Parallel Darcy–Forchheimer flow in a horizontal porous layer with an isothermal top boundary and a bottom boundary, which is subject to a third kind boundary condition, is discussed by taking into account the effect of viscous dissipation. This effect causes a nonlinear temperature profile within the layer. The linear stability of this nonisothermal base flow is then investigated with respect to the onset of convective rolls. The third kind boundary condition on the bottom boundary plane may imply adiabatic/isothermal conditions on this plane when the Biot number is either zero (adiabatic) or infinite (isothermal). The solution of the linear equations for the perturbation waves is determined by using a fourth order Runge–Kutta scheme in conjunction with a shooting technique. The neutral stability curve and the critical value of the governing parameter are obtained, where Ge is the Gebhart number and Pe is the Péclet number. Different values of the orientation angle between the direction of the basic flow and the propagation axis of the disturbances are also considered.
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e-mail: antonio.barletta@mail.ing.unibo.it
e-mail: michele.celli@mail.ing.unibo.it
e-mail: d.a.s.rees@bath.ac.uk
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Darcy–Forchheimer Flow With Viscous Dissipation in a Horizontal Porous Layer: Onset of Convective Instabilities
A. Barletta,
A. Barletta
Dipartimento di Ingegneria Energetica, Nucleare e del Controllo Ambientale (DIENCA),
e-mail: antonio.barletta@mail.ing.unibo.it
Università di Bologna
, Via dei Colli 16, I-40136 Bologna, Italy
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M. Celli,
M. Celli
Dipartimento di Ingegneria Energetica, Nucleare e del Controllo Ambientale (DIENCA),
e-mail: michele.celli@mail.ing.unibo.it
Università di Bologna
, Via dei Colli 16, I-40136 Bologna, Italy
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D. A. S. Rees
D. A. S. Rees
Department of Mechanical Engineering,
e-mail: d.a.s.rees@bath.ac.uk
University of Bath
, Bath BA2 7AY, UK
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A. Barletta
Dipartimento di Ingegneria Energetica, Nucleare e del Controllo Ambientale (DIENCA),
Università di Bologna
, Via dei Colli 16, I-40136 Bologna, Italye-mail: antonio.barletta@mail.ing.unibo.it
M. Celli
Dipartimento di Ingegneria Energetica, Nucleare e del Controllo Ambientale (DIENCA),
Università di Bologna
, Via dei Colli 16, I-40136 Bologna, Italye-mail: michele.celli@mail.ing.unibo.it
D. A. S. Rees
Department of Mechanical Engineering,
University of Bath
, Bath BA2 7AY, UKe-mail: d.a.s.rees@bath.ac.uk
J. Heat Transfer. Jul 2009, 131(7): 072602 (7 pages)
Published Online: May 14, 2009
Article history
Received:
July 17, 2008
Revised:
October 22, 2008
Published:
May 14, 2009
Citation
Barletta, A., Celli, M., and Rees, D. A. S. (May 14, 2009). "Darcy–Forchheimer Flow With Viscous Dissipation in a Horizontal Porous Layer: Onset of Convective Instabilities." ASME. J. Heat Transfer. July 2009; 131(7): 072602. https://doi.org/10.1115/1.3090815
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