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.

References

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
.
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