Skip to main content
SpringerLink
Log in
Book cover

Convective Heat and Mass Transfer in Porous Media pp 543–562Cite as

Natural Convection in Porous Media with Variable Porosity and Thermal Dispersion Effects

  • Chapter

Part of the book series: NATO ASI Series ((NSSE,volume 196))

Abstract

Recent numerical studies of variable porosity and thermal dispersion effects on natural convection in porous media are summarized. This includes natural convection in a packed rectangular cavity heated from the side and heated from below, as well as natural convection from a heated horizontal cylinder embedded in an enclosed porous cavity. Numerical results show that both variable porosity and thermal dispersion effects increase the temperature gradient adjacent to the wall resulting in the enhancement of surface heat flux. These effects become important when the dimensionless particle diameter is increased. The numerical results show that the thermal dispersion effect on Nusselt number in natural convection in porous media is small. The Prandtl number effect on Nusselt number is also small for Prandtl number greater than one; its effect decreases as the Prandtl number decreases from one. A comparison of theory and experiments shows that the calculated Nusselt numbers with variable porosity and thermal dispersion effects taken into consideration agree the best with experimental data.

This is a preview of subscription content, 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   429.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   549.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   549.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cheng, P. (1978), ‘Heat transfer in geothermal systems’, Advances in Heat Transfer 14, 1–105.

    Article  ADS  Google Scholar 

  2. Cheng, P. (1985), ‘Natural convection in porous media: external flow’, in Natural Convection: Fundamentals and Applications, 475–513, edited by S. Kakac, W. Aung, and R. Viskanta, Martinus Nijhoff Publisher, The Haque, The Netherlands.

    Google Scholar 

  3. Schneider, K. J. (1963), ‘Investigation of the influence of free thermal convection on heat transfer through granular materials’, Proc. of International Institute of Refrigeration II-4, 247–253.

    Google Scholar 

  4. Yen, Y. C. (1974), ‘Effects of density inversion on free convective heat transfer in porous layer heated from below’, Int. J. Heat Mass Transfer 17, 1349–1356.

    Article  Google Scholar 

  5. Combarnous and Bories, S. A. (1975), ‘Hydrothermal convection in saturated porous medium’, Adv. Hydrosci. 10, 231–307.

    Google Scholar 

  6. Kaneko, T., Mohtadi, M. F. and Aziz, K. (1974), ‘An experimental study of natural convection in inclined porous media’, Int. J. Heat Mass Transfer, 485–496.

    Google Scholar 

  7. Buretta, R. J. and Berman, A. S. (1976), ‘Convective heat transfer in a liquid saturated porous layer’, J. of Applied Mechanics 43, 249–253.

    Article  ADS  Google Scholar 

  8. Klarsfeld, S. (1970), Revue Generale Thermique 108, 1403–1423.

    Google Scholar 

  9. Bankvall, C. G. (1974), ‘Natural convection in vertical permeable space’, Warme Stoffubertrag 7, 22–30.

    Article  ADS  Google Scholar 

  10. Cheng, P. and Ali, C. L. (1981), ‘An experimental investigation of free convection about a heated inclined surface in a porous medium’, Paper 81-HT-85, 20th National Heat Transfer Conference, August 1981.

    Google Scholar 

  11. Cheng, P., Ali, C. L. and Verma, A. K. (1981), “An experimental study of non-Darcian effects in free convection in a saturated porous medium,’ Letters in Heat and Mass Transfer 8, 261–266.

    Article  Google Scholar 

  12. Seki, N., Fukusako, S. and Inabe (1978), ‘Heat transfer in a confined rectangular cavity packed with porous media’, Int. J. Heat Mass Transfer 21, 985–989.

    Article  Google Scholar 

  13. Jonsson, T. and Catton, I. (1987), ‘Prandtl number effect on Benard convection in porous media’, J. Heat Transfer 109, 371–377.

    Article  Google Scholar 

  14. Close, D. J., Symons, J.G. and White, R. F. (1985),’ Convective heat transfer in shallow, gas-filled porous media: experimental investigation’, Int. J. Heat Mass Transfer 28, 2371–2378.

    Article  Google Scholar 

  15. Fand, R. M., Steiberger, T., and Cheng, P. (1986), ‘Natural convection heat transfer from a horizontal cylinder embedded in a porous medium’, Int. J. Heat Mass Transfer 29, 119–133.

    Article  Google Scholar 

  16. Prasad, V., Kuklacki, F. A. and Keyhani, M. (1985),’ Natural convection in porous media’, J. Fluid Mech. 150, 89–119.

    Article  ADS  Google Scholar 

  17. Prasad, V., and Kulacki, F. A.. (1985),’ Natural Convection in porous media bounded by short concentric vertical cylinders’, J. Heat Transfer 107, 147–154.

    Article  Google Scholar 

  18. Prasad, V., Kulakci, F. A., and Kulkarni, A. V. (1986),‘Free convection in a vertical, porous annulus with constant heat flux on the inner wall-experimental results’, Int. J. Heat Mass Transfer 29, 713–723.

    Article  Google Scholar 

  19. Prasad, V. and Kladias, N. (1990),‘Non-Darcy natural convection in saturated porous media,‘(this volume).

    Google Scholar 

  20. Roblee, L. H. S., Baird, R. M. and Tient, J. W. (1958),‘Radial porosity variations in packed beds’, AICHE.J. 4, 460–464.

    Article  Google Scholar 

  21. Benenati, R. F. and Brosilow, C. B. (1962), ‘Void fraction distribution in a bed of spheres’, AICHE J. 8, 359–361.

    Article  Google Scholar 

  22. Schwartz, C. E. and Smith, J. M. (1953),‘Flow distribution in packed beds’, Ind. Engg. Chem. 45, 1209–1218.

    Article  Google Scholar 

  23. Choudhary, M., J. Szekely, J. and Weiler, S. W. (1976), ‘The effect of flow maldistribution on conversion in a catalytic papcked-bed reactor’, AICHE.J. 22, 1021–1032.

    Article  Google Scholar 

  24. Vortmeyer, D. and Schuster, J. (1983), ‘Evaluation of steady flow profiles in rectangular and circular packed beds by variation method’, Chem. Engg. Sci. 38, 1691–1699.

    Article  Google Scholar 

  25. Brinkman, H. C. (1947), ‘A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles,’, Appl. Sci. Res. Al, 27–34.

    Google Scholar 

  26. Hunt, M. L. and Tien, C. L. (1987), ‘Non-Darcian convection in clyndrical packed beds’, Pro. of 2nd ASME/JSME Thermal Engineering Joint Conference 2, 433–438.

    Google Scholar 

  27. Cheng, P. Chowdhury, A. and Hsu, C. T. (1990),’Forced convection in packed tubes and channels with variable porosity and thermal dispersion effects (this volume).

    Google Scholar 

  28. Vafai, K. (1984),‘Convective flow and heat transeer in variable porosity media’, JFM 147, 233–259.

    Article  ADS  MATH  Google Scholar 

  29. Tien, C. L. and Hong, J. T. (1985),‘Natural convection in porous media under non-Darcian and nonuniform permeablity conditions’, in Natural Convection: Fundamentals and Applications, 573–587, edited by S. Kakac, W. Aung and R. Viskanta, Martins Nighoff Publisher, The Haque, The Netherlands.

    Google Scholar 

  30. Chandrasekhara, B. C., Namboodiri, P. M. S., and Hanumanthappa, A. R. (1984), ‘similarity solutions for buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces’, Warme-und Stoffubertragung 18, 17–23.

    Article  ADS  Google Scholar 

  31. Chandrasekhara, B. C. and Namboodiri, P. M. S. (1985), ‘Influence of variable permeability on combined free and forced convection about inclined surfaces in porous medium’, Int. J. Heat Mass Transfer 28, 199–206.

    Article  MATH  Google Scholar 

  32. Cheng, P. and Vortmeyer, D. (1988),‘Transverse thermal dispersion and wall channeling in a packed bed with forced convective flow’, Chem. Engg. Sci. 43, 2523–2532.

    Article  Google Scholar 

  33. Davis, E., Lauriat, G., and Cheng, P.,‘A numerical solution of variable porosity effects on natural convection in a packed-sphere cavity’, Proc. of 25th ASME National Heat Transfer Conference 1, 605–612.

    Google Scholar 

  34. Cheng, P. and Zhang, T. M. (1986), ‘Mixed convection in the thermal plume above a horizontal line source of heat in a porous medium of infinite extent’, Proc. of the 8th International Heat Transfer Conference 4, 2671–2675.

    Google Scholar 

  35. Plumb, O. A. (1983), ‘The effect of thermal dispersion on heat transfer in packed bed boundary layers’, Proc. of ASMER/JSME Joint Thermal Engineering Conference 2, 17–22.

    Google Scholar 

  36. Hong, J. T. and Tien, C. L. (1987),‘Analysis of thermal dispersion effect on vertical-plate natural convection in porous media’, Int. J. Heat Mass Transfer 30, 143–150.

    Article  MATH  Google Scholar 

  37. Kvemvolid, O. and Tyvand, P. (1980),‘Dispersion effects on thermal convection in porous media’, JFM 99, 673–686.

    Article  ADS  Google Scholar 

  38. Georgiadis, J. G. and Catton, I. (1988), ‘Dispersion in cellular thermal convection in porous layers’, Int. J. Heat Mass Transfer 31, 1081–1091.

    Article  MATH  Google Scholar 

  39. Hong, J. T., Yamada, Y.and Tien, C. L. (1987), ‘Effects of non-Darcian and nonuniform porosity on vertical plate natural convection in porous media’, J. Heat Transfer 109, 356–362.

    Article  Google Scholar 

  40. Hsu, C. T. and Cheng, P. (1988), ‘Closure schemes of the macroscopic energy equation for convective heat transfer in porous media’, Int. Comm. Heat Mass Transfer 15, 689–703.

    Article  Google Scholar 

  41. Hsu, C. T. and Cheng, P. (1990),‘Thennal dispersion in porous media’, Int. J. Heat Mass Transfer 8, 1587–1597.

    Article  Google Scholar 

  42. Cheng, P., Hsiao, S. W., and Chen, C. K. (1990),‘Nominiform porosity and thermal dispersion effects on natural convection about a heated horizontal cylinder in an enclosed porous medium (in preparation).

    Google Scholar 

  43. Hsiao, S. W., Cheng, P. and Chen, C. K. (1990),‘Wall effects on natural convection heat transfer in a tilted porous cavity (in preparation).

    Google Scholar 

  44. Cheng, P., Hsiao, S. W. and Chen, C. K. (1990),‘Wall effects on natural convection in an inclined porous cavity with a discrete heat source on a wall’ (in preparation).

    Google Scholar 

  45. Zenher, P. and Schulender, E. U. (1970), ‘Warmeleitfahigkeit von Schuttungen bei massigen Temeraturen’, Chemie-Ingr-Tech., 42, 933–941.

    Article  Google Scholar 

  46. Prasad, V., Kulacki, F. A., and Stone, K. (1986),‘Free convection in a porous cavity with a finite wall heat source’, Natural Convection in Enclosure, ASME H.T.D. 63, 91–98.

    Google Scholar 

  47. Cheng, P. and Minkowycz, W. J. (1977), ‘Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike’, J. Geophysical Res. 82, 2040–2044.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Hawaii, Honolulu, Hawaii, 69822, USA

    Ping Cheng

  2. Department of Mechanical Engineering, National Cheng-Kung University, Tainan, Taiwan, ROC

    Shih-Wen Hsiao & Chao-Kuang Chen

Authors
  1. Ping Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shih-Wen Hsiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chao-Kuang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, University of Miami, Coral Gables, Florida, USA

    Sadik Kakaç

  2. Department of Mechanical Engineering, Middle East Technical University, Ankara, Turkey

    Birol Kilkiş  & Faruk Arinç  & 

  3. College of Engineering, Colorado State University, Ft. Collins, Colorado, USA

    Frank A. Kulacki

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Cheng, P., Hsiao, SW., Chen, CK. (1991). Natural Convection in Porous Media with Variable Porosity and Thermal Dispersion Effects. In: Kakaç, S., Kilkiş, B., Kulacki, F.A., Arinç, F. (eds) Convective Heat and Mass Transfer in Porous Media. NATO ASI Series, vol 196. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3220-6_17

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-3220-6_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5419-5

  • Online ISBN: 978-94-011-3220-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation