This document summarizes an empirical study on enhancing convective heat transfer using aluminum oxide nanoaerosols. The study aims to experimentally investigate heat transfer enhancement at low particle concentrations compared to nanofluids. An experimental setup is used to measure the Nusselt number with and without nanoparticles injected into an air flow over a range of Reynolds numbers. Results show increases in Nusselt number with higher particle mass loading that depend on the Reynolds number. A continuum model is presented to predict the enhancement based on increased thermal capacity. Models for free molecular and transition regimes are also discussed to predict behavior at different particle sizes and concentrations.

1. The Enhancement of Convec/ve
Heat Transfer in an Aluminum Oxide
Nanoaerosol
Empirical Study
Maulin Trivedi
Dec 9, 2015
Mechanical and Manufacturing Engineering

2. Applica/ons
§ Deep-cooled combined
turbojet cycle
— Thrust over wide range of Mach
number
— Intake air has very high
temperature
— Energy extracted is added back
to fuel stream
§ Heat transfer applica/ons use
fluids or air as heat carriers.
— Thermal constraints
— Physical constraints
— Cost
2
Figure 1: DASS GN 1 Engine Concept
From: h(ps://en.wikipedia.org/wiki/Space_Engine_Systems

3. Applica/ons
§ Heat transfer applica/ons use
fluids or air as heat carriers.
— Thermal constraints
— Physical constraints
— Cost
§ Reac/on Engines Ltd.
— High surface area
§ Space Engine Systems
— Enhanced thermal proper/es
Figure 2: SABRE Pre-cooler
From:
h(p://www.reac;onengines.co.uk/heatex_work.html
3

4. Background
§ Solid par/cles in suspension increases thermal conduc/vity
(Maxwell, 1881).
— Mass or volume frac/on of par/cles
— Surface area to volume ra/o
§ Nanopar/cles
— Sizes 1 - 100nm
— Very high surface area to volume ra/o
§ Nanofluids: Nanopar/cles suspended in liquid phase carriers (Choi,
1995).
§ Nanoaerosols: Nanopar/cles suspended in gaseous phase carriers.
4

5. Background: Nanofluids
§ 40% heat transfer
enhancement (Heris et
al., 2006).
§ 39% increase in heat
transfer (Xuan et al.,
2003).
§ Dependency on mass
frac/on and Reynolds
number
Figure 3: Nusselt number vs Peclet number
From:
Heris, S. Z., Etemad, S. G., & Esfahany, M. N. (2006). Experimental
inves/ga/on of oxide nanofluids laminar flow convec/ve heat transfer.
Interna;onal Communica;ons in Heat and Mass Transfer, 33(4), 529-535.
5

6. Background: Nanoaerosol
Figure 4: Nusselt number vs mass loading Figure 5: Nusselt number vs par/cle size
Adapted from: Murray, D. B. (1994). Local enhancement of heat transfer in a par/culate cross flow—II Experimental data and predicted trends.
Interna;onal journal of mul;phase flow, 20(3), 505-513.
6

7. Background: Mechanisms
§ Increased thermal capacity
§ Conduc/on between impac/ng par/cles
§ Thermal energy transport by rebounding par/cles
§ Flow structure effects
§ Other effects (Williams, 2015)
§ Limi/ng mechanisms
7

8. Mo/va/on
§ Nanopar/cles vs. Micro-par/cles
§ Availability in aerospace industry as an alterna/ve fuel
— Large energy content per unit volume and mass
— Lower igni/on temperatures and higher burning rate
— Safe and efficient storage
§ Nanofluids are proven effec/ve in heat transfer applica/ons
§ Volumetric heat capacity of nanoaerosol is much higher compared
to nanofluids
— ρCp ra/o is much higher for nanoaerosol than for nanofluids
8

9. Objec/ves
§ First experimental inves/ga/on
§ Low par/cle concentra/on
— Mass frac/on for nanofluids, O(10-1)
— Mass frac/on for nanoaerosols, O(10-4)
§ Theore/cal model to predict enhancement
§ Par/cle size vs. heat transfer enhancement
9

10. Experimental Set-up: Cont.
10 Figure 6: Experimental Schema/c

11. Experimental Set-up: Cont.
11 Figure 6: Experimental Schema/c
Hot-Wire Flow

12. Experimental Set-up
12 Figure 7: Experimental Set-up
Pressure Regulator
Compressed Air
Pressure
Gauge
Flow
Meter
Par/cle
Injector
Upstream
Thermistor
Hot
Wire
Downstream
Thermistor
Par/cle Collec/on Tank

13. Air-only Tests
§ Validate experimental apparatus
§ Performed over flow Reynolds number range of 1420 - 11,200
§ Nusselt number calculated by equa/ng convec/ve heat
transfer rate to the change in enthalpy
§ Experimental results (without par/cles) were compared to
Zukauskas empirical rela/on of
§ Establish base line
13

14. Air-only Tests: Cont.
14
0
2
4
6
8
10
12
14
16
18
20
0 2000 4000 6000 8000 10000 12000
Nusselt Number
Reynolds Number [tube diameter], Re
Zukauskas Rela/on
Experimental Air Tests
Figure 8: Valida/on of experimental set-up

15. Air Tests: Cont.
15
0
2
4
6
8
10
12
14
16
18
20
0 2000 4000 6000 8000 10000 12000
Nusselt Number
Reynolds Number [wire diameter], Re
Zukauskas Rela/on
Experimental Air Tests
Figure 8: Valida/on of experimental set-up
Flow Condi/ons For Par/cle Tests

16. Nanopar/cle: Informa/on
§ Approximately spherical
with 112 nm avg. dia.
§ Agglomerates of avg.
870 nm.
§ Dispersed through
custom-built injec/on
system.
16
Figure 9: SEM image of Al2O3 par/cles

17. Nanopar/cle: Injec/on System
§ Gravity assisted through
orifice of 0.75 mm
§ Oscilla/ons provided to
prevent clogging
§ 510 mm of tubing
allows semling of bigger
par/cles
17
Figure 10: Par/cle Injec/on System
Par/cle Housing
Off-balance Motor
Air-flow pipe
Upstream
Thermistor

18. Par/cle Tests
§ Experiments with par/cles were performed at flow Reynolds
numbers: 6000, 7500 and 8900.
§ Par/cle flow rate measured aner each test using highly
sensi/ve mass balance.
§ Par/cle mass loading ranged from 0.01%-0.33%.
§ Nusselt number at each Reynolds number calculated using
same methodology as air tests.
— Effec/ve proper/es
18

19. Experimental Results: Cont.
19
Figure 11: Effect of mass loading on Nu at Re = 6000
y = 9.5795x0.5809
R² = 0.70653
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
0.00% 0.05% 0.10% 0.15% 0.20% 0.25% 0.30% 0.35%
%Nu Increase
%Par/cle Mass Loading
Raw %Nu Increase Predicted %Nu Increase 95% Lower CI 95% Upper CI

20. Experimental Results: Cont.
20
Figure 12: Effect of mass loading on Nu at Re = 7500
y = 5.3126x0.5338
R² = 0.61755
0%
5%
10%
15%
20%
25%
30%
35%
40%
0.00% 0.05% 0.10% 0.15% 0.20% 0.25% 0.30% 0.35%
%Nu Increase
%Par/cle Mass Loading
Raw %Nu Increase Predicted %Nu Increase 95% Lower CI 95% Upper CI

21. Experimental Results: Cont.
21
Figure 13: Effect of mass loading on Nu at Re = 8900
y = 0.9927x0.2821
R² = 0.46192
0%
5%
10%
15%
20%
25%
30%
35%
40%
0.00% 0.05% 0.10% 0.15% 0.20% 0.25% 0.30% 0.35%
%Nu Increase
%Par/cle Mass Loading
Raw %Nu Increase Predicted %Nu Increase 95% Lower CI 95% Upper CI

22. Error Analysis
§ Systema/c errors calculated
based on instrumenta/on and
sensor limita/ons.
§ Random errors calculated based
on t-distribu/on for α = 0.05.
§ Random error is significantly
higher than systema/c errors.
§ Student’s t-test between baseline
test and par/cle test at lowest
par/cle concentra/on shows
significant increase in Nusselt
number.
22
9
10
11
12
13
14
15
16
17
550 600 650 700 750 800 850 900 950
Nusselt Number
Cross-flow Reynolds Number
Air Test Par/cle Test
Figure 14: Student's t-test for 95% confidence
between air-only and lowest par/cle loading tests

23. Model: Con/nuum
§ Con/nuum regime, Kn < 0.01
— Murray’s model for increased thermal capacity
— ​(​​ 𝑁 𝑢↓𝑁𝐴 /​ 𝑁 𝑢↓𝑎 )↓𝐼𝑇𝐶 =​[1+​ 𝜂↓𝑡 ​ 𝑆↓𝐿 ​​ 𝑐↓𝑝 ↓𝑟𝑎𝑡𝑖𝑜 ]↑0.37
§ ​ 𝜂↓𝑡 =​​ 𝜏↓𝑟𝑒𝑠 /​ 𝜏↓𝑟𝑒𝑙 ; ​ 𝜏↓𝑟𝑒𝑙 =​​ 𝑑↓𝑝 ​ 𝜌↓𝑝 ​​ 𝑐↓𝑝 ↓𝑝 /​6ℎ↓𝑝
§ Other effects are considered negligible due to low par/cle
loading
— Flow structure modifica/on
— Par/cle rebound
— Radia/on
23

24. Model: Free-molecular
§ Free-molecular regime, Kn > 10
— Modified Murray’s model using the free-molecular
relaxa/on /me, τrel
— Obtained from Filippov and Rosner’s energy balance
§ ​ 𝜌↓𝑝 ​ 𝐶↓​ 𝑝↓𝑝 ​ 𝑉↓𝑝 ​ 𝑑​ 𝑇↓𝑝 /𝑑𝑡 = 𝛼𝜋​ 𝑎↑2 ​ 𝑛↓𝑔 ​ 𝑐 ​ 𝑘↓𝑏 (​1/2 (​ 𝑇↓𝑝 −​
𝑇↓𝑔 )(​ 𝛾+1/𝛾−1 ))
§ ​ 𝜏↓𝑟𝑒𝑙 =​2​ 𝜌↓𝑝 ​ 𝑐↓𝑝 ​ 𝑑↓𝑝 /9​ 𝑛↓𝑔 ​ 𝑐 ​ 𝑘↓𝑏 ; ​ 𝑛↓𝑔 =​ 𝑃​ 𝑁↓𝑎𝑣 /𝑅𝑇 ; ​ 𝑐
=√⁠​8​ 𝑘↓𝑏 ​ 𝑇↓𝑔 /𝜋​ 𝑚↓𝑔
— Subs/tute τrel into Murray’s model to obtain Nusselt
number enhancement
24

25. Model: Transi/on
§ Transi/on regime, 0.01 < Kn < 10
— Harmonic mean suggested by Sherman (1963) was used to
interpolate ​​ 𝑞↓𝑡𝑟 .
— ​ 𝜏↓𝑟𝑒𝑙, 𝑡𝑟 =​​ 𝜌↓𝑝 ​ 𝑐↓𝑝 ​​ 𝑑↓𝑝 ↑2 /​​​ 𝑞↓𝑡𝑟 /​​ 𝑞↓𝑐 12​ 𝑘↓𝑓 ; ​​​ 𝑞↓𝑡𝑟 /​​
𝑞↓𝑐 = ​1/1+​19/6 𝐾𝑛
— The ra/o ​​​ 𝑞↓𝑡𝑟 /​​ 𝑞↓𝑐 can be obtained from Liu (2006).
— Knudsen number effects are incorporated into the
/mescale
25

26. Model: Comparison
26
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
0.00% 0.05% 0.10% 0.15% 0.20% 0.25% 0.30% 0.35%
Nu Ra/o [Nu_su/Nu_a]
Solid Mass Frac/on, % [m_solid/m_air *100]
Experimental Fit Experimental Data Transi/onal Model
Murray Model Free Molecular Model 95% Confidence Band
Figure 15: Comparison of con;nuum model, free-molecular model, transi;onal
model and experimental data for Re = 6000

27. 27
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
0.00% 0.05% 0.10% 0.15% 0.20% 0.25% 0.30% 0.35%
Nu Ra/o [Nu_su/Nu_a]
Solid Mass Frac/on, % [m_solid/m_air *100]
Experimental Fit Experimental Data Transi/onal Model
Murray Model Free Molecular 95% Confindence Band
Figure 16: Comparison of con;nuum model, free-molecular model, transi;onal
model and experimental data for Re = 7500
Model: Comparison

28. 28
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
0.00% 0.05% 0.10% 0.15% 0.20% 0.25% 0.30% 0.35%
Nu Ra/o [Nu_su/Nu_a]
Solid Mass Frac/on, % [m_solid/m_air *100]
Experimental Fit Experimental Data Transi/onal Model
Murray Model Free Molecular Model 95% Experimental Band
Figure 17: Comparison of con;nuum model, free-molecular model, transi;onal
model and experimental data for Re = 9000
Model: Comparison

29. Model: Effect of Par/cle Size
29
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
0 10 20 30 40 50 60 70 80 90 100
Nusselt Number Ra/o
Par/cle Diameter, [nm]
Solid Loading 0.25% Solid Loading 0.5% Solid Loading 0.75% Solid Loading 1%
Figure 18: Effect of par/cle size on Nusselt number ra/o at Re = 9000 using
transi/onal model

30. Discussion: Experimental
§ Only small par/cle mass loading is required
to provide a large increase to Nusselt
number.
§ Murray (1994) required ~100% mass
loading to achieve similar results.
§ Higher enhancement amributed to:
— Smaller par/cles
— Lower Reynolds number
30
From: Murray, D. B. (1994).
Local enhancement of heat
transfer in a par/culate
cross flow—II Experimental
data and predicted trends.
Interna;onal journal of
mul;phase flow, 20(3),
505-513.

31. Discussion: Experimental
§ Only small par/cle mass loading is required
to provide a large increase to Nusselt
number.
§ Murray (1994) required ~100% mass
loading to achieve similar results.
§ Higher enhancement amributed to:
— Smaller par/cles
— Lower Reynolds number
31
From: Murray, D. B. (1994).
Local enhancement of heat
transfer in a par/culate
cross flow—II Experimental
data and predicted trends.
Interna;onal journal of
mul;phase flow, 20(3),
505-513.

32. Discussion: Model
§ Effects of increased Reynolds number and turbulence
modifica/on are insignificant.
§ The relaxa/on /me represents 63% of heat transfer, thus
resul/ng in higher predic/on of heat transfer enhancement.
§ Experimental data between con/nuum and free-molecular
predic/on.
§ Transi/onal model agrees with experimental data.
— For 0.01 < Kn < 10
§ Many other effects are not included.
32

33. Conclusion
§ Heat transfer enhancement using nanoaerosol has been experimentally
demonstrated for the first /me.
§ Large heat transfer enhancement (~36%) was observed at rela/vely low par/cle
loading (~0.35%).
§ Experimental data is proved to be sta/s/cally significant.
§ Observed trends are consistent with theory proposed by Murray.
§ Murray’s model is modified for free-molecular and transi/on regime.
— Transi/on model agrees with experimental data.
— Transi/on model extended to predict effect of par/cle size over mass loading
0.25% - 1%.
— Other effects need to be incorporated.
33

34. Acknowledgements
§ Alberta Innovates Technology Futures
§ Natural Sciences and Engineering Research Council
§ Space Engine Systems
§ University of Calgary
§ Dr. Craig Johansen
34

35. References
1. Maxwell, J. C. (1881). A trea;se on electricity and magne;sm (Vol. 1). Clarendon press.
2. Choi, S. U. S. (1995). Enhancing thermal conduc/vity of fluids with nanopar/cles. ASME-
Publica;ons-Fed, 231, 99-106.
3. Zeinali Heris, S., Etemad, S. G., & Nasr Esfahany, M. (2006). Experimental inves/ga/on
of oxide nanofluids laminar flow convec/ve heat transfer.Interna;onal Communica;ons
in Heat and Mass Transfer, 33(4), 529-535.
4. Xuan, Y., & Li, Q. (2003). Inves/ga/on on convec/ve heat transfer and flow features of
nanofluids. Journal of Heat transfer, 125(1), 151-155
5. Murray, D. B. (1994). Local enhancement of heat transfer in a par/culate cross flow—I
Heat transfer mechanisms. Interna;onal journal of mul;phase flow, 20(3), 493-504.
6. Murray, D. B. (1994). Local enhancement of heat transfer in a par/culate cross flow—II
Experimental data and predicted trends. Interna;onal journal of mul;phase flow, 20(3),
505-513.
7. Bianco, V., Manca, O., Nardini, S., and Vafai, K., Heat Transfer Enhancement With
Nanouids, April 1 2015, CRC Press
35