Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls

Hooman, Kamel and Haji-Sheikh, A. (2007) Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls. International Journal of Heat and Mass Transfer, 50 21-22: 4180-4194.

Attached Files (Some files may be inaccessible until you login with your UQ eSpace credentials)
Name Description MIMEType Size Downloads
H2_Draft4.pdf H2_Draft4.pdf application/pdf 221.43KB 464

Author Hooman, Kamel
Haji-Sheikh, A.
Title Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls
Journal name International Journal of Heat and Mass Transfer   Check publisher's open access policy
ISSN 0017-9310
Publication date 2007-10
Sub-type Article (original research)
DOI 10.1016/j.ijheatmasstransfer.2007.02.036
Volume 50
Issue 21-22
Start page 4180
End page 4194
Total pages 15
Editor W. J. Minkowycz
J. P. Harnett
Place of publication Oxford, England
Publisher Pergamon Elsevier
Collection year 2008
Language eng
Subject 290000 Engineering and Technology
290501 Mechanical Engineering
Abstract Heat transfer and entropy generation analysis of the thermally developing forced convection in a porous-saturated duct of rectangular cross-section, with walls maintained at a constant and uniform heat flux, is investigated based on the Brinkman flow model. The classical Galerkin method is used to obtain the fully developed velocity distribution. To solve the thermal energy equation, with the effects of viscous dissipation being included, the Extended Weighted Residuals Method (EWRM) is applied. The local (three dimensional) temperature field is solved by utilizing the Green’s function solution based on the EWRM where symbolic algebra is being used for convenience in presentation. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate, the aspect ratio, the Darcy number, the viscosity ratio, and the Brinkman number. With the velocity and temperature field being determined, the Second Law (of Thermodynamics) aspect of the problem is also investigated. Approximate closed form solutions are also presented for two limiting cases of MDa values. It is observed that decreasing the aspect ratio and MDa values increases the entropy generation rate.
Keyword Thermodynamics
Engineering, Mechanical
Mechanics
porous media
viscous dissipation
extended weighted residuals method
thermal development
rectangular duct
Brinkman-Brinkman problem
entropy generation
Saturated Circular Tube
Greens-function Solution
Viscous Dissipation
Porous Passages
Fluid-flow
Transfer Augmentation
Entrance Region
Cross-section
Temperature
Channel
References [1] D.A. Nield, A. Bejan, Convection in Porous Media, 3rd ed., Springer, New York, 2006. [2] H. I. Ene, E. Sanchez-Palencia, On thermal equation for flow in porous media, Int. J. Engng. Sci. 20 (1982) 623–630. [3] D. A. Nield, Resolution of a paradox involving viscous dissipation and nonlinear drag in a porous medium, Transport Porous Media 41 (2000) 349-357. [4] A. K. Al-Hadhrami, L. Elliot, D. B. Ingham, A new model for viscous dissipation in porous media across a range of permeability values, Transport Porous Media 53 (2003) 117-122. [5] W. P. Breugem, D.A.S. Rees, A derivation of the volume-averaged Boussinesq equations for flow in porous media with viscous dissipation, Transport Porous Media (2006) 63: 1–12. [6] 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. [7] D.A. Nield, A note on a Brinkman-Brinkman forced convection problem, Transport Porous Media 64 (2006) 185–188 [8] D. Bercovici, Generation of plate tectonics from lithosphere–mantle flow and void-volatile self-lubrication, Earth Planetary Science Letters 154 (1998) 139–151. [9] G. P. Celata, G. L. Morini, V. Marconi, S.J. McPhail, G. Zummo, Using viscous heating to determine the friction factor in microchannels - An experimental validation, Experimental Thermal Fluid Sci. 30 (2006) 725-731. [10] Y. Murakami, B. Mikic, Parametric investigation of viscous dissipation effects on optimized air cooling microchanneled heat sinks, Heat Transfer Engng., 24 (2003) 53-62. [11] A. Bejan, Entropy Generation through Heat and Fluid Flow, Wiley, New York, 1982. [12] A.Z. Sahin, Irreversibilities in various duct geometries with constant wall heat flux and laminar flow, Energy 23 (1998) 465-473 [13] E.B. Ratts, A.G. Raut, Entropy generation minimization of fully developed internal flow with constant heat flux, ASME J. Heat Transfer 126 (2004) 656-659. [14] A.C. Baytas, Entropy generation for free and forced convection in a porous cavity and a porous channel, in Emerging Technology and Techniques in Porous Media (Eds. D.B. Ingham et al.), Kluwer Academic Publishers (2004) 259-270. [15] K. Hooman, A. Ejlali, Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature, Int. Comm. Heat Mass Transfer 34 (2007) 408-419. [16] 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. [17] K. Hooman, A. Ejlali, Second law analysis of laminar flow in a channel filled with saturated porous media: a numerical solution, Entropy, 7 (2005) 300-307. [18] A. Haji-Sheikh, K. Vafai, Analysis of flow and heat transfer in porous media imbedded inside various-shaped ducts, Int. J. Heat Mass Transfer 47 (2004) 1889-1905. [19] A. Haji-Sheikh, Fully developed heat transfer to fluid flow in rectangular passages with filled with porous materials, ASME J. Heat Transfer 128 (2006) 822–828. [20] A. Haji-Sheikh, W. J. Minkowycz, E. M. Sparrow, Green’s function solution of temperature field for flow in porous passages, Int. J. Heat Mass Transfer 47 (2004) 4685-4695. [21] A. Haji-Sheikh, D. A. Nield, K. Hooman, Heat transfer in thermal entrance region for flow through rectangular porous passages, Int. J. Heat Mass Transfer 49 (2006) 3004–3015 [22] A. Haji-Sheikh, W. J. Minkowycz, E. M. Sparrow, A numerical study of the heat transfer to fluid flow through circular porous passages, Num. Heat Transfer A 46 (2004) 929-955. [23] 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. [24] K. Hooman, A. Haji-Sheikh, D.A. Nield, Thermally developing Brinkman-Brinkman forced convection in rectangular ducts with isothermal walls, Int. J. Heat Mass Transfer, in press. [25] 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. [26] 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. 28 (2007) 69-78 [27] K. Hooman, Fully developed temperature distribution in porous saturated duct of elliptical cross-section, with viscous dissipation effects and entropy generation analysis, Heat Transfer Research 36 (2005) 237-245. [28] K. Hooman, Analysis of entropy generation in porous media imbedded inside elliptical passages, Int. J. Heat Technology 23 (2005) 145-149. [29] K. Hooman, H. Gurgenci, A.A., Merrikh, Heat transfer and entropy generation optimization of forced convection in a porous-saturated duct of rectangular cross-section, International Journal of Heat and Mass Transfer 50 (2007) 2051-2059. [30] R.K. Shah, A.L. London, Laminar Flow Forced Convection in Ducts (Advances in Heat Transfer, Supplement 1), Academic Press, New York, 1978. [31] L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis, Wiley, New York, 1960. [32] J.V. Beck, K. Cole, A. Haji-Sheikh, B. Litkouhi, Heat Conduction Using Green's Functions, Hemisphere Publ. Corp., Washington D. C., 1992. [33] S. Kakaç, R.K. Shah, W. Aung, Handbook of Single-Phase Convective Heat Transfer, Wiley, New York, 1987. [34] K. Hooman, H. Gurgenci, Effects of viscous dissipation and boundary conditions on forced convection in a channel occupied by a saturated porous medium, Transport in Porous Media (2007), doi:10.1007/s11242-006-9049-4 [35] 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. [36] D. A. Nield, K. Hooman, Comments on “Effects of viscous dissipation on the heat transfer in forced pipe flow. Part 1: both hydrodynamically and thermally fully developed flow, and Part 2: thermally developing flow” by O. Aydin, Energy Conv. Manag., 47 (2006) 3501-3503. [37] 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. 27 (2006) 617-626. [38] A. Haji-Sheikh, Estimation of average and local heat transfer in parallel plates and circular ducts filled with porous materials, ASME J. Heat Transfer 126 (2004) 400-409. [39] A.R.A. Khaled, K. Vafai, Analysis of flow and heat transfer inside nonisothermal squeezed thin films, Numerical Heat Transfer Part A, 47 (10) (2005) 981-996. [40] S. V. Iyer, K. Vafai, Passive heat transfer augmentation in a cylindrical annulus utilizing a porous perturbation, Numerical Heat Transfer Part A, 36 (2) (1999) 115-128. [41] S.S. Mousavi, K. Hooman, Heat and fluid flow in entrance region of a channel with staggered baffles, Energy Conversion and Management, 47 (15-16) (2006) 2011-2019 [42] K. Khanafer, K. Vafai, Double-diffusive mixed convection in a lid-driven enclosure filled with a fluid-saturated porous medium, Numerical Heat Transfer Part A, 42 (5) (2002) 465-486. [43] K. Hooman, A perturbation solution for forced convection in a porous-saturated duct, J. Comput. Appl. Math. (2006), doi: 10.1016/j.cam.2006.11.005 [44] A. Narasimhan, J. L. Lage, Forced convection of a fluid with temperature-dependent viscosity flowing through a porous medium channel, Numerical Heat Transfer Part A, 40 (2001): 801-820. [45] S. C. Chen, K. Vafai, Non-Darcian surface tension effects on free surface transport in porous media Numerical Heat Transfer Part A, 31 (1997) 235-254. [46] P. C. Huang, K. Vafai, Internal heat transfer augmentation in a channel using an alternate set of porous cavity-block obstacles, Numerical Heat Transfer Part A, 25 (1994) 519-539.
Q-Index Code C1
Additional Notes This is an author version of an article originally published as K. Hooman and A. Haji-Sheikh (2007) Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls, International Journal of Heat and Mass Transfer 50 (21-22): 4180-4194. doi: 10.1016/j.ijheatmasstransfer.2007.02.036 Copyright 2007 Elsevier. All rights reserved. Single copies only may be downloaded and printed for a user's personal research and study. -- Available online 3 May 2007.

 
Versions
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 31 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 33 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Access Statistics: 298 Abstract Views, 464 File Downloads  -  Detailed Statistics
Created: Tue, 31 Jul 2007, 17:00:10 EST by Kamel Hooman on behalf of School of Engineering