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Natural, Forced, and Mixed Convection Heat Transfer in External Flows Through Porous Media

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Rheology of Drag Reducing Fluids
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Abstract

Chapter 6 turns to external flows through porous media and derives expressions for natural, forced and mixed convection heat transfer past a vertical plate embedded in a porous medium. The final form of the equation for mixed convection is like those of the correlating equations for combined laminar forced and free convection heat transfer for Newtonian fluids and for non- Newtonian fluids in homogeneous media. Such equations which interpolate the two extremes of forced and free convection have been shown to give reasonably accurate results for homogeneous media. In the case of convective flow through porous media, too, such correlating equations are very effective.

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References

  • Bejan, A. (1984). Convective heat transfer. New York: Wiley.

    MATH  Google Scholar 

  • Bejan, A. (1987). In S. Kakac, R. K. Shah, & W. Aung (Eds.), Handbook of single-phase convective heat transfer, convective heat transfer in porous media. New York: Wiley.

    Google Scholar 

  • Bejan, A., & Poulikakos, D. (1984). The non-Darcy regime for vertical boundary layer natural convection in a porous medium. International Journal of Heat and Mass Transfer, 27(5), 717–722.

    Article  MATH  Google Scholar 

  • Boger, D. V. (1977/78). A highly elastic constant viscosity fluid. Journal of Non-Newtonian Fluid Mechanics, 3, 87–91.

    Google Scholar 

  • Brinkman, H. C. (1947). A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Applied Scientific Research, A1, 27–34.

    MATH  Google Scholar 

  • Broadbent, J. M., & Mena, B. (1974). Slow flow of an elastico-viscous fluid past cylinders and spheres. Chemical Engineering Journal, 8(1), 11–19.

    Article  Google Scholar 

  • Cao, Y., & Cui, X. (2015). Natural convection of power-law fluids in porous media with variable thermal and mass diffusivity. International Journal of Heat and Technology, 33(2), 85–90.

    Article  Google Scholar 

  • Caswell, B., & Schwarz, W. H. (1962). The creeping motion of a non-newtonian fluid past a sphere. Journal of Fluid Mechanics, 13(3), 417–426.

    Article  MathSciNet  MATH  Google Scholar 

  • Chamkha, A. J., & Ben-Nakhi, A. (2007). Coupled heat and mass transfer in mixed convection flow of a non-newtonian fluidover a permeable surface embedded in a non-darcian porous medium. International Journal of Heat and Technology, 25(1), 33–41.

    Google Scholar 

  • Chen, H.-T., & Chen, C.-K. (1988a). Free convection of non-newtonian fluids along a vertical surface embedded in a porous medium. Transactions ASME, Journal Heat Transfer, 110, 257–260.

    Article  Google Scholar 

  • Chen, H.-T., & Chen, C.-K. (1988b). Natural convection of a non-newtonian fluid about a horizontal cylinder and a sphere in a porous medium. International Communications in Heat and Mass Transfer, 15, 605–614.

    Article  Google Scholar 

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

    Google Scholar 

  • Chhabra, R. P. (1986). Encyclopedia of fluid mechanics, vol. 1, ch. 30. In N. P. Cheremisinoff (Ed.), Steady non-newtonian flow about a rigid sphere (pp. 983–1033). Houston, TX: Gulf Publishing Co.

    Google Scholar 

  • Chhabra, R. P., Uhlherr, P. H., & Boger, D. V. (1980). The influence of fluid elasticity on the drag coefficient for creeping flow around a sphere. Journal of Non-Newtonian Fluid Mechanics, 6(3–4), 187–199.

    Article  Google Scholar 

  • Choplin, L., Carreau, P., & Aitkadi, A. (1983). Highly elastic constant viscosity fluids. Polymer Engineering & Science, 23(8), 459–464.

    Article  Google Scholar 

  • Churchill, S. W. (1977). A comprehensive correlating equation for laminar, assisting, forced and free convection. AICHE Journal, 23(1), 10–16.

    Article  MathSciNet  Google Scholar 

  • Combarnous, M. A., & Bories, S. A. (1975). Hydrothermal convection in saturated porous media. Advances Hydroscience, 10, 231–307.

    Article  Google Scholar 

  • Ergun, S. (1952). Fluid flow through packed columns. Chemical Engineering Progress, 48(2), 89–94.

    Google Scholar 

  • Fand, R. M., Steinberger, T. E., & Cheng, P. (1986). Combined natural and forced convection heat transfer from a horizontal cylinder embedded in a porous medium. International Journal of Heat and Mass Transfer, 29(1), 119–133.

    Article  Google Scholar 

  • Forchheimer, P. (1901). Wasserbewegung durch boden. Zeitschrift des Vereins Deutscher Ingenieure, 45, 1782–1788.

    Google Scholar 

  • Giesekus, H. (1963). Die simultane translations- und rotationsbewegung einer kugel in einer elastikoviskosen flussigkeit. Rheologica Acta, 3, 59–71.

    Article  MATH  Google Scholar 

  • Hellums, J. D., & Churchill, S. W. (1964). Simplification of the mathematical description of boundary and initial value problems. AICHE Journal, 10(1), 110–114.

    Article  Google Scholar 

  • Ingham, D. B. (1986). The non-darcy free convection boundary layer on axisymmetric and two-dimensional bodies of arbitrary shape. International Journal of Heat and Mass Transfer, 29, 1759–1763.

    Article  Google Scholar 

  • Kafoussias, N. G. (1990). Principles of flow through porous media with heat transfer. In Encyclopedia of fluid mechanics, vol. 10, ch. 20 (pp. 663–686). London: Gulf Publishing Co.

    Google Scholar 

  • Lauriat, G., & Prasad, V. (1987). Natural convection in a vertical porous cavity: A numerical study for brinkman-extended darcy formulation. Transactions ASME Journal of Heat Transfer, 109(3), 688–696.

    Article  Google Scholar 

  • Leslie, F. M., & Tanner, R. I. (1961). The slow flow of a visco-elastic liquid past a sphere. The Quarterly Journal of Mechanics and Applied Mathematics, 14(1), 36–48.

    Article  MathSciNet  MATH  Google Scholar 

  • Mena, B., & Caswell, B. (1974). Slow flow of an elastic-viscous fluid past an immersed body. Chemical Engineering Journal, 8(2), 125–134.

    Article  Google Scholar 

  • Metzner, A. B., White, J. L., & Denn, M. M. (1966). Constitutive equations for viscoelastic fluids for short deformation periods and for rapidly changing flows: Significance of the Deborah number. AICHE Journal, 12(5), 863–866.

    Article  Google Scholar 

  • Muskat, M. (1946). The flow of homogeneous fluids through porous media. Ann Arbor, MI: Edwards.

    Google Scholar 

  • Nakayama, A., & Koyama, H. (1991). Buoyancy-induced flow of non-newtonian fluids over a non-isothermal body of arbitrary shape in a fluid-saturated porous medium. Applied Scientific Research, 48(1), 55–70.

    Article  MATH  Google Scholar 

  • Nakayama, A., & Pop, I. (1991). A unified similarity transformation for free, forced and mixed convection in darcy and non-darcy porous media. International Journal of Heat and Mass Transfer, 34, 357–367.

    Article  MATH  Google Scholar 

  • Nakayama, A., & Shenoy, A. V. (1992). A unified similarity transformation for darcy and non-darcy forced, free and mixed convection heat transfer in non-newtonian inelastic fluid-saturated porous media. Chemical Engineering Journal, 50(1), 33–45.

    Article  Google Scholar 

  • Nakayama, A., & Shenoy, A. V. (1993). Combined forced and free convection heat transfer in non-newtonian fluid saturated porous medium. Applied Scientific Research, 50(1), 83–95.

    Article  MATH  Google Scholar 

  • Nield, D. A., & Joseph, D. D. (1985). Effects of quadratic drag on convection in a saturated porous medium. Physics of Fluids, 28(3), 995–997.

    Article  Google Scholar 

  • Pascal, H. (1990a). Non-isothermal flow of non-newtonian fluids through a porous medium. International Journal of Heat and Mass Transfer, 33(9), 1937–1944.

    Article  MATH  Google Scholar 

  • Pascal, H. (1990b). Some self-similar two-phase flows of non-newtonian fluids through a porous medium. The journal Studies in Applied Mathematics, 82, 305–318.

    Article  MathSciNet  MATH  Google Scholar 

  • Pascal, H., & Pascal, J. P. (1989). Non-linear effects of non-newtonian fluids on natural convection in a porous medium. Physica D, 40(3), 393–402.

    Article  MathSciNet  MATH  Google Scholar 

  • Plumb, O. A., & Huenefeld, J. C. (1981). Non-darcy natural convection from heated surfaces in saturated porous medium. International Journal of Heat and Mass Transfer, 24(4), 765–768.

    Article  MATH  Google Scholar 

  • Poulikakos, D., & Bejan, A. (1985). The departure from darcy flow in natural convection in a vertical porous layer. Physics of Fluids, 28(12), 3477–3484.

    Article  MathSciNet  MATH  Google Scholar 

  • Ruckenstein, E. (1978). Interpolating equations between two limiting cases for the heat transfer. AICHE Journal, 24(5), 940–941.

    Article  Google Scholar 

  • Rumer, R. R. (1969). In R. J. De Wiest (Ed.), Flow through porous media. Academic Press: New York.

    Google Scholar 

  • Shenoy, A. V. (1980a). A correlating equation for combined laminar forced and free convection heat transfer to power-law fluids. AICHE Journal, 26(3), 505–507.

    Article  Google Scholar 

  • Shenoy, A. V. (1980b). Combined laminar forced and free convection heat transfer to viscoelastic fluids. AICHE Journal, 26(4), 683–685.

    Article  Google Scholar 

  • Shenoy, A. V. (1986). Handbook of heat mass transfer, vol. 1, ch. 5. In N. P. Cheremisinoff (Ed.), Natural convection heat transfer to power-law fluids (pp. 183–210). Houston, TX: Gulf Publishing Co.

    Google Scholar 

  • Shenoy, A. V. (1988). Encyclopedia of fluid mechanics, vol. 7, ch. 10. In N. P. Cheremisinoff (Ed.), Natural convection heat transfer to viscoelastic fluids (pp. 287–304). Houston, TX: Gulf Publishing Co.

    Google Scholar 

  • Shenoy, A. V. (1992). Darcy natural, forced and mixed convection heat transfer from an isothermal vertical flat plate embedded in a porous medium saturated with an elastic fluid of constant viscosity. International Journal of Engineering Science, 30(4), 455–467.

    Article  MATH  Google Scholar 

  • Shenoy, A. V. (1993). Darcy-forchheimer natural, forced and mixed convection heat transfer in non-newtianian power-law fluid-saturated porous media. Transport in Porous Media, 11(3), 219–241.

    Article  Google Scholar 

  • Shenoy, A. V. (1994). Non-newtonian fluid heat transfer in porous media. Advanced Heat Transfer, 24, 101–190.

    Article  Google Scholar 

  • Tien, C. L., & Vafai, K. (1990). Convective and radiative heat transfer in porous media. Advances in Applied Mechanics, 27, 225–281.

    Article  MATH  Google Scholar 

  • Tong, T. W., & Subramanian, E. (1985). A boundary layer analysis for natural convection in vertical porous enclosures – use of the Brinkman-extended Darcy model. International Journal of Heat and Mass Transfer, 28(3), 563–571.

    Article  MATH  Google Scholar 

  • Trevisan, O. V., & Bejan, A. (1990). Combined heat and mass transfer by natural convection in a porous medium. Advances Heat Transfer, 20, 315–352.

    Article  Google Scholar 

  • Vasantha, R., Pop, I., & Nath, G. (1986). Non-darcy natural convection over a slender vertical frustum of a cone in a saturated porous medium. International Journal of Heat and Mass Transfer, 29(1), 153–156.

    Article  Google Scholar 

  • Wang, C., & Tu, C. (1989). Boundary layer flow and heat transfer of non-newtonian fluids in porous media. International Journal of Heat and Fluid Flow, 10(2), 160–165.

    Article  Google Scholar 

  • Wang, C., Tu, C., & Zhang, X. (1990). Mixed convection of non-newtonian fluids from a vertical plate embedded in a porous medium. Acta Mechanica Sinica, 6(3), 214–220.

    Article  MATH  Google Scholar 

  • Ward, J. C. (1964). Turbulent flow in porous media. Journal of the Hydraulics Division ASCE, 90(5), 1–12.

    Google Scholar 

  • White, J. L. (1964). Dynamics of viscoelastic fluids, melt fracture, and the rheology of fiber spinning. Journal of Applied Polymer Science, 8(5), 2339–2357.

    Article  Google Scholar 

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Shenoy, A. (2020). Natural, Forced, and Mixed Convection Heat Transfer in External Flows Through Porous Media. In: Rheology of Drag Reducing Fluids. Springer, Cham. https://doi.org/10.1007/978-3-030-40045-3_6

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  • DOI: https://doi.org/10.1007/978-3-030-40045-3_6

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