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A perturbation solution for forced convection in a porous saturated duct
Hooman, Kamel (2008) A perturbation solution for forced convection in a porous saturated duct. Journal of Computational and Applied Mathematics, 211 1: 57-66.
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Attached Files
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Matchede-PPC.pdf
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Matchede-PPC.pdf
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application/pdf
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120.99KB
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506
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| Author
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Hooman, Kamel
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| Title
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A perturbation solution for forced convection in a porous saturated duct
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| Journal name
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Journal of Computational and Applied Mathematics (ERA 2012 Listed) (ERA 2010 Rank A) Check publisher's open access policy
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| Publication date
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2008-01-15
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| Sub-type
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Article
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| Year available
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2006
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| DOI
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10.1016/j.cam.2006.11.005
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| Volume number
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211
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| Issue number
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1
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| ISSN
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0377-0427
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| Start page
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57
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| End page
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66
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| Total pages
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10
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| Editor
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M. J. Goovaerts
S. C. Brenner
T. Mitsui
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| Place of publication
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Dordrecht, The Netherlands
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| Publisher
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Elsevier
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| Language
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eng
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| Subject
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230100 Mathematics
230116 Numerical Analysis
290000 Engineering and Technology
0913 Mechanical Engineering
C1
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| Abstract
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Fully developed forced convection through a porous medium bounded by two isoflux parallel plates is investigated analytically on the basis of a Brinkman-Forchheimer model. The matched asymptotic expansion method is applied for small values of the Darcy number. For the case of large Darcy number the solution for the Brinkman-Forchheimer momentum equation is found in terms of an asymptotic expansion. With the velocity distribution determined, the energy equation is solved using the same asymptotic technique. The results for limiting cases are found to be in good agreement with those available in the literature and the numerical results obtained here.
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| Keyword
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Forced convection
Porous media
Pipe flow
Brinkman-Forchheimer model
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| References
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[1] D. A. Nield, The boundary condition for the Rayleigh-Darcy problem: limitation of the Brinkman equation, J. Fluid Mech. 128 (1983) 37-40. [2] D. A. Nield, A. Bejan, Convection in Porous Media, 3rd ed., Springer, New York, 2006. [3] D. A. Nield, S. L. M. Junqueira, J. L. Lage, Forced convection in a fluid-saturated porous-medium channel with isothermal or isoflux boundaries, J. Fluid Mech. 322 (1996) 201-214. [4] K. Vafai, S. J. Kim, Forced convection in a channel filled with porous medium: an exact solution, ASME J. Heat Transfer 111 (1989) 1103-1106. [5] V. V. Calmidi, R. L. Mahajan, Forced convection in high porosity metal foams, ASME J. Heat Transfer 122(2000) 557-565. [6] M. Kaviany, Laminar flow through a porous channel bounded by isothermal parallel plates, Int. J. Heat Mass Transfer 28 (1985) 851-858. [7] A. H. Nayfeh, Problems in Perturbation, 2nd ed., Wiley, New York, 1993. [8] R. K. Shah, A. L. London, Laminar Flow Forced Convection in Ducts (Advances in Heat Transfer, Supplement 1), Academic press, New York, (1978). [9] K. Hooman, A. A. Ranjbar-Kani, A perturbation based analysis to investigate forced convection in a porous saturated tube, J. Comput. Appl. Math. 162 (2004) 411-419. [10] A. A. Merrikh, A. A. Mohamad, Non-Darcy effects in buoyancy driven flows in an enclosure filled with vertically layered porous media, Int. J. Heat Mass Transfer 45 (2002) 4305–4313. [11] D. A. Nield, Modelling fluid flow in saturated porous media and at interfaces, in Transport Phenomena in Porous Media II (D. B. Ingham and I. Pop, eds.), Elsevier Science, Oxford, 2002. [12] A. W. Bush, Perturbation Methods for Engineers and Scientists, CRC Press, 1992. [13] K. Hooman, A. A. Ranjbar-Kani, Forced convection in a fluid-saturated porous–medium tube with isoflux wall, Int. Comm. Heat Mass Transfer 30 (2003) 1015-1026. [14] K. Hooman, A. Pourshaghaghy, A. Ejlali, Effects of viscous dissipation on thermally developing forced convection in a porous saturated circular tube with an isoflux wall, Appl. Math. Mech. - English edition 27 (2006) 617-626. [15] K. Hooman, A. A. Merrikh, Analytical Solution of Forced Convection in a Duct of Rectangular Cross Section Saturated by a Porous Medium, ASME J. Heat Transfer 128 (2006) 596-600. [16] D. A. Nield, A. V. Kuznetsov, M. Xiong, Effects of viscous dissipation and flow work on forced convection in a channel filled by a saturated porous medium, Transport Porous Media 56 (2004) 351-367. [17] D.A. Nield, A.V. Kuznetsov, Forced convection in porous media: transverse heterogeneity effects and thermal development, in Handbook of Porous Media (K. Vafai, ed.), 2nd ed., Taylor and Francis, New York, 2005, pp. 143-193. [18] A. Haji-Sheikh, D.A. Nield, K. Hooman, Heat transfer in the thermal entrance region for flow through rectangular porous passages, Int. J. Heat Mass Transfer 49 (2006) 3004–3015. [19] K. Hooman, H. Gurgenci, Effects of viscous dissipation and boundary conditions on forced convection in a channel occupied by a saturated porous medium, Transport Porous Media, in press. [20] A. Haji-Sheikh, E.M. Sparrow, W.J. Minkowycz, Heat transfer to flow through porous passages using extended weighted residuals method–A Green’s function solution, Int. J. Heat Mass Transfer 48 (2005) 1330-1349. [21] K. Hooman, M. Gorji-Bandpy, Laminar dissipative flow in a porous channel bounded by isothermal parallel plates, Appl. Math. Mech. - English edition 26 (2005) 578-593. [22] K. Hooman, Entropy-energy analysis of forced convection in a porous-saturated circular tube considering temperature-dependent viscosity effects, Int. J. Exergy 3 (2006) 436–451. [23] K. Hooman, H. Gurgenci, Effects of temperature-dependent viscosity variation on entropy generation, heat, and fluid flow through a porous-saturated duct of rectangular cross-section, Appl. Math. Mech. - English edition, in press. [24] D. A. Nield, A. V. Kuznetsov, Effect of heterogeneity in forced convection in a porous medium: parallel plate channel or circular duct, Int. J. Heat Mass Transfer 43, (2000), 4119-4134
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| Q-Index Code
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C1
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| Additional Notes
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Available online 18 December 2006.
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