Al-Sumaily, G. F., Nakayama, A., Sheridan, J. & Thompson, M. C.
2012
The effect of porous media particle size on forced convection from a circular cylinder without assuming local thermal equilibrium between phases. Intl J. Heat Mass Transfer
55, 3366–3378.

Barletta, A.
2013
Instability of mixed convection in a vertical porous channel with uniform wall heat flux. Phys. Fluids
25, 084108.

Barletta, A.
2016
Instability of stationary two-dimensional mixed convection across a vertical porous layer. Phys. Fluids
28, 014101.

Bera, P. & Khalili, A.
2002
Stability of mixed convection in an anisotropic porous channel. Phys. Fluids
14, 1617–1630.

Bera, P. & Khalili, A.
2006
Influence of Prandtl number on stability of mixed convective flow in a vertical channel filled with a porous medium. Phys. Fluids
18, 124103.

Bera, P. & Khalili, A.
2007
Stability of buoyancy opposed mixed convection in a vertical channel and its dependency on permeability. Adv. Water Resour.
30, 2296–2308.

Bera, P. & Khandelwal, M. K.
2016
A thermal non-equilibrium perspective on instability mechanism of non-isothermal Poiseuille flow in a vertical porous-medium channel. Intl J. Therm. Sci.
105, 159–173.

Bhattacharya, A. & Mahajan, R.
2002
Finned metal foam heat sinks for electronics cooling in forced convection. ASME J. Electron. Packag.
124, 155–163.

Busse, F. H.
2003
The sequence-of-bifurcations approach towards understanding turbulent fluid flow. Surv. Geophys.
24, 269–288.

Calmidi, V. V. & Mahajan, R. L.
2000
Forced convection in high porosity foams. Trans. ASME J. Heat Transfer
122, 557–565.

Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A.
1986
Spectral Method in Fluid Dynamics. Springer.

Chen, Y. C.
2004
Non-Darcy flow stability of mixed convection in a vertical channel filled with a porous medium. Intl J. Heat Mass Transfer
47, 1257–1266.

Chen, Y. C. & Chung, J. N.
1996
The linear stability of mixed convection in a vertical channel. J. Fluid Mech.
325, 29–51.

Chen, Y. C. & Chung, J. N.
1998
Stability of shear flow in a vertical heated channel filled with a porous medium. Proc. Intl Heat Transfer. Conf.
11, 435–440.

Delache, A. & Ouarzazi, M. N.
2008
Weakly nonlinear interaction of mixed convection patterns in porous media heated from below. Intl J. Therm. Sci.
47, 709–722.

Drazin, P. G. & Reid, W. H.
2004
Hydrodynamic Stability. Cambridge University Press.

Dukhan, N.
2013
Metals Foams: Fundamentals and Applications. DEStech Publications.

Gill, A. E.
1969
A proof that convection in a porous vertical slab is stable. J. Fluid Mech.
35, 545–547.

Giorgi, T.
1997
Derivation of the Forchheimer law via matched asymptotic expansions. Trans. Porous Med.
29, 191–206.

Grossmann, S.
2000
The onset of sheer flow turbulence. Rev. Mod. Phys.
72, 603–618.

Hof, B., van Doorne, C. W. H., Westerweel, J., Nieuwstadt, F. T. M., Faisst, H., Eckhardt, B., Wedin, H., Kerswell, R. R. & Waleffe, F.
2004
Experimental observation of nonlinear travelling waves in turbulent pipe flow. Science
305, 1594–1598.

Hof, B., Westerweel, J., Schneider, T. M. & Eckhardt, B.
2006
Finite lifetime of turbulence in shear flows. Nature
443, 59–62.

Hsu, C. T. & Cheng, P.
1990
Thermal dispersion in a porous medium. Intl J. Heat Mass Transfer
33, 1587–1597.

Jin, Y. & Kuznetsov, A. V.
2017
Turbulence modeling for flows in wall bounded porous media: an analysis based on direct numerical simulations. Phys. Fluids
29, 045102.

Kamath, P. M., Balaji, C. & Venkateshan, S. P.
2011
Experimental investigation of flow assisted mixed convection in high porosity foams in vertical channels. Intl J. Heat Mass Transfer
54, 5231–5241.

Khandelwal, M. K. & Bera, P.
2015
Weakly nonlinear stability analysis of non-isothermal Poiseuille flow in a vertical channel. Phys. Fluids
27, 064103.

Kumar, J., Bera, P. & Khalili, A.
2010
Influence of inertia and drag terms on the stability of mixed convection in a vertical porous-medium channel. Intl J. Heat Mass Transfer
53, 5261–5273.

Kurtbas, I. & Celik, N.
2009
Experimental investigation of forced and mixed convection heat transfer in a foam-filled horizontal rectangular channel. Intl J. Heat Mass Transfer
52, 1313–1325.

Lage, J. L.
1998
The fundamental theory of flow through permeable media from Darcy to turbulence. In Transport Phenomena in Porous Media (ed. Ingham, D. B. & Pop, I.), pp. 1–30. Pergamon.

Lefebvre, L. P., Banhart, J. & Dunand, D. C.
2008
Porous metals and metallic foams: current status and recent developments. Adv. Engng Mater.
10, 775–787.

Nasr, K., Ramadhyani, S. & Viskanta, R.
1994
Experimental investigation on forced convection heat transfer from a cylinder embedded in packed bed. Trans. ASME J. Heat Transfer
116, 73–80.

Nield, D. A. & Bejan, A.
2013
Convection in Porous Media. Springer.

Niemela, J. J., Skrbek, L., Sreenivasan, K. R. & Donnelly, R.
2005
Turbulent convection at very high Rayleigh numbers. Nature
404, 837–840.

Orszag, S. A.
1971
Accurate solution of the Orr–Sommerfeld stability equation. J. Fluid Mech.
27, 465–492.

Qin, Y. & Kaloni, P. N.
1993
A nonlinear stability problem of convection in a porous vertical slab. Phys. Fluids A
5, 2067–2069.

Rachedi, R. & Chikh, S.
2001
Enhancement of electronic cooling by insertion of foam materials. Heat Mass Transfer
37, 371–378.

Riahi, N.
1983
Nonlinear convection in a porous layer with finite conducting boundaries. J. Fluid Mech.
129, 153–171.

Rogers, B. B., Moulic, S. G. & Yao, L. S.
1993
Finite-amplitude instability of mixed convection. J. Fluid Mech.
254, 229–250.

Schlichting, H. & Gersten, K.
2004
Boundary Layer Theory, 8th edn. Springer.

Scott, N. L. & Straughan, B.
2013
A nonlinear stability analysis of convection in a porous vertical channel including local thermal nonequilibrium. J. Math. Fluid Mech.
15, 171–178.

Shukla, P. & Alam, M.
2011
Weakly nonlinear theory of shear-banding instability in a granular plane Couette flow: analytical solution, comparison with numerics and bifurcation. J. Fluid Mech.
666, 204–253.

Straus, J. M.
1974
Large amplitude convection in porous media. J. Fluid Mech.
64, 51–63.

Stewartson, K. & Stuart, J. T.
1971
A non-linear instability theory for a wave system in plane Poiseuille flow. J. Fluid Mech.
48, 529–545.

Stuart, J. T.
1958
On the non-linear mechanics of hydrodynamics stability. J. Fluid Mech.
4, 1–21.

Stuart, J. T.
1960
On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. Part 1. The basic behavior in plane-Poiseuille flow. J. Fluid Mech.
9, 353–370.

Suslov, S. A. & Paolucci, S.
1999b
Nonlinear stability of mixed convection flow under non-Boussinesq condition. Part 2. Mean flow characteristics. J. Fluid Mech.
398, 87–108.

Tang, W. H., Wu, Q. H. & Richardson, Z. J.
2002
Equivalent heat circuit based power transformer thermal model. IEE Pros. Electr. Power Appl.
149, 87–92.

Tilton, N. & Cortelezzi, L.
2008
Linear stability analysis of pressure-driven flows in channels with porous walls. J. Fluid Mech.
604, 411–445.

Vafai, K. & Kim, S. J.
1995
On the limitations of the Brinkman–Forchheimer–extended Darcy equation. Intl J. Heat Fluid Flow
16, 11–15.

Vafai, K. & Tien, C. L.
1981
Boundary and inertia effects on flow and heat transfer in porous media. Intl J. Heat Mass Transfer
24, 195–203.

Whitaker, S.
1996
The Forchheimer equation: a theoretical development. Trans. Porous Med.
25, 27–61.

Yao, L. S. & Rogers, B. B.
1992
Finite-amplitude instability of non-isothermal flow in a vertical annulus. Proc. R. Soc Lond. A
437, 267–290.

Zhang, W., Li, W. & Nakayamayao, A.
2015
An analytical consideration of steady-state forced convection within a nanofluid-saturated metal foam. J. Fluid Mech.
769, 590–620.