exergy balance for each piece of plant, and why every audit must state its dead state.
Method explained here · KEVOS® original book
Recovering engine heat: exhaust, jacket water and the exergy limit
In On-Site Power and Heat by the Numbers
What it covers: Where an engine's rejected heat goes, the exergy of a stream that cools as it gives up heat, matching each stream to a demand at the right temperature, and testing a heat-to-power claim.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.