Boundary and internal heat source effects on the onset of Darcy–Brinkman convection in a porous layer saturated by nanofluid

Abstract The effect of internal heat source on the onset of Darcy–Brinkman convection in a porous layer saturated by nanofluid is studied. The boundaries are considered to be free–free, rigid–rigid and lower-rigid and upper-free boundaries. The Brinkman–Darcy equation with fluid viscosity different from effective viscosity is used to characteristic the nanofluid motion. The model used for nanofluid includes the effects of Brownian motion and thermophoresis. The linear stability theory is employed and the resulting eigenvalue problem is solved numerically using the Galerkin technique with the Rayleigh number as the eigenvalue. The influence of internal heat source strength, nanoparticle Rayleigh number, modified particle-density increment, modified diffusivity ratio, Lewis number, Darcy number and the porosity on the stability of the system is investigated graphically. It is found that the internal heat source, nanoparticle Rayleigh number, modified diffusivity ratio and Lewis number have a destabilizing effect while Darcy number and the porosity show stabilizing effects on the system.

[1]  Abdoul R. Ghotbi,et al.  On the analytical solution for MHD natural convection flow and heat generation fluid in porous medium , 2009 .

[2]  Y. Takeda,et al.  Experimental investigation of natural convection induced by internal heat generation , 2005 .

[3]  A. Kuznetsov,et al.  The Effect of Local Thermal Nonequilibrium on the Onset of Convection in a Nanofluid , 2010 .

[4]  A. Kuznetsov,et al.  Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: Brinkman Model , 2010 .

[5]  Dhananjay,et al.  Effect of Internal Heat Source on the Onset of Convection in a Nanofluid Layer , 2011 .

[6]  Ephraim M Sparrow,et al.  Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile , 1964, Journal of Fluid Mechanics.

[7]  D. Tritton.  Internally heated convection in the atmosphere of Venus and in the laboratory , 1975, Nature.

[8]  A. Kuznetsov,et al.  The onset of double-diffusive convection in a nanofluid layer , 2011 .

[9]  A. Kuznetsov,et al.  The Onset of Double-Diffusive Nanofluid Convection in a Layer of a Saturated Porous Medium , 2010 .

[10]  A. Kuznetsov,et al.  THE EFFECT OF LOCAL THERMALNONEQUILIBRIUM ON THE ONSET OF CONVECTION IN A POROUS MEDIUM LAYER SATURATED BY A NANOFLUID: BRINKMAN MODEL , 2011 .

[11]  R. Bhargava.  RAYLEIGH-BÉNARD CONVECTION IN NANOFLUID , 2011 .

[12]  S. Agarwal,et al.  Convective Transport in a Nanofluid Saturated Porous Layer With Thermal Non Equilibrium Model , 2011 .

[13]  Seok Pil Jang,et al.  Flow and convective heat transfer characteristics of water-based Al2O3 nanofluids in fully developed laminar flow regime , 2009 .

[14]  D. Tzou.  Thermal instability of nanofluids in natural convection , 2008 .

[15]  Da Yu Tzou,et al.  Instability of Nanofluids in Natural Convection , 2008 .

[16]  A. Noghrehabadi,et al.  Influence of Darcy number on the onset of convection in a porous layer with a uniform heat source , 2008 .

[17]  M. El-Hakiem.  Natural Convection in a Micropolar Fluid with Thermal Dispersion and Internal Heat Generation , 2004 .

[18]  A. Khalili,et al.  Onset of convection in a porous layer with net through-flow and internal heat generation , 1998 .

[19]  Donald A. Nield,et al.  Thermal instability in a porous medium layer saturated by a nanofluid , 2009 .

[20]  Yasushi Takeda,et al.  Effects of heat source distribution on natural convection induced by internal heating , 2005 .

[21]  W. Roetzel,et al.  TEMPERATURE DEPENDENCE OF THERMAL CONDUCTIVITY ENHANCEMENT FOR NANOFLUIDS , 2003 .

[22]  J. Buongiorno.  Convective Transport in Nanofluids , 2006 .

[23]  A. Kuznetsov,et al.  The Effect of Vertical Throughflow on Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid , 2011 .

[24]  Young I Cho,et al.  HYDRODYNAMIC AND HEAT TRANSFER STUDY OF DISPERSED FLUIDS WITH SUBMICRON METALLIC OXIDE PARTICLES , 1998 .

[25]  William W. Yu,et al.  ANOMALOUSLY INCREASED EFFECTIVE THERMAL CONDUCTIVITIES OF ETHYLENE GLYCOL-BASED NANOFLUIDS CONTAINING COPPER NANOPARTICLES , 2001 .

[26]  G. Domairry,et al.  Analytical solution of non-Newtonian micropolar fluid flow with uniform suction/blowing and heat generation , 2009 .

[27]  A. Kuznetsov,et al.  Effect of Local Thermal Non-equilibrium on the Onset of Convection in a Porous Medium Layer Saturated by a Nanofluid , 2010 .

[28]  A. Kuznetsov,et al.  The onset of convection in a horizontal nanofluid layer of finite depth , 2010 .

[29]  K. Rajagopal,et al.  On the Oberbeck–Boussinesq approximation for fluids with pressure dependent viscosities , 2009 .

[30]  H. May.  A numerical study on natural convection in an inclined square enclosure containing internal heat sources , 1991 .

[31]  A. Solomon,et al.  Thermal Performance of cylindrical Heat Pipe Using Nanofluids , 2010 .

[32]  S. Phillpot,et al.  Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids) , 2002 .

[33]  E. Abu-Nada.  Rayleigh-Bénard convection in nanofluids: Effect of temperature dependent properties , 2011 .

[34]  S. Agarwal,et al.  Natural Convection in a Nanofluid Saturated Rotating Porous Layer: A Nonlinear Study , 2011 .

[35]  Marcelo Reggio,et al.  Natural convection of nanofluids in a shallow cavity heated from below , 2011 .

[36]  C. T. Nguyen,et al.  New temperature dependent thermal conductivity data for water-based nanofluids , 2009 .

[37]  M. Yaghoubi,et al.  Combined thermophoresis, Brownian motion and Dufour effects on natural convection of nanofluids , 2011 .

[38]  I. Shivakumara,et al.  Effects of throughflow and internal heat generation on the onset of convection in a fluid layer , 2000 .

[39]  Y. Xuan,et al.  Investigation on Convective Heat Transfer and Flow Features of Nanofluids , 2003 .

[40]  C. Choi,et al.  Analysis of convective instability and heat transfer characteristics of nanofluids , 2004 .

[41]  N. Weiss,et al.  Convection in the earth's mantle: towards a numerical simulation , 1974, Journal of Fluid Mechanics.

[42]  Sarit K. Das,et al.  Onset of natural convection in a rotating fluid layer with non-uniform volumetric heat sources , 2008 .

[43]  Jinho Lee,et al.  Effect of internal heat generation on the onset of Brinkman–Benard convection in a ferrofluid saturated porous layer , 2011 .

[44]  K. Chiang,et al.  Stability analysis of Benard-Marangoni convection in fluids with internal heat generation , 1994 .

[45]  R. Bhargava,et al.  Thermal instability of rotating nanofluid layer , 2011 .

[46]  B. W. Webb,et al.  Natural convection from two-dimensional discrete heat sources in a rectangular enclosure , 1991 .

[47]  H. Masuda,et al.  ALTERATION OF THERMAL CONDUCTIVITY AND VISCOSITY OF LIQUID BY DISPERSING ULTRA-FINE PARTICLES. DISPERSION OF AL2O3, SIO2 AND TIO2 ULTRA-FINE PARTICLES , 1993 .