Fully developed and stationary forced convection in a plane-parallel porous channel is analyzed. The boundary walls are modeled as impermeable and subject to external heat transfer. Different Biot numbers are defined at the two boundary planes. It is shown that the combined effects of temperature-dependent viscosity and viscous heating may induce flow instability. The instability takes place at the lowest parametric singularity of the basic flow solution. The linear stability analysis is carried out analytically for the longitudinal modes and numerically for general oblique modes. It is shown that longitudinal modes with vanishingly small wave number are selected at the onset of instability.
Issue Section:
Porous Media
References
1.
Nield
, D. A.
, and Bejan
, A.
, 2013
, Convection in Porous Media
, 4th ed., Springer
, New York
.2.
Barletta
, A.
, 2015
, “On the Thermal Instability Induced by Viscous Dissipation
,” Int. J. Therm. Sci.
, 88
, pp. 238
–247
.3.
Joseph
, D. D.
, 1965
, “Stability of Frictionally-Heated Flow
,” Phys. Fluids
, 8
(12
), pp. 2195
–2200
.4.
Sukanek
, P. C.
, Goldstein
, C. A.
, and Laurence
, R. L.
, 1973
, “The Stability of Plane Couette Flow With Viscous Heating
,” J. Fluid Mech.
, 57
(4
), pp. 651
–670
.5.
Ho
, T. C.
, Denn
, M. M.
, and Anshus
, B. E.
, 1977
, “Stability of Low Reynolds Number Flow With Viscous Heating
,” Rheol. Acta
, 16
(1
), pp. 61
–68
.6.
Yueh
, C. S.
, and Weng
, C. I.
, 1996
, “Linear Stability Analysis of Plane Couette Flow With Viscous Heating
,” Phys. Fluids
, 8
(7
), pp. 1802
–1813
.7.
White
, J. M.
, and Muller
, S. J.
, 2002
, “Experimental Studies on the Stability of Newtonian Taylor–Couette Flow in the Presence of Viscous Heating
,” J. Fluid Mech.
, 462
, pp. 133
–159
.8.
Nouar
, C.
, and Frigaard
, I.
, 2009
, “Stability of Plane Couette–Poiseuille Flow of Shear-Thinning Fluid
,” Phys. Fluids
, 21
(6
), p. 064104
.9.
Barletta
, A.
, Celli
, M.
, and Rees
, D. A. S.
, 2009
, “The Onset of Convection in a Porous Layer Induced by Viscous Dissipation: A Linear Stability Analysis
,” Int. J. Heat Mass Transfer
, 52
(1–2
), pp. 337
–344
.10.
Barletta
, A.
, and Nield
, D. A.
, 2012
, “Variable Viscosity Effects on the Dissipation Instability in a Porous Layer With Horizontal Throughflow
,” Phys. Fluids
, 24
(10
), p. 104102
.11.
Barletta
, A.
, and Celli
, M.
, 2014
, “Onset of Instability Due to Variable Viscosity and Dissipation in a Plane Porous Channel
,” J. Phys.: Conf. Ser.
, 547
, p. 012038
.12.
Çengel
, Y. A.
, 2008
, Introduction to Thermodynamics and Heat Transfer
, 2nd ed., McGraw-Hill
, New York
.13.
Nahme
, R.
, 1940
, “Beiträge zur Hydrodynamischen Theorie der Lagerreibung
,” Arch. Appl. Mech.
, 11
(3
), pp. 191
–209
.Copyright © 2016 by ASME
You do not currently have access to this content.