Research Papers: Porous Media

Effect of Apex Angle, Porosity, and Permeability on Flow and Heat Transfer in Triangular Porous Ducts

[+] Author and Article Information
S. Negin Mortazavi

Department of Mechanical Engineering,
University of Texas at Dallas,
Richardson, TX 75080
e-mail: negin@utdallas.edu

Fatemeh Hassanipour

Department of Mechanical Engineering,
University of Texas at Dallas,
Richardson, TX 75080
e-mail: fatemeh@utdallas.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 9, 2013; final manuscript received July 28, 2014; published online August 26, 2014. Assoc. Editor: Oronzio Manca.

J. Heat Transfer 136(11), 112602 (Aug 26, 2014) (8 pages) Paper No: HT-13-1532; doi: 10.1115/1.4028177 History: Received October 09, 2013; Revised July 28, 2014

This paper presents an analysis of forced convection flow and heat transfer in triangular ducts containing a porous medium. The porous medium is isotropic and the flow is laminar, fully developed with constant properties. Numerical results for velocity and temperature distribution (in dimensionless format) in the channel are presented for a wide range of porosity, permeability, and apex angles. The effects of apex angle and porous media properties (porosity and permeability) are demonstrated on the velocity and temperature distribution, as well as the friction factor (fRe) and Nusselt numbers in the channel for both Isoflux (NuH) and Isothermal (NuT) boundary conditions. The consistency of our findings has been verified with earlier results in the literature on empty triangular ducts, when the porosity in our models is made to approach one.

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Lauriat, G., and Ghafir, R., 2000, “Forced Convective Transfer in Porous Media,” Handbook of Porous Media, Marcel Dekker, New York.
Mohamad, A., 2003, “Heat Transfer Enhancements in Heat Exchangers Fitted With Porous Media Part I: Constant Wall Temperature,” Int. J. Therm. Sci., 42, pp. 385–395. [CrossRef]
Alkam, M., and Al-Nimr, M., 1999, “Solar Collectors With Tubes Partially Filled With Porous Substrate,” ASME J. Sol. Energy Eng., 121, pp. 20–24. [CrossRef]
Walsh, E., and Walsh, P., 2010, “Simple Models for Laminar Thermally Developing Slug Flow in Noncircular Ducts and Channels,” ASME J. Heat Transfer, 132, p. 111702. [CrossRef]
Muzychka, Y. S., and Yovanovich, M. M., 1998, “Modeling Nusselt Numbers for Thermally Developing Laminar Flow in Non-Circular Ducts,” AIAA Paper No. 98-2586. [CrossRef]
Bergles, A., 1985, “Techniques to Augment Heat Transfer,” Handbook of Heat Transfer Applications, 2nd ed., W. M.Rohsenow, J. P.Hartnett, and E. N.Ganic, eds., McGraw-Hill, New York.
Metwally, H. M., and Manglik, R. M., 2004, “Enhanced Heat Transfer Due to Curvature-Induced Lateral Vortices in Laminar Flows in Sinusoidal Corrugated-Plate Channels,” Int. J. Heat Mass Transfer, 47, pp. 2283–2292. [CrossRef]
Sparrow, E., and Haji-Sheikh, A., 1966, “Flow and Heat Transfer in Ducts of Arbitrary Shape With Arbitrary Thermal Boundary Conditions,” ASME J. Heat Transfer, 88, pp. 351–358. [CrossRef]
Shah, R., 1975, “Laminar Flow Friction and Forced Convection Heat Transfer in Ducts of Arbitrary Geometry,” Int. J. Heat Mass Transfer, 18, pp. 849–862. [CrossRef]
Haji-Sheikh, A., Mashena, M., and Haji-Sheikh, M. J., 1983, “Heat Transfer Coefficient in Ducts With Constant Wall Temperature,” ASME J. Heat Transfer, 105, pp. 878–883. [CrossRef]
Rao, V., Kumar, P. R., and Rao, P. S., 2006, “Laminar Flow Heat Transfer in Concentric Equilateral Triangular Annular Channel,” Indian J. Chem. Technol., 13, pp. 614–622.
Baliga, B., and Azrak, R., 1986, “Laminar Fully Developed Flow and Heat Transfer in Triangular Plate-Fin Ducts,” ASME J. Heat Transfer, 108(1), pp. 24–32. [CrossRef]
Aparecido, J., and Cotta, R., 1992, “Laminar Thermally Developing Flow Inside Right-Angularly Triangular Ducts,” Appl. Sci. Res., 49(4), pp. 355–368. [CrossRef]
Zhang, L. Z., 2007, “Laminar Flow and Heat Transfer in Plate-Fin Triangular Ducts in Thermally Developing Entry Region,” Int. J. Heat Mass Transfer, 50(7), pp. 1637–1640. [CrossRef]
Farhanieh, B., and Sunden, B., 1991, “Three-Dimensional Laminar Flow and Heat Transfer in the Entrance Region of Trapezoidal Ducts,” Int. J. Numer. Methods Fluids, 13(5), pp. 537–556. [CrossRef]
Asako, Y., and Faghri, M., 1988, “Three-Dimensional Laminar Heat Transfer and Fluid Flow Characteristics in the Entrance Region of a Rhombic Duct,” ASME J. Heat Transfer, 110(4A), pp. 855–861. [CrossRef]
Lu, T., 1998, “Heat Transfer Efficiency of Metal Honeycombs,” Int. J. Heat Mass Transfer, 42(11), pp. 2031–2040. [CrossRef]
Ding, J., and Manglik, R. M., 1996, “Analytical Solutions for Laminar Fully Developed Flows in Double-Sine Shaped Ducts,” Int. J. Heat Mass Transfer, 31, pp. 269–277. [CrossRef]
Shah, R., and London, A., 1978, Laminar Flow Forced Convection in Ducts, Academic, New York.
Haji-Sheikh, A., Sparrow, E., and Minkowycz, W., 2005, “Heat Transfer to Flow Through Porous Passages Using Extended Weighted Residuals Method a Greens Function Solution,” Int. J. Heat Mass Transfer, 48(7), pp. 1330–1349. [CrossRef]
Banerjee, A., Haji-Sheikh, A., and Nomura, S., 2012, “Heat Transfer With Axial Conduction in Triangular Ducts Filled With Saturated Porous Materials,” Numer. Heat Transfer, Part A, 62(1), pp. 1–24. [CrossRef]
Nield, D., Junqueria, S., and Lage, J., 1996, “Forced Convection in a Fluid Saturated Porous Medium Channel With Isothermal or Isoflux Boundaries,” J. Fluid Mech., 322, pp. 201–214. [CrossRef]
Kaviany, M., 1985, “Laminar Flow Through a Porous Channel Bounded by Isothermal Parallel Plates,” Int. J. Heat Mass Transfer, 28, pp. 851–858. [CrossRef]
Lakshminarayanan, R., 1988, “Integral Solutions for Laminar Entrance Problems in Irregular Ducts,” Ph.D. dissertation, University of Texas at Arlington, Arlington, TX.
Shah, R., and Bhatti, M., 1987, “Laminar Convective Heat Transfer in Ducts,” Handbook of Single-Phase Convective Heat Transfer, Vol. 3, Wiley, New York.
Cotta, R. M., 1993, Integral Transforms in Computational Heat and Fluid Flow, 3rd ed., CRC Press, Boca Raton, FL.
Manglik, R., and Ding, J., 1997, “Laminar Flow Heat Transfer to Viscous Power Law Fluids in Double-Sine Ducts,” Int. J. Heat Mass Transfer, 40, pp. 1379–1390. [CrossRef]
Lakshminarayanan, R., and Haji-Sheikh, A., 1988, “Extended Graetz Problems in Irregular Ducts,” ASME Proceedings of the National Heat Transfer Conference, H. R. Jacobs, ed., HTD-96, Vol. 1, pp. 475–482.
Cole, K. D., Haji-Sheikh, A., and Litkouhi, B., 1992, Heat Conduction Using Green's Function, 1st ed., Hemisphere Publishing Corporation, Washington DC.
Haji-Sheikh, A., and Vafai, K., 2004, “Analysis of Flow and Heat Transfer in Porous Media Embedded Inside Various-Shaped Ducts,” Int. J. Heat Mass Transfer, 47, pp. 1889–1905. [CrossRef]
Tien, C. L., and Vafai, K., 1978, “Statistical Bounds for the Effective Thermal Conductivity of Microsphere and Fibrous Insulation,” Thermophysics and Heat Transfer Conference, AIAA Progress Series 65, pp. 135–148.
Kantorovich, L. V., and Krylov, V. I., 1964, Approximate Methods of Higher Analysis, 3rd ed., Noordhoff Groningen, The Netherlands.
Borse, G. J., 1985, FORTRAN 77 and Numerical Methods for Engineers, PWS-KENT, Boston, MA.


Grahic Jump Location
Fig. 1

Geometry and coordinate system for a triangular porous duct

Grahic Jump Location
Fig. 5

Effect of (a) apex angle (ɛ = 0.6,K = 10-4m2), (b) porosity (2β = 60 deg,K = 10-4m2), and (c) permeability (2β = 60 deg,ɛ = 0.6) on the velocity distribution

Grahic Jump Location
Fig. 4

Validation of friction factor (fRe)

Grahic Jump Location
Fig. 3

Validation of Nusselt number for isothermal boundary condition

Grahic Jump Location
Fig. 2

Validation of Nusselt number for isoflux boundary condition

Grahic Jump Location
Fig. 6

Effect of (a) apex angle (ɛ = 0.6,K = 10-4m2), (b) porosity (2β = 60 deg,K = 10-4m2), and (c) permeability (2β = 60 deg,ɛ = 0.6) on the temperature distribution

Grahic Jump Location
Fig. 7

Variation of friction factor with (a) apex angle, (b) porosity, and (c) permeability

Grahic Jump Location
Fig. 8

Variation of Nusselt number with (a) apex angle, (b) porosity, and (c) permeability



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