The aim of this study is the analysis of the onset conditions for the thermal instability in a fluid saturated porous medium. The investigation refers to an infinitely wide horizontal porous layer with vertical heterogeneity, such that the lower plane boundary is impermeable and thermally insulated (adiabatic). The temperature distribution on the upper plane boundary is assumed to be prescribed and linearly varying in the horizontal direction. It is shown that these boundary conditions are compatible with a buoyancy-induced parallel-flow solution such that the temperature gradient is inclined with respect to the vertical direction. The basic parallel flow is perturbed by small–amplitude roll disturbances, so that a linear analysis of the neutral stability is carried out. The local balance equations for the disturbances are solved numerically. The critical conditions for the onset of convection are determined.
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Heterogeneity and Onset of Instability in Darcy’s Flow With a Prescribed Horizontal Temperature Gradient
A. Barletta,
A. Barletta
DIENCA, Alma Mater Studiorum—Università di Bologna
, Viale Risorgimento 2, 40136 Bologna, Italy
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M. Celli,
M. Celli
DIENCA, Alma Mater Studiorum—Università di Bologna
, Viale Risorgimento 2, 40136 Bologna, Italy
; Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695
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A. V. Kuznetsov
A. V. Kuznetsov
Department of Mechanical and Aerospace Engineering, North Carolina State University
, Raleigh, NC 27695
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A. Barletta
DIENCA, Alma Mater Studiorum—Università di Bologna
, Viale Risorgimento 2, 40136 Bologna, Italy
M. Celli
DIENCA, Alma Mater Studiorum—Università di Bologna
, Viale Risorgimento 2, 40136 Bologna, Italy
; Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695
A. V. Kuznetsov
Department of Mechanical and Aerospace Engineering, North Carolina State University
, Raleigh, NC 27695 J. Heat Transfer. Apr 2012, 134(4): 042602 (8 pages)
Published Online: February 13, 2012
Article history
Received:
June 14, 2011
Revised:
August 29, 2011
Online:
February 13, 2012
Published:
February 13, 2012
Citation
Barletta, A., Celli, M., and Kuznetsov, A. V. (February 13, 2012). "Heterogeneity and Onset of Instability in Darcy’s Flow With a Prescribed Horizontal Temperature Gradient." ASME. J. Heat Transfer. April 2012; 134(4): 042602. https://doi.org/10.1115/1.4005112
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