# Entropy Generation of Desalination Powered by Variable Temperature Waste Heat

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Derivation of Performance Parameters for Desalination

**Figure 1.**A control volume is selected around a black-box, waste heat driven desalination system such that the seawater (sw), product (p) and brine (b) streams are all at the environmental temperature, ${T}_{0}$, and pressure ${p}_{0}$.

**Figure 2.**Least heat of separation, ${\dot{Q}}_{\mathrm{least}}$ is a function of recovery ratio and source temperature. Results are shown for environmental temperature of 25 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$.

**Figure 3.**Second Law Efficiency ${\eta}_{II}$ for seawater desalination with an environmental temperature at 25 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$.

## 3. Entropy Generation Mechanisms

**Table 1.**Entropy Generation for Different Processes in Desalination, Partly Organized by Largest Total Contribution to the Technologies Modeled [16].

Entropy Generation | Occurrence | Equation |
---|---|---|

${S}_{\mathrm{gen}}^{\mathrm{HeatExchanger}}$ | unbalanced heat exchangers | ${\left(\right)}_{\dot{m}}\text{stream}\phantom{\rule{4.pt}{0ex}}\text{1}+{\left(\right)}_{\dot{m}}\text{stream}\phantom{\rule{4.pt}{0ex}}\text{2}$ |

${\dot{s}}_{\mathrm{gen}}^{\text{T}\phantom{\rule{4.pt}{0ex}}\text{gradient}}$ | heat transfer across $\Delta T$ | $\dot{Q}(\frac{1}{{T}_{C}}-\frac{1}{{T}_{H}})$ |

${s}_{\mathrm{gen}}^{\text{R}ankine}$ | attainable Rankine Cycle losses | $\frac{{\dot{W}}_{\text{sep}}(1-{\eta}_{\mathit{II}})}{{T}_{0}}$ |

${\dot{s}}_{\mathrm{gen}}^{\text{Q}\phantom{\rule{4.pt}{0ex}}\text{lost}\phantom{\rule{4.pt}{0ex}}\text{to}\phantom{\rule{4.pt}{0ex}}\text{environment}}$ | heat lost to environment | $\dot{m}cln\frac{{T}_{out}}{{T}_{in}}$ |

${s}_{\mathrm{gen}}^{T\phantom{\rule{4.pt}{0ex}}\text{disequilibrium}}$ | $\Delta T$ between output and environment | ${c}_{i}\left(\right)open="["\; close="]">ln\left(\right)open="("\; close=")">\frac{{T}_{0}}{{T}_{i}}+\frac{{T}_{i}}{{T}_{0}}-1$ |

${s}_{\mathrm{gen}}^{\text{flashing}}$ | flashing: evaporation from rapid pressure drop (throttling) | $cln\frac{{T}_{2}}{{T}_{1}}+x\left(\right)open="\{"\; close="\}">({c}_{p}-c)ln{T}_{2}-Rln{p}_{2}$ $+x\left(\right)open="\{"\; close="\}">\left(\right)open="["\; close="]">{s}_{\mathrm{ref}}^{\mathrm{IG}}-{s}_{\mathrm{ref}}^{\mathrm{IF}}-({c}_{p}-c)ln{T}_{\mathrm{ref}}+Rln{p}_{\mathrm{ref}}$ |

${s}_{\mathrm{gen}}^{\text{expansion,IF}}$ | reverse osmosis pressure recovery | $cln\left(\right)open="["\; close="]">1+\frac{v}{c{T}_{1}}({p}_{1}-{p}_{2})\left(\right)open="("\; close=")">1-{\eta}_{e}$ $\approx \frac{v}{{T}_{1}}({p}_{1}-{p}_{2})\left(\right)open="("\; close=")">1-{\eta}_{e}$ |

${s}_{\mathrm{gen}}^{\text{expansion,IG}}$ | turbines | ${c}_{p}ln\left(\right)open="\{"\; close="\}">1+{\eta}_{e}\left(\right)open="["\; close="]">{\left(\right)}^{\frac{{p}_{2}}{{p}_{1}}}R/{c}_{p}-1$ |

${s}_{\mathrm{gen}}^{\Delta p,\mathrm{IF}}$ | throttling (valves) for fluids | $cln\left(\right)open="["\; close="]">1+\frac{v}{c{T}_{1}}({p}_{1}-{p}_{2})\approx \frac{v}{{T}_{1}}({p}_{1}-{p}_{2})$ |

${s}_{\mathrm{gen}}^{\Delta p,\mathrm{IG}}$ | throttling (valves) for gases | $-Rln\frac{{p}_{2}}{{p}_{1}}$ |

${s}_{\mathrm{gen}}^{\text{compression}}$ | compressors, e.g., in MVC | ${c}_{p}ln\left(\right)open="\{"\; close="\}">1-\frac{1}{{\eta}_{p}}\left(\right)open="["\; close="]">1-{\left(\right)}^{\frac{{p}_{2}}{{p}_{1}}}R/{c}_{p}$ |

${s}_{\mathrm{gen}}^{\text{pumping}}$ | pump efficiency for fluids | $cln\left(\right)open="["\; close="]">1+\frac{v}{c{T}_{1}}({p}_{2}-{p}_{1})\left(\right)open="("\; close=")">\frac{1}{{\eta}_{p}}-1$ $\approx \frac{v}{{T}_{1}}({p}_{2}-{p}_{1})\left(\right)open="("\; close=")">\frac{1}{{\eta}_{p}}-1$ |

${\dot{s}}_{\mathrm{gen}}^{\text{Chem}\phantom{\rule{4.pt}{0ex}}\text{disequilibrium}}$ | salinity difference between environment and output stream | $\frac{1}{{T}_{0}}\left(\right)open="["\; close="]">{\dot{W}}_{\text{least}}-{\dot{W}}_{\text{least}}^{\text{min}}$ |

## 4. Unused Temperature Reduction of Waste Heat Sources

**Figure 4.**Efficiency factor ${\eta}_{\mathrm{reduced}}$ versus temperature reduction (${T}_{source}-{T}_{H}$) for various source temperatures. All results shown for environmental temperature at 25 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$.

## 5. Entropy Generation Analysis of Seawater Desalination Technologies

#### 5.1. Modeling Approximations and Assumptions

**Table 2.**Standard input conditions used for desalination system models. Note, ${T}_{stage}^{last}$ is only applicable to thermal technologies.

Input and Output Streams for All Systems | ||||
---|---|---|---|---|

${T}_{H1}$ | 50 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | ${T}_{sw}$ | 25 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | |

${T}_{H2}$ | 70 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | ${T}_{stage}^{last}$ | 35 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | |

${T}_{H3}$ | 90 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | ${S}_{p}$ | 0 $\mathrm{g}/\mathrm{kg}$ | |

${T}_{H4}$ | 110 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | ${S}_{sw}$ | 35 $\mathrm{g}/\mathrm{kg}$ |

- (1)
- All processes are modeled as steady state.
- (2)
- Heat transfer to the environment is negligible.
- (3)
- All streams are considered well mixed and bulk physical properties are used.
- (4)
- Heat transfer coefficients are constant within a given heat exchanger.
- (5)
- Seawater properties can be calculated using correlations from Sharqawy et al. [19].
- (6)
- Product water is pure (zero salinity).
- (7)
- In systems with multiple stages, the number of stages was proportionally reduced for lower waste heat temperature.
- (8)
- In systems with multiple stages, the recovery in each remaining stage stays roughly the same for lower temperatures.
- (9)
- Pumping power may be neglected in thermal systems.
- (10)
- Temperature drop across heat exchangers is between 2.5 and $3.3$ ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$

#### 5.2. Multistage Flash

- In systems with multiple stages, the $\Delta T$ across each stage is constant.
- $\Delta {T}_{\text{exchanger}}^{heat}=3$ ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ and $\Delta {T}_{\text{stages}}=$ $2.85$ ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$, where the latter sets the number of stages [16].

Parameter | ${T}_{H}$ | |||||
---|---|---|---|---|---|---|

Output | $110{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\text{C}$ | $90{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\text{C}$ | $70{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\text{C}$ | $50{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\text{C}$ | ||

Number of stages | n | (-) | 24 | 17 | 11 | 4 |

Gained output ratio | GOR | (-) | 10.3 | 7.3 | 4.4 | 1.4 |

Recovery ratio | RR | (-) | 11.1% | 7.7% | 4.3% | 1.3% |

Steam flow rate | ${\dot{m}}_{s}$ | (kg/s) | 0.0983 | 0.137 | 0.222 | 0.674 |

Brine salinity | ${y}_{n}$ | (g/kg) | 39.4 | 37.9 | 36.6 | 35.5 |

Second Law efficiency | ${\eta}_{II}$ | (%) | 6.28% | 5.67% | 4.98% | 3.25% |

Entropy generation | ${\mathcal{S}}_{\text{gen}}$ | (J/kgK) | 182.6 | 203.2 | 233.2 | 364.5 |

**Figure 7.**Entropy generation per kilogram product water produced in each multistage flash (MSF) component at a heat source temperature of 110 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$.

**Figure 8.**Entropy generation per kilogram product water produced in each multistage flash (MSF) component for all four temperatures modeled.

#### 5.3. Multiple Effect Distillation

- Exchanger area in the effects is just large enough to condense vapor to saturated liquid (i.e., $x=0$) at the previous effect’s pressure.
- Seawater is an incompressible liquid and the properties are only a function of temperature and salinity.
- Non-equilibrium allowance (NEA) is negligible [9].
- Brine (liquid) and distillate (vapor) streams leave each effect at that effect’s temperature. Distillate vapor is slightly superheated.
- The overall heat transfer coefficient in each effect, feed heater, and condenser is a function of temperature only [9].

**Table 4.**Summary of results for a forward feed multi-effect distillation system operating at 50 and 70 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$.

Parameter | ${T}_{H}$ | |||
---|---|---|---|---|

Output | $70{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\text{C}$ | $50{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\text{C}$ | ||

Number of stages | n | (-) | 12 | 5 |

Gained output ratio | GOR | (-) | 9.349 | 4.048 |

Recovery ratio | RR | [%] | 40% | 17.5% |

Steam flow rate | ${\dot{m}}_{s}$ | (kg/s) | 0.1119 | 0.2526 |

Brine salinity | ${y}_{n}$ | (g/kg) | 58.3 | 42.4 |

Second Law efficiency | ${\eta}_{II}$ | (%) | 10.59 | 6.58 |

Entropy generation | ${\mathcal{S}}_{\text{gen}}$ | (J/kgK) | 102.4 | 139.1 |

**Figure 10.**Entropy generation per kilogram product water produced in each multi-effect distillation component at a heat source temperature of 110 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$.

**Figure 11.**Entropy generation per kilogram product water produced in each multi-effect distillation component for all temperatures modeled.

#### 5.4. MSVMD

- Heat exchanger area is just enough to fully condense the vapor; saturated liquid leaves the exchanger.
- Smallest temperature difference between any heat exchanging streams are set to be 3 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$.
- Heat transfer coefficient and mass transfer coefficient are calculated using pure water properties.

Parameter | ${T}_{H}$ | ||||
---|---|---|---|---|---|

Output | $90{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\text{C}$ | $70{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\text{C}$ | $50{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\text{C}$ | ||

Number of stages | n | [-] | 18 | 11 | 4 |

Gained output ratio | GOR | [-] | 7.8 | 4.8 | 1.8 |

Recovery ratio | RR | [%] | 8.48 | 5.25 | 1.97 |

Second Law efficiency | ${\eta}_{II}$ | [%] | 4.84 | 4.05 | 2.57 |

Entropy generation | ${\mathcal{S}}_{\text{gen}}$ | [J/kgK] | 178.7 | 215.5 | 344.1 |

**Figure 13.**Entropy generation per kilogram product water produced for each component in multistage vacuum membrane distillation (MSVMD) for a heat source temperature of 90 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$.

**Figure 14.**Entropy generation per kilogram product water produced for each component in multistage vacuum membrane distillation (MSVMD) for all 3 temperatures modeled.

#### 5.5. Humidification-Dehumidification

Parameter | |||
---|---|---|---|

Input | Symbol | Units | Value |

Temperature pinch | $\Delta {T}_{\mathrm{pinch}}$ | (${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$) | 3 |

Dehumidifier Heat Capacity Ratio | $HC{R}_{\text{d}}$ | (-) | 1 |

Moist Air Relative Humidity | $R{H}_{\mathrm{ma}}$ | (%) | 100 |

**Table 7.**Summary of results for a Humidification-dehumidification system operating at 50, 70 and 90 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$.

Parameter | ${T}_{\mathrm{H}}$ | ||||
---|---|---|---|---|---|

Output | Symbol | Units | $90{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\text{C}$ | $70{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\text{C}$ | $50{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\text{C}$ |

Gained output ratio | GOR | (-) | 2.1 | 2.2 | 1.7 |

Recovery ratio | RR | (%) | 7.1 | 4.8 | 2.4 |

Heat input | ${Q}_{H}$ | (kJ/kg) | 1173 | 1118 | 1405 |

Water-air mass flow rate ratio | MR | (-) | 4.1 | 2.5 | 1.6 |

Brine salinity | ${y}_{b}$ | (g/kg) | 37.7 | 36.8 | 35.8 |

Entropy generation | ${S}_{gen}$ | (J/kgK) | 564 | 414 | 325 |

Second Law efficiency | ${\eta}_{II}$ | (%) | 1.29 | 1.85 | 2.49 |

**Figure 16.**Entropy generation per kilogram product water produced in each humidification-dehumidification component for all 3 temperatures modeled.

**Figure 17.**Temperature-enthalpy profiles for water and moist air streams in Humidification Dehumidification Desalination. The dehumidifier and humidifier T-H curves for ${T}_{\mathrm{H}}$ = 50 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ and 90 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ are shown. The minimum temperature pinch is set between cases. The larger curvature in the 70 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ case increased the average temperature gradient for heat exchange, and is the reason humidification-dehumidification (HDH) efficiency decreases at higher temperature, unlike other technologies.

#### 5.6. Organic Rankine Cycle

**Figure 19.**Organic Rankine cycle Second Law efficiency vs. evaporating temperature with ${T}_{0}=26{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ from Shengjun et al. [13].

#### 5.7. Mechanical Vapor Compression

Input | Symbol | Value |
---|---|---|

Top brine temperature | ${T}_{b}$ | 60 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ |

Pinch: evaporator-condenser | $\Delta {T}_{evap}$ | $2.5$ ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ |

Pinch: regenerator | $\Delta {T}_{regen}$ | 3 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ |

Compressor inlet pressure | ${P}_{c,in}$ | 19.4 kPa |

Recovery ratio | RR | 40% |

Isentropic compressor efficiency | ${\eta}_{c}$ | 70% |

Output | Symbol | Value |
---|---|---|

Specific electricity consumption | ${\dot{W}}_{elec}$ | 8.84 kWh/m^{3} |

Discharged brine temperature | ${T}_{b}$ | 27.2 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ |

Product water temperature | ${T}_{p}$ | 29.7 ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ |

Compression ratio | $CR$ | 1.15 |

Second Law efficiency | ${\eta}_{\mathit{II}}$ | 8.5% |

**Figure 21.**Entropy generation per kilogram product water produced in each mechanical vapor compression component for all three temperatures modeled.

#### 5.8. Reverse Osmosis

Input | Symbol | Value |
---|---|---|

Pump efficiency | ${\eta}_{pump}$ | 85% |

Pressure exchanger efficiency | ${\eta}_{PX}$ | 96% |

Feed pressure | ${P}_{feed}$ | 2 bar |

RO pressure | ${P}_{RO}$ | 69 bar |

Recovery ratio | RR | 40% |

Output | Symbol | Value |
---|---|---|

Specific electricity consumption | ${\dot{W}}_{elec}$ | 2.35 kWh/m^{3} |

RO unit Second Law efficiency | ${\eta}_{II,RO}$ | 31.9% |

Total Second Law efficiency, ${T}_{H}=90{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | ${\eta}_{II,90}$ | 17.3% |

Total Second Law efficiency, ${T}_{H}=70{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | ${\eta}_{II,70}$ | 15.3% |

Total Second Law efficiency, ${T}_{H}=50{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | ${\eta}_{II,50}$ | 10.8% |

**Figure 23.**Entropy generation per kilogram product water produced in each reverse osmosis component for all four temperatures modeled.

## 6. Applicability of Analysis to Systems of Different Costs and Sizes

## 7. Technology Comparison

## 8. Comparison of Entropy Generation in Desalination System Components at Different Temperatures

- (1)
- Temperature Gradients Across Heat Exchangers (In order from most to least ${\mathcal{S}}_{\text{gen}}$: Feed Heaters, Stages or Effects, Top Heaters, Condensers, Regenerators,).
- (2)
- Rankine Cycle Losses.
- (3)
- Temperature Disequilibrium of Product and Brine
- (4)
- Compressors (MVC)
- (5)
- Phase Change (Flashing etc.)
- (6)
- RO Module
- (7)
- Throttling/Expansion
- (8)
- Pumping Losses (RO)
- (9)
- Chemical Disequilibrium of Brine

## 9. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

Roman symbols | Units | |

B | membrane permeability | ${\mathrm{m}}^{2}$s/kg |

c | specific heat | kJ/kg-K |

${c}_{p}$ | specific heat at constant pressure | kJ/kg-K |

g | specific Gibbs free energy | kJ/kg |

h | specific enthalpy | kJ/kg |

h | specific enthalpy | kJ/kg |

h_{fg} | latent heat of vaporization | kJ/kg |

$\dot{m}$ | mass flow rate | kg/s |

J | membrane flux | kg/ ${\mathrm{m}}^{2}$s |

n | number of effects or stages | |

p | pressure | kPa |

P | vapor pressure | kPa |

$\dot{Q}$ | heat transfer | kW |

${\dot{Q}}_{\mathrm{least}}$ | least heat of separation | kW |

${\dot{Q}}_{\mathrm{least}}^{\mathrm{min}}$ | minimum least heat of separation (zero recovery) | kW |

${\dot{Q}}_{H}$ | heat of separation, kW, added at ${T}_{H}$ | |

${\dot{Q}}_{0}$ | heat rejected to environment, kW, exiting at ${T}_{0}$ | |

R | ideal gas constant | kJ/kg-K |

r | recovery ratio | (kg/s product)/(kg/s feed) |

${\dot{S}}_{\mathrm{gen}}$ | entropy generation rate | kW/K |

s | specific entropy | kJ/kg-K |

${s}_{\mathrm{gen}}$ | specific entropy generation per unit flow | kJ/kg-K |

${\mathcal{S}}_{\mathrm{gen}}$ | specific entropy generation per unit water produced | kJ/kg-K |

T | temperature | K |

${T}_{0}$ | ambient (dead state) temperature | K |

${T}_{H}$ | temperature of heat reservoir | K |

v | specific volume | m^{3}/kg |

${\dot{W}}_{\mathrm{least}}$ | least work of separation | kW |

${\dot{W}}_{\mathrm{least}}^{\mathrm{min}}$ | minimum least work of separation | kW |

${\dot{W}}_{\mathrm{sep}}$ | work of separation | kW |

x | vapor quality | |

Greek | ||

Δ | change in a variable | |

${\eta}_{e}$ | isentropic efficiency of expander | (-) |

${\eta}_{p}$ | isentropic efficiency of pump/compressor | (-) |

${\eta}_{\mathit{II}}$ | Second Law/exergetic efficiency | (-) |

${\eta}_{reduced}$ | efficiency reduction from decreasing ${T}_{H}$ | (-) |

${\eta}_{p}$ | pump or compressor efficiency | (-) |

ρ | density | (kg/m^{3}) |

$\dot{\Xi}$ | Exergy flow rate | kW |

${\dot{\Xi}}_{H}$ | Exergy input | kW |

ρ | density | (kg/m^{3}) |

Subscripts | ||

∞ | environment | |

b | brine | |

flash | flashing | |

f | feed | |

i | state | |

p | product | |

$\mathrm{sw}$ | feed seawater | |

ref | reference value | |

1 | initial value | |

2 | final value | |

Superscripts | ||

IF | incompressible fluid | |

IG | ideal gas | |

${}^{\prime}$ | stream before exiting CV | |

$\Delta p$ | Pressure Change | |

Acronyms | ||

CD | chemical disequilibrium | |

GOR | gained output ratio | |

HD | humidification-dehumidification | |

MED | multiple effect distillation | |

MSF | multistage flash | |

MSVMD | Ms multistage vacuum membrane distillation | |

MVC | mechanical vapor compression | |

ORC | organic Rankine cycle | |

RO | reverse osmosis | |

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**MDPI and ACS Style**

Warsinger, D.M.; Mistry, K.H.; Nayar, K.G.; Chung, H.W.; Lienhard, J.H., V.
Entropy Generation of Desalination Powered by Variable Temperature Waste Heat. *Entropy* **2015**, *17*, 7530-7566.
https://doi.org/10.3390/e17117530

**AMA Style**

Warsinger DM, Mistry KH, Nayar KG, Chung HW, Lienhard JH V.
Entropy Generation of Desalination Powered by Variable Temperature Waste Heat. *Entropy*. 2015; 17(11):7530-7566.
https://doi.org/10.3390/e17117530

**Chicago/Turabian Style**

Warsinger, David M., Karan H. Mistry, Kishor G. Nayar, Hyung Won Chung, and John H. Lienhard, V.
2015. "Entropy Generation of Desalination Powered by Variable Temperature Waste Heat" *Entropy* 17, no. 11: 7530-7566.
https://doi.org/10.3390/e17117530