Nonlinear thermal instability in a horizontal porous layer with an internal heat source and mass flow
Tóm tắt
Linear and nonlinear stability analyses of Hadley–Prats flow in a horizontal fluid-saturated porous medium with a heat source are performed. The results indicate that, in the linear case, an increase in the horizontal thermal Rayleigh number is stabilizing for both positive and negative values of mass flow. In the nonlinear case, a destabilizing effect is identified at higher mass flow rates. An increase in the heat source has a destabilizing effect. Qualitative changes appear in R
z
as the mass flow moves from negative to positive for different internal heat sources.
Tài liệu tham khảo
Chen X., Li A.: An experimental study on particle deposition above near-wall heat source. Build. Environ. 81, 139–149 (2014)
Aihara T., Fu W., Shimoyama M.H.T.: Experimental study of heat and mass transfer from a horizontal cylinder in downward air–water mist flow with blockage effect. Exp. Therm. Fluid Sci. 3, 623–631 (1990)
Bendrichi G., Shemilt L.W.: Mass transfer in horizontal flow channels with thermal gradients. Can. J. Chem. Eng. 75, 1067–1074 (1997)
Kwon O., Bae K., Park C.: Cooling characteristics of ground source heat pump with heat exchange methods. Renew. Energy 71, 651–657 (2014)
Schwiderskei W., Schwabh J.A.: Convection experiments with electrolytically heated fluid layers. J. Fluid Mech. 48, 703–719 (1971)
Trittond J., Zarraua M.N.: Convection in horizontal layers with internal heat generation. J. Fluid Mech. 30, 21–31 (1967)
Roberts P.H.: Convection in horizontal layers with internal heat generation: theory. J. Fluid Mech. 30, 33–49 (1967)
Thirlby R.: Convection in an internally heated layer. J. Fluid Mech. 44, 673–693 (1970)
Parthiban C., Patil P.R.: Effect of non-uniform boundary temperatures on thermal instability in a porous medium with internal heat source. Int. Commun. Heat Mass Transf. 22, 683–692 (1995)
Parthiban C., Patil P.R.: Thermal instability in an anisotropic porous medium with internal heat source and inclined temperature gradient. Int. Commun. Heat Mass Transf. 24, 1049–1058 (1997)
Barletta A., Celli M., Nield D.A.: Unstable buoyant flow in an inclined porous layer with an internal heat source. Int. J. Therm. Sci. 79, 176–182 (2014)
Rionero S., Straughan B.: Convection in a porous medium with internal heat source and variable gravity effects. Int. J. Eng. Sci. 28, 497–503 (1990)
Alex, S.M., Patil, P.R.: Effect of a variable gravity field on convection in an anisotropic porous medium with internal heat source and inclined temperature gradient. ASME J. Heat Transf. 124, 144–150 (2002)
Hill A.A.: Double-diffusive convection in a porous medium with a concentration based internal heat source. Proc. R. Soc. A 461, 561–574 (2005)
Chamka A.J., Raheem A., Khaled A.: Similarity solutions for hydromagnetic simultaneous heat and mass transfer by natural convection from an inclined plate with internal heat generation or absorption. J. Heat Mass Transf. 37, 117–123 (2001)
Bhadauria B.S.: Double diffusive convection in a saturated anisotropic porous layer with internal heat source. Transp. Porous Media 92, 299–320 (2012)
Borujerdi A., Noghrehabadi A.R., Rees D.A.S.: Onset of convection in a horizontal porous channel with uniform heat generation using a thermal nonequilibrium model. Transp. Porous Media 69, 343–357 (2007)
Borujerdi A.N., Noghrehabadi A.R., Rees D.A.S.: Influence of Darcy number on the onset of convection in a porous layer with a uniform heat source. Int. J. Therm. Sci. 47, 1020–1025 (2008)
Nield D.A., Bejan A.: Convection in Porous Media. 4th edn. Springer, Berlin (2013)
Capone F., Rionero S.: Nonlinear stability of a convective motion in a porous layer driven by a horizontally temperature gradient, Continuum Mech. Thermodyn. 15, 529–538 (2003)
Guo J., Kaloni P.N.: Nonlinear stability and convection induced by inclined thermal and solutal gradients. Z. Angew. Math. Phys. 46, 645–654 (1995)
Kaloni P.N., Qiao Z.: Non-linear stability of convection in a porous medium with inclined temperature gradient. Int. J. Heat Mass Transf. 40, 1611–1615 (1997)
Kaloni P.N., Qiao Z.: Nonlinear convection induced by inclined thermal and solutal gradients with mass flow. Contin. Mech. Thermodyn. 12, 185–194 (2000)
Kaloni P.N., Qiao Z.: Non-linear convection in a porous medium with inclined temperature gradient and variable gravity effects. Int. J. Heat Mass Transf. 44, 1585–1591 (2001)
Kaloni P.M., Lou J.X.: Nonlinear convection of a viscoelastic fluid with inclined temperature gradient. Contin. Mech. Thermodyn. 17, 17–27 (2005)
Nield D.A.: Convection in a porous medium with inclined temperature gradient: additional result. Int. J. Heat Mass Transf. 37, 3021–3025 (1994)
Weber J.E.: Convection in a porous medium with horizontal and vertical temperature gradients. Int. J. Heat Mass Transf. 17, 241–248 (1974)
Nield D.A.: Convection in a porous medium with inclined temperature gradient and horizontal mass flow. Heat Transf. 5, 153–185 (1990)
Straughan B.: The Energy Method, Stability, and Nonlinear Convection. Springer, New York (2010)