Skip to main content
SpringerLink
Log in

Mathematical Modeling and Available Computer Codes

  • Chapter
  • First Online:
Heat Pipe Design and Technology

  • 3030 Accesses

Abstract

Heat pipes and its closed two-phase thermosyphons are highly efficient heat transfer devices utilizing the continuous evaporation–condensation of suitable working fluid for two-phase heat transport in a closed system. Due to a variety of advantageous features, these devices have found a number of applications both in space, terrestrial, nuclear power plant, and electronics technology. The operational principles and the performance characteristics of the different types of heat pipes are described. For the heat pipes designs, which have found the widest application, versus the classical capillary-wick heat pipes and the wickless heat pipes or closed two-phase thermosyphons, mathematical schemes are given to calculate the performance and performance limits in Chap. 2. Here in this chapter, we will discuss the design criteria and steps for a heat pipe depending on its application. This chapter also provides few computer code descriptions that are available from both Galaxy Advanced Engineering and other commercial companies and open source, and the author has identified those codes wherever are appropriate. In this chapter, also few design examples are gathered from different authors or researchers in this field to provide a better guideline and procedures to the readers.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Chi, S. W. (1971, December). Mathematical modeling of high and low temperature heat pipes. George Washington University Final NASA, Grant No. NGR 09-010-070.

    Google Scholar 

  2. Chi, S. W. (1970, September). Mathematical models of cryogenic heat pipes. Final Report to NASA, Goddard Space Flight Center, Grant No. NGR09-005-071.

    Google Scholar 

  3. Bienert, W. B., & Skrabeck, E. A. (1972, August). Heat pipe design handbook. Dynatherm Corporation. Report to NASA, Contract No., NASA 9-11927.

    Google Scholar 

  4. Reay, D. A., & Kew, P. A. (2006). Heat pipes (5th ed.). Tarrytown, NY: Butterworth-Heinemann.

    Google Scholar 

  5. Chi, S. W. (1976). Heat pipe theory and practice. New York: McGraw-Hill.

    Google Scholar 

  6. Cotter, T. P. (1965, February). Theory of heat pipes. Los Alamos Scientific Laboratory Report LA-3246-MS.

    Google Scholar 

  7. Marcus, B. D. (1972, April). Theory and design of variable conductance heat pipes. TRW Systems Group, NASA CR-2018.

    Google Scholar 

  8. Ribando, R. J. (2004) View factor for aligned parallel rectangles. Mechanical and Aerospace Engineering, University of Virginia

    Google Scholar 

  9. ASME Boiler and Pressure Vessel Committee. (1965). ASME boiler and pressure vessel code-Section VIII Unfired pressure vessel. New York: American Society of Mechanical Engineering.

    Google Scholar 

  10. Tien, C. L., & Jun, K. H. (1971). Minimum meniscus radius of heat pipe wick materials. International Journal of Heat and Mass Transfer, 14, 1853–1855.

    Article  Google Scholar 

  11. Colwell, G. T., Jang, J. H., & Camarda, J. C. (1987, May). Modeling of startup from the frozen state. Presented at the Sixth International Heat Pipe Conference, Grenoble, France.

    Google Scholar 

  12. Peterson, G. P. (1994). An introduction to heat pipes—Modeling, testing and applications. New York: John Wiley & Sons.

    Google Scholar 

  13. Faghri, A. (1995). Heat pipe science and technology. Washington, DC: Taylor & Francis.

    Google Scholar 

  14. Faghri, A., & Harley, C. (1994). Transient lumped heat pipe analysis. Heat Recovery Systems and CHP, 14(4), 351–363.

    Article  Google Scholar 

  15. Jang, J. H., Faghri, A., & Chang, W. S. (1991). Analysis of the one-dimensional transient compressible vapor flow in heat pipes. International Journal of Heat and Mass Transfer, 34, 2029–2037.

    Article  Google Scholar 

  16. Carslaw, H. S., & Jaeger, J. C. (1959). Conduction of heat in solids (2nd ed.). London: Oxford University Press.

    MATH  Google Scholar 

  17. Chang, W. S. (1981, March). Heat pipe startup form the supercritical state. Ph.D. Dissertation, Georgia Institute of Technology.

    Google Scholar 

  18. Colwell, G. T., & Chang, W. S. (1984). Measurement of the transient behavior of a capillary structure under heavy thermal loading. International Journal of Heat and Mass Transfer, 27(4), 541–551.

    Article  Google Scholar 

  19. Change, W. S., & Colwell, G. T. (1985). Mathematical modeling of the transient operating characteristic of low-temperature heat pipe. Numerical Heat Transfer, 8, 159–186.

    Google Scholar 

  20. Colwell, G. T. Modeling of transient heat pipe operation. Final Report NASA GRANT NAG-1-392, Period Covered August 19, 1983 through December 31, 1988, Submitted January 15, 1989.

    Google Scholar 

  21. Cotter, T. P. (1967, October). Heat pipe startup dynamics. Proc. IEEE Thermionic Conversion Specialist Conference, Palo Alto, California (pp. 344–348).

    Google Scholar 

  22. Luikov, A. V. (1968). Analytical heat diffusion theory. New York: Academic.

    Google Scholar 

  23. Silverstein, C. C. (1992). Design and technology of heat pipes for cooling and heat exchange. Washington, DC: Taylor and Francis.

    Google Scholar 

  24. Pakdemirli, M., & Sahin, A. Z. (2006). A similarity solution of fin equation with variable thermal conductivity and heat transfer coefficient. Mathematical and Computational Applications, 11(1), 25–30.

    Article  MATH  Google Scholar 

  25. Jiji, L. M. (2009). Heat conduction (3rd ed.). Berlin: Springer.

    Book  MATH  Google Scholar 

  26. Nnanna, A. G. A., Haji-Sheikh, A., & Agonafer, D. (2003). Effect of variable heat transfer coefficient, fin geometry, and curvature on the thermal performance of extended surfaces. Journal of Electronic Packaging, Transactions of the ASME, 125, 456–460.

    Article  Google Scholar 

  27. Lee, H.-L., Yang, Y.-C., & Chu, S.-S. (2002). Transient thermoelastic analysis of an annular fin with coupling effect and variable heat transfer coefficient. Journal of Thermal Stresses, 25, 1105–1120.

    Article  Google Scholar 

  28. Campo, A., & Salazar, A. (1996). Similarity between unsteady-state conduction in a planar slab for short times and steady-state conduction in a uniform, straight fin. Heat and Mass Transfer, 31, 365–370.

    Article  Google Scholar 

  29. Kuehn, T. H., Kwon, S. S., & Tolpadi, A. K. (1983). Similarity solution for conjugate natural convection heat transfer from a long vertical plate fin. International Journal of Heat and Mass Transfer, 26, 1718–1721.

    Article  Google Scholar 

  30. Rozza, G., & Patera, A. T. The thermal fin (“Tfin”) problem. In collaboration with D. B. P. Huynh, N. C. Nguyen and, previously, S. Sen and S. Deparis.

    Google Scholar 

  31. Holman, J. P. (1986). Heat transfer (6th ed.). New York: McGraw-Hill.

    Google Scholar 

  32. Nellis, G., & Klein, S. (2008). Heat transfer (1st ed.). Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  33. Marcus, B. D. (1965, May). On the operation of heat pipes. TRW Report 9895-6001-TU-000.

    Google Scholar 

  34. Brennan, P. J., & Kroliczek, E. J. (1979). Heat pipe design handbook (Contract Report No NAS5-23406, Vols. I and II). Washington, DC: National Aeronautics and Space Administration.

    Google Scholar 

  35. Asselman, G. A., & Green, D. B. (1973). Heat pipes. Phillips Technical Review, 16, 169–186.

    Google Scholar 

  36. Eninger, J. E. (1974, August 1). Computer program grade for design and analysis of graded-porosity heat-pipe wicks. NASA-CR-137618.

    Google Scholar 

  37. Eninger, J. E., & Edwards, D. K. (1976, November). Computer program grade II for the designed analysis of heat pipe wick. NASA-CR-137954.

    Google Scholar 

  38. Brennan, P. J., & Kroliczek, E. J. (1979, June). Heat pipe design handbook. Towson, MD: B & K Engineering, Inc. NASA Contract No. NAS5-23406 Report N81-70113.

    Google Scholar 

  39. Tower, L. K. (1992, September). NASA Lewis steady-state heat pipe code users manual Version 1.0. Cleveland, OH: NASA Lewis Research Center. NASA TM-105161.

    Google Scholar 

  40. Busse, C. A. (1967). Pressure drop in the vapor phase of long heat pipes. IEEE Conference Record of the Thermionic Conversion Specialist Conference (pp. 391–398), IEEE.

    Google Scholar 

  41. Tower, L. K., & Hainley, D. C. (1989). An improved algorithm for the modeling of vapor flow in heat pipes. NASA CR-185179.

    Google Scholar 

  42. Tower, L. K. (2000, April). NASA Glenn steady-state heat pipe code users manual Version 2.0. Cleveland, OH: NASA Glenn Research Center. NASA TM-2000-209807.

    Google Scholar 

  43. McLennan, G. A. (1983, November). ANL/HTTP: A computer code for the simulation of heat pipe operation. Argonne National Laboratory, Report No. ANL-83-108.

    Google Scholar 

  44. Marcus, B. D. (1972, April). Theory and design of variable conductance heat pipes. NASA CR-2018.

    Google Scholar 

  45. Soliman, M. M., Grauman, D. W., & Berenson, P. J. (1970). Effective thermal conductivity of saturated wicks. ASME Paper No. 70-HT//SpT-40.

    Google Scholar 

  46. Ferrel, K. J., & Alleavitch, J. (1970). Vaporization heat transfer in capillary wick structures. Chemical Eng., Prog. Symposium Series V66, Heat Transfer, Minneapolis, MN.

    Google Scholar 

  47. Glass, D. Closed form equations for the preliminary design of a heat-pipe-cooled leading edge. NASA/CR-1998-208962

    Google Scholar 

  48. Edelstein, F., & Haslett, R. (1974, August). Heat pipe manufacturing study. Final Report prepared by Grumman Aerospace Corp. for NASA No. NAS5-23156.

    Google Scholar 

  49. Jen, H. F., & Kroliczek, E. J. (1976). Grooved analysis program. Towson, MD: B & K Engineering. NAS5-22562.

    Google Scholar 

  50. Nguyen, T. M. (1994, February). User’s manual for groove analysis program (GAP) IBM PC Version 1.0. OAO Corporation.

    Google Scholar 

  51. Skrabek, E. A., & Bienert, W. B. (1972, August). Heat pipe design handbook (Parts I and II). Cockeysville, MD: Dynatherm Corporation. NASA CR-1342.

    Google Scholar 

  52. Marcus, B. D., Eninger, J. E., & Edwards, D. K. (1976). MULTIWICK. Redondo Beach, CA: TRW System Group.

    Google Scholar 

  53. Edward, D. K., Fleischman, G. L., & Marcus, B. D. (1973, October). User’s manual for the TRW Gaspipe 2 Program. Moffet Field, CA: NASA—Ames Research Center. NASA CR-114672.

    Google Scholar 

  54. Woloshun, K. A., Merrigm, M. A., & Best, E. D. (1988, November). Analysis program a user’s manual. Los Alamos National Laboratory. LA-11324-M.

    Google Scholar 

  55. Kamotani, Y. (1978, September). User’s manual for thermal analysis program of axially grooved heat pipes (HTGAP). NASA-CR-170563.

    Google Scholar 

  56. Marcus, B. D., & Fleischman, G. L. Steady-state and transient performance of hot reservoir gas-controlled heat pipes. A.S.M.E. Paper No. 70-HT/SpT-11.

    Google Scholar 

  57. Bienert, W. (1969). Heat pipes for temperature control. Proc: Fourth Intersociety Energy Conversion Engineering Conference, Washington, DC.

    Google Scholar 

  58. Antoniuk, D., Edwards, D. K., & Luedke, E. E. (1978, September 1). Extended development of variable conductance heat pipes. NASA-CR-152183, TRW-31183-6001-RU-00.

    Google Scholar 

  59. Ponnappan, R. Studies on the startup transients and performance of a gas loaded sodium heat pipe. Technical Report for Period June 1989, WRDC-TR-89-2046.

    Google Scholar 

  60. Myers, G. E. (1987). Analytical methods in conduction heat transfer (2nd ed.). Schenectady, NY: Genium Publishing Corp.

    Google Scholar 

  61. Scott, S. E. (1983). MONTE—A two-dimensional monte carlo radiative heat transfer code. M.S. Thesis, Department of Mechanical Engineering, Colorado State University, Fort Collins, CO 80523.

    Google Scholar 

  62. Maltby, J. D. (1987). Three-dimensional simulation of radiative heat transfer by the MonteCarlo method. M.S. Thesis, Department of Mechanical Engineering, Colorado State University, Fort Collins, CO 80523.

    Google Scholar 

  63. Maltby, J. D., & Burns, P. J. (1986). MONT2D and MONT3D user's manual. Internal Publication, Department of Mechanical Engineering, Colorado State University.

    Google Scholar 

  64. Burns, P. J., & Pryor, D. V. (1989). Vector and parallel Monte Carlo radiative heat transfer. Numerical Heat Transfer, Part B: Fundamentals, 16(101), 191–209.

    MATH  Google Scholar 

  65. Burns, P., Christon, M., Schweitzer, R., Wasserman, H., Simmons, M., Lubeck, O. et al. (1988). Vectorization of Monte Carlo particle transport—An architectural study using the LANL benchmark GAMTEB. Proceedings, Supercomputing '89, Reno, NV (pp. 10–20).

    Google Scholar 

  66. Maltby, J. D., & Burns, P. J. (1988). MONT2D and MONT3D user's manual. Internal Publication, Department of Mechanical Engineering, Colorado State University.

    Google Scholar 

  67. Arthur, B., & Shapiro. (1983). FACET—A radiation view factor computer code for axismmetric, 2D planar, and 3D geometries with shadowing, August, 1983. Lawrence Livermore Laboratory.

    Google Scholar 

  68. Maltby, J. D. (1990). Analysis of electron heat transfer via Monte Carlo simulation. Ph.D. Dissertation, Department of Mechanical Engineering, Colorado State University, Fort Collins, CO 80523.

    Google Scholar 

  69. Antoniuk, D., & Edwards, D. K. (1980). Depriming of arterial heat pipe: An investigation of CTS thermal excursions. NASA CR 165153, Final Report August 20, 1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Galaxy Advanced Engineering, Inc., Albuquerque, NM, USA

    Bahman Zohuri

Authors
  1. Bahman Zohuri
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Zohuri, B. (2016). Mathematical Modeling and Available Computer Codes. In: Heat Pipe Design and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-29841-2_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-29841-2_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29840-5

  • Online ISBN: 978-3-319-29841-2

  • eBook Packages: EnergyEnergy (R0)

Publish with us

Policies and ethics

Search

Navigation