Some Boundary-Layer Problems in Convective Flow in Porous Media

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Emerging Technologies and Techniques in Porous Media

Part of the book series: NATO Science Series ((NAII,volume 134))

Abstract

Convective heat transfer in fluid-saturated porous media has received much attention in recent years because of its important applications both in technology and geothermal energy recovery. Detailed reviews of the subject, including exhaustive lists of references, were recently performed by Ingham and Pop [17,18], Nield and Bejan [32], Vafai [40], and Pop and Ingham [33]. Most of the recent research on convective flow in porous media has been directed on the problems of steady free and mixed convection flows over heated bodies embedded in fluid-saturated porous media. However, unsteady convective boundary-layer flow problems have not, so far, received as much attention. Perhaps, the first study on unsteady boundary-layer flow on flat surfaces in porous media was made by Johnson and Cheng [19] who found similarity solutions for certain variations of the wall temperature distributions. The more common cases, in general, involve transient convection, which is non-similar and hence more complicated mathematically. The interested reader can find an excellent collection of papers on unsteady convective flow problems over heated bodies embedded in a fluid-saturated porous medium in the review papers by Bradean et al. [2] and Pop et al. [34], and in the book by Pop and Ingham [33].

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References

  1. Abramowitz, M. and Stegun, I. A. (ed.) (1966). Handbook of mathematical functions. Dover, New York.

    Google Scholar 

  2. Bradean, R., Heggs, P. J., Ingham, D. B. and Pop, I. (1998). Convective heat flow from suddenly heated surfaces embedded in porous media. In Transport phenomena in porous media (ed. D. B. Ingham and I. Pop), pp. 411-38. Pergamon, Oxford.

    Google Scholar 

  3. Brinkman, H. C. (1947). A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl Sci. Res., 1, 27–34.

    Article  Google Scholar 

  4. Cebeci, T. and Bradshaw, P. (1984). Physical and computational aspects of convective heat transfer. Springer, New York.

    Google Scholar 

  5. Chan, B. K. C, Ivey, C. M. and Barry, I. M. (1970). Natural convection in enclosed porous media with rectangular boundaries. Trans. ASME J. Heat Transfer, 92, 21–7.

    Article  Google Scholar 

  6. Chen, C.-K., Chen, C.-H., Minkowycz, W. J. and Gill, U. S. (1992). Non-Darcian effects on mixed convection about a vertical cylinder embedded in a saturated porous medium. Int. J. Heat Mass Transfer, 35, 3041–6.

    Article  Google Scholar 

  7. Cheng, P. (1977). Combined free and forced boundary layer flows about inclined surfaces in a porous medium. Int. J. Heat Mass Transfer, 20, 807–14.

    Article  MATH  Google Scholar 

  8. Cheng, P. (1982). Mixed convection about a horizontal cylinder and a sphere in a fluid-saturated porous medium. Int. J. Heat Mass Transfer, 25, 1245–7.

    Article  MATH  Google Scholar 

  9. Cheng, P. and Minkowycz, W. J. (1977). Free convection about a vertical flat plate embedded in a porous medium with applications to heat transfer from a dike. J. Geophys. Res., 82, 2040–4.

    Article  Google Scholar 

  10. Evans, G. H. and Plumb, O. A. (1978). Natural convection from a vertical isothermal surface embedded in a saturated porous medium. In Proceedings of the AI A A-ASME thermophysics and heat transfer conference. Paper No. 78-HT-55.

    Google Scholar 

  11. Fand, R. M., Steinberg, T. E. and Cheng, P. (1986). Natural convection heat transfer from a horizontal cylinder embedded in a porous medium. Int. J. Heat Mass Transfer, 29, 119–33.

    Article  Google Scholar 

  12. Harris, S. D., Ingham, D. B. and Pop, I. (1999). Unsteady mixed convection boundary-layer flow on a vertical surface in a porous medium. Int. J. Heat Mass Transfer, 42, 357–72.

    Article  MATH  Google Scholar 

  13. Harris, S. D., Ingham, D. B. and Pop, I. (2002). Thermal capacity effect on transient free convection adjacent to a vertical surface in a porous medium. Transport in Porous Media, 46, 1–18.

    Article  MathSciNet  Google Scholar 

  14. Hong, J. T., Tien, C. L. and Kaviany, M. (1985). Non-Darcian effects on vertical-plate natural convection in porous media with high porosities. Int. J. Heat Mass Transfer, 28, 2149–57.

    Article  Google Scholar 

  15. Hossain, M. A., Banu, N. and Nakayama, A. (1994). Non-Darcy forced convection boundary layer flow over a wedge embedded in a saturated porous medium. Numer. Heat Transfer, Part A, 26, 399–414.

    Article  Google Scholar 

  16. Hsu, C. T. and Cheng, P. (1985). The Brinkman model for the natural convection about a semi-infinite vertical flat plate in a porous medium. Int. J. Heat Mass Transfer, 28, 683–97.

    Article  MATH  Google Scholar 

  17. Ingham, D. B. and Pop, I. (ed.) (1998). Transport phenomena in porous media. Pergamon, Oxford.

    Google Scholar 

  18. Ingham, D. B. and Pop, I. (ed.) (2002). Transport phenomena in porous media II. Pergamon, Oxford.

    Google Scholar 

  19. Johnson, C. H. and Cheng, P. (1978). Possible similarity solutions for free convection boundary layers adjacent to flat plates in porous media. Int. J. Heat Mass Transfer, 21, 709–18.

    Article  MATH  Google Scholar 

  20. Kim, S. J. and Vafai, K. (1989). Analysis of natural convection about a vertical plate embedded in a porous medium. Int. J. Heat Mass Transfer, 32, 665–77.

    Article  MATH  Google Scholar 

  21. Kimura, S., Kiwata, T., Okajima, A. and Pop, I. (1997). Conjugate natural convection in porous media. Adv. Water Res., 20, 111–26.

    Article  Google Scholar 

  22. Lai, F. C. (2000). Mixed convection in saturated porous media. In Handbook of porous media (ed. K. Vafai), pp. 605-61. Marcel Dekker, New York.

    Google Scholar 

  23. Magyari, E., Pop, I. and Keller, H. (2003). Analytical solutions for unsteady free convection in porous media. J. Eng. Math. In press.

    Google Scholar 

  24. Méndez, F., Luna, E., Trevino, C. and Pop, I. (2003). Asymptotic and numerical transient analysis of the free convection cooling of a vertical plate embedded in a porous medium. Heat Mass Transfer. In press.

    Google Scholar 

  25. Méndez, F., Trevino, C. and Pop, I. (2002). Conjugate free convection along a thin vertical plate with internal nonuniform heat generation in a porous medium. Heat Mass Transfer, 38, 631–8.

    Article  Google Scholar 

  26. Merkin, J. H. (1977). Mixed convection from a horizontal cylinder. Int. J. Heat Mass Transfer, 20, 73–7.

    Article  Google Scholar 

  27. Merkin, J. H. (1980). Mixed convection boundary layer flow on a vertical surface in a saturated porous medium. J. Eng. Math., 14, 301–13.

    Article  MathSciNet  MATH  Google Scholar 

  28. Nakayama, A. (1995). PC-aided numerical heat transfer and convective flow. CRC Press, Tokyo.

    Google Scholar 

  29. Nazar, R., Amin, N. and Pop, I. (2003). Mixed convection boundary layer flow from a horizontal circular cylinder in micropolar fluids: case of constant wall temperature. Int. J. Numer. Meth. Heat Fluid Flow, 13, 86–109.

    Article  MATH  Google Scholar 

  30. Nazar, R., Amin, N. and Pop, I. (2003). Unsteady mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium. J. Eng. Math. In press.

    Google Scholar 

  31. Nazar, R., Amin, N., Filip, D. and Pop, I. (2003). The Brinkman model for the mixed convection boundary layer flow past a horizontal circular cylinder in a porous medium. Int. J. Heat Mass Transfer, 46, 3167–78.

    Article  MATH  Google Scholar 

  32. Nield, D. A. and Bejan, A. (1999). Convection in porous media (2nd edn). Springer, New York.

    Google Scholar 

  33. Pop, I. and Ingham, D. B. (ed.) (2001). Convective heat transfer: mathematical and computational modelling of viscous fluids and porous media. Pergamon, Oxford.

    Google Scholar 

  34. Pop, I., Ingham, D. B. and Merkin, J. H. (1998). Transient convection heat transfer in a porous medium: external flows. In Transport phenomena in porous media (éd. D. B. Ingham and I. Pop), pp. 205-31. Pergamon, Oxford.

    Google Scholar 

  35. Ramachandran, N., Chen, T. S. and Armaly, B. F. (1988). Mixed convection in stagnation flows adjacent to vertical surfaces. Trans. ASME J. Heat Transfer, 110, 373–7.

    Article  Google Scholar 

  36. Seshadri, R., Sreeshylan, N. and Nath, G. (2002). Unsteady mixed convection flow in the stagnation region of a heated vertical plate due to impulsively motion. Int. J. Heat Mass Transfer, 45, 1345–52.

    Article  MATH  Google Scholar 

  37. Shu, J.-J. and Pop, I. (1998). Transient conjugate free convection along a vertical surface in porous media. Int. J. Eng. Sci., 38, 207–14.

    Article  Google Scholar 

  38. Smith, S. H. (1967). The impulsive motion of a wedge in a viscous fluid. J. Appl. Math. Phys. (ZAMP), 18, 508–22.

    Article  MATH  Google Scholar 

  39. Vafai, K. and Tien, C. L. (1981). Boundary and inertia effects on flow and heat transfer in porous media. Int. J. Heat Mass Transfer, 24, 195–203.

    Article  MATH  Google Scholar 

  40. Vafai, K. (ed.) (2000). Handbook of porous media. Marcel Dekker, New York.

    Google Scholar 

  41. Vynnycky, M. and Kimura, S. (1995). Transient conjugate free convection due to a vertical plate in a porous medium. Int. J. Heat Mass Transfer, 38, 219–31.

    Article  MATH  Google Scholar 

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Pop, I. (2004). Some Boundary-Layer Problems in Convective Flow in Porous Media. In: Ingham, D.B., Bejan, A., Mamut, E., Pop, I. (eds) Emerging Technologies and Techniques in Porous Media. NATO Science Series, vol 134. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0971-3_5

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  • DOI: https://doi.org/10.1007/978-94-007-0971-3_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1874-9

  • Online ISBN: 978-94-007-0971-3

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