The thermal entrance region in a plane-parallel channel filled by a fluid saturated porous medium is investigated with reference to steady forced convection and to a thermal boundary condition given by a wall temperature longitudinally varying with a sinusoidal law. The effect of viscous dissipation in the fluid is taken into account, and a two-temperature model is employed in order to evaluate separately the local fluid and solid matrix temperatures. The asymptotic temperature distributions are determined analytically. The governing equations in the thermal entrance region are solved numerically by a finite element method and by the method of lines.
1.
Nield
, D. A.
, Kuznetsov
, A. V.
, and Xiong
, M.
, 2003, “Thermally Developing Forced Convection in a Porous Medium: Parallel Plate Channel With Walls at Uniform Temperature, With Axial Conduction and Viscous Dissipation Effects
,” Int. J. Heat Mass Transfer
0017-9310, 46
, pp. 643
–651
.2.
Kuznetsov
, A. V.
, Xiong
, M.
, and Nield
, D. A.
, 2003, “Thermally Developing Forced Convection in a Porous Medium: Circular Duct With Walls at Constant Temperature, With Longitudinal Conduction and Viscous Dissipation Effects
,” Transp. Porous Media
0169-3913, 53
, pp. 331
–345
.3.
Barletta
, A.
, and Rossi di Schio
, E.
, 2000, “Periodic Forced Convection With Axial Heat Conduction in a Circular Duct
,” Int. J. Heat Mass Transfer
0017-9310, 43
, pp. 2949
–2960
.4.
Zniber
, K.
, Oubarra
, A.
, and Lahjomri
, J.
, 2005, “Analytical Solution to the Problem of Heat Transfer in an MHD Flow Inside a Channel With Prescribed Sinusoidal Wall Heat Flux
,” Energy Convers. Manage.
0196-8904, 46
, pp. 1147
–1163
.5.
Barletta
, A.
, Rossi di Schio
, E.
, Comini
, G.
, and D’Agaro
, P.
, 2008, “Conjugate Forced Convection Heat Transfer in a Plane Channel: Longitudinally Periodic Regime
,” Int. J. Therm. Sci.
1290-0729, 47
, pp. 43
–51
.6.
Barletta
, A.
, Rossi di Schio
, E.
, Comini
, G.
, and D’Agaro
, P.
, 2009, “Wall Coupling Effect in Channel Forced Convection With Streamwise Periodic Boundary Heat Flux Variation
,” Int. J. Therm. Sci.
1290-0729, 48
, pp. 699
–707
.7.
Kuznetsov
, A. V.
, 1998, “Thermal Nonequilibrium Forced Convection in Porous Media
,” Transport Phenomena in Porous Media
, D. B.
Ingham
and I.
Pop
, eds., Pergamon
, New York
.8.
Rees
, D. A. S.
, and Pop
, I.
, 2005, “Local Thermal Non-Equilibrium in Porous Medium Convection
,” Transport Phenomena in Porous Media III
, D. B.
Ingham
and I.
Pop
, eds., Pergamon
, New York
.9.
Celli
, M.
, Rees
, D. A. S.
, and Barletta
, A.
, 2010, “The Effect of Local Thermal Non-Equilibrium on Forced Convection Boundary Layer Flow From a Heated Surface in Porous Media
,” Int. J. Heat Mass Transfer
0017-9310, 53
, pp. 3533
–3539
.10.
Nield
, D. A.
, 2007, “The Modeling of Viscous Dissipation in a Saturated Porous Medium
,” ASME J. Heat Transfer
0022-1481, 129
, pp. 1459
–1463
.11.
Barletta
, A.
, and Magyari
, E.
, 2006, “The Graetz-Brinkman Problem in a Plane-Parallel Channel With Adiabatic-to-Isothermal Entrance
,” Int. Commun. Heat Mass Transfer
0735-1933, 33
, pp. 677
–685
.12.
Shah
, R. K.
, and London
, A. L.
, 1978, “Laminar Flow Convection in Ducts
,” Advances in Heat Transfer
, T. F.
Irvine
and J. P.
Hartnett
, eds., Academic Press
, New York
.13.
Knapp
, R.
, 2008, “A Method of Lines Framework in Mathematica
,” J. Numer. Anal. Ind. Appl. Math. (JNAIAM)
, 3
, pp. 43
–59
.Copyright © 2011
by American Society of Mechanical Engineers
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