Posts by Flavius Patrulescu

Abstract

This paper studies the steady, free convection boundary layer flow about a vertical, isothermal plate embedded in a non-Darcy bidisperse porous medium (BDPM). An appropriate mathematical model is proposed. The boundary layer analysis leads to a system of partial differential equations containing inertial, interphase momentum, thermal diffusivity ratio, thermal conductivity ratio, permeability ratio, modified thermal capacity, and convection parameters. These equations that govern the flow and heat transfer in the f-phase and the p-phase are solved numerically using an algorithm based on the bvp4c routine from matlab. The dependences of the dimensionless velocities and temperatures profiles, as well as of the Nusselt numbers on the governing parameters are investigated. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed in details.

Authors

F.O. Pătrulescu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

T. Groşan
Babes-Bolyai University, Cluj-Napoca, Romania

I. Pop
Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

bidisperse porous medium, free convection, boundary layer, non-Darcy flow, numerical results.

References

See the expanding block below.

Paper coordinates

O. Pătrulescu, T. Groşan, I. Pop, Natural convection from a vertical plate embedded in a non-Darcy bidisperse porous medium, J. Heat Transfer, 142 (2020) no. 1, 012504 (11 pp.)
DOI:  https://doi.org/10.1115/1.4045067.

PDF

not available yet.

About this paper

Journal

Journal of Heat Transfer

Publisher Name

ASME

Print ISSN
Online ISSN
Google Scholar Profile

not yet

[1] Ingham, D. B., and Pop, I., 2005, Transport Phenomena in Porous Media, Vol.  III, Elsevier, Oxford, UK.
[2] Straughan, B., 2015, Convection With Local Thermal Non-Equilibrium and Microfluidic Effects, Springer, Berlin. Google Scholar Crossref
[3] Nield, D. A., and Bejan, A., 2017 Convection in Porous Media, 5th ed., Springer, New York, Google Scholar, Crossref
[4] Bear, J., 2018, Modeling Phenomena of Flow and Transport Media, Springer, New York. Google Scholar , Crossref
[4] Ghalambaz, M., Hendizadeh, H., Zargartaleb, H., and Pop, I., 2017 “ Free Convection in a Square Cavity Filled With a Tridisperse Porous Medium,” Transp. PorousMedia, 116 (1), pp. 379–392. 10.1007/s11242-016-0779-7 Google Scholar Crossref
[6] Lin, F. C., Liu, B. H., Juan, C. C., and Chen,  Y. M., 2011, “ Effect of Pore Size Distribution in Bidisperse Wick on Heat Transfer in a Loop Heat Pipe,” Heat Mass Transfer, 47 (8), pp. 933–940.10.1007/s00231-011-0841-5, Google Scholar, Crossref
[7] Szczygieł, J., 2006, “ Enhancement of Reforming Efficiency by Optimizing the Porous Structure of Reforming Catalyst: Theoretical Considerations,” Fuel, 85, pp. 1579–1590.10.1016/j.fuel.2005.11.016, Google Scholar, Crossref
[8] Shi, J. Q., and Durucan, S., 2005, “ Gas Storage and Flow in Coalbed Reservoirs: Implementation of a Bidisperse Pore Model for Gas Diffusion in a Coal Matrix,” SPE, Reservoir Eval. Eng., 8(2), pp. 169–175.10.2118/84342-PA Google Scholar Crossref
[9] Nield, D. A., and Kuznetsov, A. V. , 2005, “ Heat Transfer in Bidisperse Porous Media,” Transport in Porous Media, Vol. III, D. B.Ingham, and I.Pop, eds.,
Elsevier, Oxford, UK, pp. 34–59.Google Scholar Crossref
[10] Nield, D. A., and Kuznetsov, A. V. , 2008, “ Natural Convection About a Vertical Plate Embedded in a Bidisperse Porous Medium,” Int. J. Heat Mass Transfer, 51(7–8), pp. 1658–1664.10.1016/j.ijheatmasstransfer.2007.07.011, Google Scholar Crossref
[11] Rees, D. A. S., Nield, D. A., and Kuznetsov, A. V., 2008, “ Vertical Free Convective Boundary-Layer Flow in a Bidisperse Porous Medium,” ASME J. Heat Transfer., 130(9), p. 092601.10.1115/1.2943304, Google Scholar Crossref
[12] Cheng, C.-Y., 2013, “ Natural Convection Heat Transfer From an Inclined Wavy Plate in a Bidisperse Porous Medium,” Int. Commun. Heat Mass Transfer, 43, pp. 69–74. 10.1016/j.icheatmasstransfer.2013.01.001, Google Scholar, Crossref
[13] Cheng, C.-Y., 2015, “ Mixed Convection Heat Transfer From a Vertical Plate Embedded in a Bidisperse Porous Medium,” Proceedings of the World Congress on Engineering 2015 II, S. I. Ao, L.Gelman, D. W. L.Hukins, A.Hunter, and A. M.Korsunsky, eds., Newswood Limite, London, pp. 1330–1335.
[14] Kumari, M , and Pop, I. , 2009, “ Mixed Convection Boundary Layer Flow Past a Horizontal Circular Cylinder Embedded in a Bidisperse Porous Medium,” Transp. Porous Media, 77(2), pp. 287–303.10.1007/s11242-008-9293-x Google Scholar Crossref
[15] Cheng, C.-Y., 2014, “ Nonsimilar Boundary Layer Analysis of Free Convection Heat Transfer Over a Vertical Cylinder in Bidisperse Porous Media,” Transp. Porous Media, 101(3), pp. 401–412.10.1007/s11242-013-0251-x, Google Scholar, Crossref
[16] Kuznetsov, A. V., and Nield, D. A., 2010, “ Forced Convection in a Channel Partly Occupied by a Bidisperse Porous Medium: Asymmetric Case,” Int. J. Heat Mass Transfer, 53(23–24), pp. 5167–5175. 10.1016/j.ijheatmasstransfer.2010.07.046, Google ScholarCrossref
[17] Nield, D. A., and Kuznetsov, A. V., 2011, “ Forced Convection in a Channel Partly Occupied by a Bidisperse Porous Medium: Symmetric Case,” ASME J. Heat Transfer, 133(7), p. 072601. 10.1115/1.4003667, Google Scholar, Crossref
[18] Nield, D. A., and Kuznetsov, A. V., 2013, “ A Note on Modeling High Speed Flow in a Bidisperse Porous Medium,” Transp. Porous Media, 96(3), pp. 495–499.10.1007/s11242-012-0102-1, Google Scholar, Crossref
[19] Magyari, E., 2013, “ Normal Mode Analysis of the High Speed Channel Flow in a Bidisperse Porous Medium,” Transp. Porous Media, 97(3), pp. 345–352.10.1007/s11242-013-0127-0, Google Scholar, Crossref
[20] Revnic, C., Grosan, T., Pop, I., and Ingham, D. B., 2009, “ Free Convection in a Square Cavity Filled With a Bidisperse Porous Medium,” Int. J. Therm. Sci., 48(10), pp.1876–1883.10.1016/j.ijthermalsci.2009.02.016 Google Scholar Crossref
[21] Narashiman, A., and Reddy, B. V. K., 2010, “ Natural Convection Inside a Bidisperse Porous Medium Enclosure,” ASME J. Heat Transfer, 132(1), p. 012502.10.1115/1.3192134, Google Scholar Crossref
[22] Pop, I., Ghalambaz, M., and Sheremet, M., 2016, “ Free Convection in a Square Porous Cavity Filled With a Nanofluid Using Thermal Non Equilibrium and Buongiorno Models,” Int. J. Numer. Methods Heat Fluid Flow, 26(3/4), pp. 671–693.10.1108/HFF-04-2015-0133  Google Scholar Crossref
[23] Zargartalebi, H., Ghalambaz, M., Noghrehabadi, A., and Chamkha, A. J., 2016, “ Natural Convection of a Nanofluid in an Enclosure With an Inclined Local Thermal Non-Equilibrium Porous Fin Considering Buongiorno’s Model,” Numer. Heat Transfer, Part A, 70(4), pp. 432–445.10.1080/10407782.2016.1173483Google Scholar Crossref
[24] Zargartalebi, H., Ghalambaz, M., Sheremet, M., and Pop, I., 2017, “ Unsteady Free Convection in a Square Porous Cavity Saturated With Nanofluid: The Case of Local Thermal Nonequilibrium and Buongiorno’s Mathematical Models,” J. Porous Media, 20(11), pp.999–1016.10.1615/JPorMedia.v20.i11.50 Google Scholar Crossref
[25] Tahmasebi, A., Mahdavi, M., and Ghalambaz, M. , 2018, “ Local Thermal Nonequilibrium Conjugate Natural Convection Heat Transfer of Nanofluids in a CavityPartially Filled With Porous Media Using Buongiorno’s Model,” Numer. Heat Transfer, Part A, 73(4), pp. 254–276.10.1080/10407782.2017.1422632 Google Scholar Crossref
[26] Forchheimer, P. H., 1901, “ Wasserbewegung Durch Boden,” Z. Verein Deutscher Ingenieure, 45, pp. 1782–.27.Brinkman, H. C., 1952, “ The Viscosity of ConcentratedSuspensions and Solutions,” J. Chem. Phys., 20(4), pp. 571–581.10.1063/1.1700493 Google Scholar Crossref
[28] Ergun, S., 1952, “ Fluid Flow Through Packed Columns,” Chem. Eng. Progr., 48, pp. 88–94.
[29]Berghian-Grosan, C., Radu, T., Biris, A. R., D, M., Voica, C. , Watanabe, F., Biris, A. S., and Vulcu, A., 2020, “ Platinum Nanoparticles Coated by Graphene Layers: A Low-Metal Loading Catalyst for Methanol Oxidation in Alkaline Media,” J.Energy Chem., 40, pp. 81–88.10.1016/j.jechem.2019.03.003 Google Scholar Crossref
[30] Noghrehabadi, A. , Behseresht, A. , Ghalambaz, M. , and Behseresht, J. , 2013, “ Natural-Convection Flow of Nanofluids Over Vertical Cone Embedded in non-Darcy Porous Media,” J. Thermophys. Heat Transfer, 27(2), pp. 334–341 10.2514/1.T3965 Google Scholar Crossref
[31] Riley, D. S. , and Rees, D. A. S. , 1985, “ Non-Darcy Natural Convection From Arbitrarily Inclined Heated Surfaces in Saturated Porous Media,” Q. J. Mech. Appl. Math., 38(2), pp. 277–295. 10.1093/qjmam/38.2.277  Google Scholar  Crossref
[32] Rees, D. A. S. , and Pop, I. , 1995, “ Non-Darcy Natural Convection From a Vertical Wavy Surface in a Porous Medium,” Transp. Porous Media, 20(3), pp. 223–234. 10.1007/BF01073173[33] Alazmi, B. , and Vafai, K. , 2002, “ Constant Wall Heat Flux Boundary Conditions in Porous Media Under Local Thermal Non-Equilibrium Conditions,” Int. J. Heat Mass Transfer, 45(15), pp. 3071–3087. 10.1016/S0017-9310(02)00044-3

[34] Kierzenka, J. , and Shampine, L. F. , 2001, “ A BVP Solver Based on Residual Control and MATLAB PSE,” ACM Trans. Math. Software, 27(3), pp. 299–316. 10.1145/502800.502801

[35] Bufnea, D. , Niculescu, V. , Silaghi, G. , and Sterca, A. , 2016, “ Babeş-Bolyai University’s High Performance Computing Center,” Studia Universitatis Babes-Bolyai Informatica, 61, pp. 54–69. https://www.cs.ubbcluj.ro/~bufny/wp-content/uploads/04-BufneaNiculescuSilaghiSterca.pdf

[36] Hooman, K. , Sauret, E. , and Dahari, M. , 2015, “ Theoretical Modelling of Momentum Transfer Function of bi-Disperse Porous Media,” Appl. Therm. Eng., 75, pp. 867–870. 10.1016/j.applthermaleng.2014.10.067

[37] Grosan, T. , Revnic, C. , Pop, I. , and Ingham, D. B. , 2015, “ Free Convection Heat Transfer in a Square Cavity Filled With a Porous Medium Saturated by a Nanofluid,” Int. J. Heat Mass Transfer, 87, pp. 36–41. 10.1016/j.ijheatmasstransfer.2015.03.078

Related Posts