Skip to main content
SpringerLink
Log in

New water-stainless steel rod-plate heat pipe: model and experiments

  • Original Article
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

This work proposes a novel flat heat pipe technology, namely the rod-plate heat pipe, formed by the diffusion bonding of a set of parallel rods, of around 8 mm diameter, between flat plates of approximately 500 × 60 × 2 mm3. This design is inspired by the mini wire-plate heat pipe concept. This work is the first in the literature to apply this technology to large size heat pipes. A theoretical model is devised and used to predict the fluid distribution along the heat pipe, detect regions of flooding and dry-out and determine the best charging volume. Experiments are performed with a stainless-steel device operating in horizontal orientation with water as working fluid. Electrical cartridge resistances play the role of the evaporator heat source, while the condenser is cooled by either natural convection and radiation or heat exchangers linked to a thermal bath. For the experiments using a device with an exposed condenser, the minimum thermal resistance is 0.147 °C/W, for 88.50 W for heat input. The operation temperature increases with heat input up to 326.56 °C for a heat load of 191.40 W. The thermal resistances of the heat pipe cooled by heat exchangers have a minimum of 0.123 °C/W at 171.57 W heat transport rate, for a 40 °C thermal bath temperature. The theoretical results and data obtained so far corroborate the feasibility of this technology, with devices able to transfer up to 22.18 W per groove.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36
Fig. 37
Fig. 38
Fig. 39
Fig. 40
Fig. 41
Fig. 42
Fig. 43
Fig. 44

Similar content being viewed by others

Abbreviations

A:

Cross-section area, m2

cp :

Specific heat capacity, J kg-1 K-1

Dh :

Hydraulic diameter, m

Dφ :

Deviation

f:

Friction factor

FR:

Filling ratio

g:

Gravity, kg m s-2

H:

Meniscus height, m

h:

Step size, m

hlv :

Latent heat, J kg-1

\(\overline{h_{si}}\) :

Convection heat transfer coefficient, W °C-1 m-2

I:

Current, A

L:

Length, m

l:

Axial position, m

\(\dot{m}\) :

Mass flow rate, kg s-1

N:

Number of nodes

\(\overline{{Nu }_{L}}\) :

Nusselt number

P:

Pressure, Pa

Pr:

Prandtl number

pl :

Liquid cross-section perimeter, m

ps :

Surface perimeter, m

pv :

Vapor wetted perimeter, m

pwl :

Liquid wetted perimeter, m

Q:

Heat transfer rate, W

q'':

Heat flux, W m-2

R:

Rod radius, m

RaL :

Rayleigh number

\({Re}_{h}\) :

Reynolds number

Rt :

Thermal resistance, K W-1

rm :

Radius-of-meniscus, m

T:

Temperature, °C

u:

Velocity, m s-1

vc :

Charging volume, m3

U:

Standard uncertainty

V:

Voltage, V

W:

Meniscus width, m

w:

Rod pitch (center-to-center distance), m

x:

Axial position, m

α:

Contact angle, rad

α:

Thermal diffusivity, m2 s-1

β:

Thermal expansion coefficient, K-1

β1 :

Half- angle of the rod-liquid opening, rad

β2 :

Half-angle of the meniscus curvature, rad

ε:

Emissivity

ξ:

Shape factor

λ:

Thermal conductivity, W m-1 °C-1

ν:

Momentum diffusivity, m2 s-1

ρ:

Density, kg m-3

ρc :

Charged density, kg m-3

σ:

Boltzmann constant, W m-2 K-4

σl :

Liquid surface tension, N m-1

τ:

Shear stress, N m-2

φ:

Generic variable

ψ:

Angle of inclination, rad

ψs :

Irregularity shape factor

ϕ:

Channel aspect ratio

A:

System A

a:

Adiabatic section

B:

System B

b:

Bibliography

c:

Condenser

e:

Evaporator

f:

Buoyant fluid

l:

Liquid

loss:

Loss

max:

Maximum

nc:

Natural convection

op:

Operation

p:

Present

rad:

Radiation

s:

Surface

tb:

Thermal bath

v:

Vapor

w:

Water

∞:

Environment

References

  1. Cotter TP (1984) Principles and prospects for micro heat pipes. In 5th International Heat Pipe Conference, Tsukuba, Japan. pp 328–335

  2. Vasiliev LL (2008) Micro and miniature heat pipes - electronic component coolers. Appl Therm Eng 28(4):266–273. https://doi.org/10.1016/j.applthermaleng.2006.02.023

    Article  Google Scholar 

  3. Vieira de Paiva K, Barbosa Henriques Mantelli M, Kessler Slongo L (2011) Thermal behavior analysis of wire mini heat pipe. J Heat Transfer 133(12):1–9. https://doi.org/10.1115/1.4004526

    Article  Google Scholar 

  4. Panahi M, Heydari HR, Karimi G (2021) Effects of micro heat pipe arrays on thermal management performance enhancement of cylindrical lithium-ion battery cells. Int J Energy Res 1–13. https://doi.org/10.1002/er.6604

  5. Qu J, Wu H, Cheng P, Wang Q, Sun Q (2017) Recent advances in MEMS-based micro heat pipes. Int J Heat Mass Transf 110:294–313. https://doi.org/10.1016/j.ijheatmasstransfer.2017.03.034

    Article  Google Scholar 

  6. Wang YX, Peterson GP (2002) Analysis of wire-bonded micro heat pipe arrays. J Thermophys Heat Transf 16(3)

  7. Rag RL, Sobhan CB, Peterson GP (2018) Computational analysis of wire-bonded micro heat pipe: Influence of thermophysical parameters. J Thermophys Heat Transf 32(4):925–932. https://doi.org/10.2514/1.T5359

    Article  Google Scholar 

  8. Launay S, Sartre V, Mantelli MBH, De Paiva KV, Lallemand M (2004) Investigation of a wire plate micro heat pipe array. Int J Therm Sci 43(5):499–507. https://doi.org/10.1016/j.ijthermalsci.2003.10.006

    Article  Google Scholar 

  9. Paiva KV, Mantelli MBH (2015) Theoretical thermal study of wire-plate mini heat pipes. Int J Heat Mass Transf 83:146–163. https://doi.org/10.1016/j.ijheatmasstransfer.2014.11.049

    Article  Google Scholar 

  10. Batista JVC (2021) Development of a hybrid mini heat pipe for electronics cooling applications. Universidade Federal de Santa Catarina

    Google Scholar 

  11. Rag RL, Sobhan CB (2009) Computational analysis of fluid flow and heat transfer in wire-sandwiched microheat pipes. J Thermophys Heat Transf. https://doi.org/10.2514/1.44101

    Article  Google Scholar 

  12. Mantelli MBH (2021) Thermosyphons and heat pipes: theory and applications. Springer

    Book  Google Scholar 

  13. Sandemeyer Steel Company (2013) Specification sheet: alloy 316 / 316L (UNS S31600, S31603). https://www.sandmeyersteel.com/images/316-316l-317l-spec-sheet.pdf

  14. Mortean MVV (2017) Trocador de Calor Compactos Soldados por Difusão: Fabricação e Modelagem (Doctoral Thesis). Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil

    Google Scholar 

  15. Klein S, Alvarado F (2002) Engineering equation solver. F-Chart Software. p 2. https://www.fchartsoftware.com/ees/

  16. Carey VP (2020) Liquid-vapor phase-change phenomena: an introduction to the thermophysics of vaporization and condensation processes in heat transfer equipment, 3rd edn. CRC Press. Taylor & Francis Group, Boca Raton, Florida, United States. ISBN-13: 978-1-4987-1661-1

    Book  Google Scholar 

  17. Longtin JP, Badran B, Gerner FM (1994) A one-dimensional model of a micro heat pipe during steady- state operation. J Heat Transfer 116(3):709–715. https://doi.org/10.1115/1.2910926

    Article  Google Scholar 

  18. Ma HB, Peterson GP, Lu XJ (1994) The influence of vapor-liquid interactions on the liquid pressure drop in triangular microgrooves. Int J Heat Mass Transf 37(15):2211–2219. https://doi.org/10.1016/0017-9310(94)90364-6

    Article  Google Scholar 

  19. Shah RK, Bhatti MS (1987) Laminar convective heat transfer in ducts, in handbook of single-phase convective heat transfer. Wiley, New York, p 3.45–3.70

    Google Scholar 

  20. Adrian B (2013) Convection Heat Transfer. Wiley, New York

    Google Scholar 

  21. Song JW, Zeng DL, Fan LW (2020) Temperature dependence of contact angles of water on a stainless steel surface at elevated temperatures and pressures: In situ characterization and thermodynamic analysis. J Colloid Interface Sci 561:870–880. https://doi.org/10.1016/j.jcis.2019.11.070

    Article  Google Scholar 

  22. Armstrong JS, Collopy F (1992) Error measures for generalizing about forecasting methods: Empirical comparisons. Int J Forecast 8(1):69–80. https://doi.org/10.1016/0169-2070(92)90008-W

    Article  Google Scholar 

  23. Ziegelheim J, Hiraki S, Ohsawa H (2007) Diffusion bondability of similar/dissimilar light metal sheets. J Mater Process Technol 186(1–3):87–93. https://doi.org/10.1016/j.jmatprotec.2006.12.020

    Article  Google Scholar 

  24. Bucklow IA (1983) Diffusion bonding for product improvement and cost reduction (Seminar Handbook). The Welding Institute, London

    Google Scholar 

  25. Martinelli AE (1996) Diffusion bonding of silicon carbide and silicon nitride to molybdenum. McGill University

    Google Scholar 

  26. American Welding Society (A.W.S) (1978) Welding Handbook: Welding Processes, Arc and Gas Welding and Cutting, Brazing and Soldering, Vol 2, 7th edn. ISBN-10 087171486

  27. Gatti GM (2020) Análise Termo-Hidráulica e Efeitos do Escalonamento em Trocadores de Calor Compactos Unidos por Difusão (Dissertação de Mestrado). Universidade Federal de Santa Catarina, Florianópolis, Santa Catarina, Brazil

    Google Scholar 

  28. Mortean MVV, Buschinelli AJDA, Paiva KVD, Mantelli MBH, Remmel J (2016) Soldagem por difusão de aços inoxidáveis para fabricação de trocadores de calor compactos. Soldag Insp 21(1):103–114. https://doi.org/10.1590/0104-9224/SI2101.10

    Article  Google Scholar 

  29. Li Y, Li Q, Wang Y, Chen J, Cai WH (2022) Optimization of a Zigzag-channel printed circuit heat exchanger for supercritical methane flow. Cryogenics (Guildf) 121(December):2021. https://doi.org/10.1016/j.cryogenics.2021.103415

    Article  Google Scholar 

  30. Shah RK, Sekulic DP (2003) Fundamentals of Heat Exchanger Design. John Wiley & Sons, New York

    Book  Google Scholar 

  31. Incropera FP, Dewitt DP (2011) Fundamentals of heat and mass transfer, 7th edn. John Wiley & Sons, Jefferson City

    Google Scholar 

  32. Goldstein RJ, Sparrow EM, Jones DC (1973) Natural convection mass transfer adjacent to horizontal plates. Int J Heat Mass Transf 16(5):1025–1035. https://doi.org/10.1016/0017-9310(73)90041-0

    Article  Google Scholar 

  33. Lloyd JR, Moran WR (1974) Natural convection adjacent to horizontal surface of various planforms ASME. J Heat Transf 96(4):443–447

    Article  Google Scholar 

  34. Radziemska E, Lewandowski WM (2001) Heat transfer by natural convection from an isothermal downward-facing round plate in unlimited space. Appl Energy 68(4):347–366. https://doi.org/10.1016/S0306-2619(00)00061-1

    Article  Google Scholar 

  35. Churchill SW, Chu HHS (1975) Correlating equations for laminar and turbulent free convection from a vertical plate. Int J Heat Mass Transf 18(11):1323–1329. https://doi.org/10.1016/0017-9310(75)90243-4

    Article  Google Scholar 

  36. Cisterna LHR (2019) Técnicas de Fabricação, Modelagem e Testes de Termossifões Bifásicos de Sódio - Efeitos de Geyser Boiling e de Ponta Fria. FederaL University of Santa Catarina

    Google Scholar 

  37. Joint Committee For Guides In Measurement (2008) Evaluation of measurement data — Guide to the expression of uncertainty in measurement, 1st edn. JCGM 100:2008

  38. Ronald H (1997) Dieck, Measurement uncertainty: methods and applications, 2nd edn. Instrument Society of America, Durham, North Carolina

    Google Scholar 

  39. Omega Engineering Inc. (2023) Thermocouple types. https://www.omega.com/en-us/resources/thermocouple-types. Accessed 6 Aug 2023

  40. Camahan B, L HA, Wilkes JO (1969) Applied numerical methods. Krieger Publishing Company, Malabar, Florida

    Google Scholar 

  41. Faghri A (2012) Review and advances in heat pipe science and technology. J Heat Transfer. https://doi.org/10.1115/1.4007407

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the educational fellowship and financial support from the National Council for Scientific and Technological Development – CNPq and the Brazilian Air Force – FAB.

Funding

This work was supported by the National Council for Scientific and Technological Development – CNPq and the Brazilian Air Force – FAB.

Author information

Authors and Affiliations

  1. Heat Pipe Laboratory, Federal University of Santa Catarina, Florianópolis, Brazil

    Elvis Falcão de Araújo, Juan Pablo Flórez Mera & Márcia Barbosa Henriques Mantelli

  2. Institute for Advanced Studies, Department of Aerospace Science and Technology, São José dos Campos, Brazil

    Elvis Falcão de Araújo

  3. School of Mechanical Engineering, Industrial University of Santander, Bucaramanga, Colombia

    Juan Pablo Flórez Mera

  4. University of Tarapacá, Arica, Chile

    Luis H. R. Cisterna

Authors
  1. Elvis Falcão de Araújo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juan Pablo Flórez Mera
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luis H. R. Cisterna
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Márcia Barbosa Henriques Mantelli
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Elvis Falcão de Araújo. The first draft of the manuscript was written by Elvis Falcão de Araújo and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Elvis Falcão de Araújo.

Ethics declarations

Competing interests

The authors have no relevant financial or non-financial interests to disclose.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Highlights

• The rod-plate heat pipe technology is developed for large heat pipes.

• A one-dimensional theoretical model is developed to study the flow in rod-plate heat pipes.

• Stainless steel 316 L rod-plate heat pipes are manufactured using the diffusion bonding technique.

• Electrical resistance cartridges are used to deliver and a thermal bath heat exchanger to remove heat in rod-plate heat pipes.

• Structural and thermal performance parameters of the rod-plate heat pipes are evaluated.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

de Araújo, E.F., Mera, J.P.F., Cisterna, L.H.R. et al. New water-stainless steel rod-plate heat pipe: model and experiments. Heat Mass Transfer (2024). https://doi.org/10.1007/s00231-024-03471-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00231-024-03471-2

Search

Navigation