Natural convection of nanofluids in a shallow cavity heated from below

This paper reports an analytical and numerical study of natural convection in a shallow rectangular cavity filled with nanofluids. Neumann boundary conditions for temperature are applied to the horizontal walls of the enclosure, while the two vertical ones are assumed insulated. The governing parameters for the problem are the thermal Rayleigh number, Ra, the Prandtl number Pr, the aspect ratio of the cavity, A and the solid volume fraction of nanoparticles, F. For convection in an infinite layer ðA[1Þ, analytical solutions for the stream function and temperature are obtained using a parallel flow approximation in the core region of the cavity and an integral form of the energy equation. The critical Rayleigh number for the onset of supercritical convection of nanofluids is predicted explicitly by the present model. Furthermore, a linear stability analysis of the parallel flow solution is studied and the threshold for Hopf bifurcation is determined. Also, results are obtained from the analytical model for finite amplitude convection for which the flow and heat transfer is presented in terms of the governing parameters of the problem. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations.

[1]  A. Bejan.  Convection Heat Transfer , 1984 .

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

[3]  A. Bejan.  The boundary layer regime in a porous layer with uniform heat flux from the side , 1983 .

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

[5]  Seok Pil Jang,et al.  Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity , 2007 .

[6]  Stephen U. S. Choi,et al.  Free Convection in a Rectangular Cavity (Benard Convection) With Nanofluids , 2004 .

[7]  C. H. Wang,et al.  THE BRINKMAN MODEL FOR NATURAL CONVECTION IN A SHALLOW POROUS CAVITY WITH UNIFORM HEAT FLUX , 1989 .

[8]  G. Peterson,et al.  Experimental Studies of Natural Convection Heat Transfer of Al2O3/DI Water Nanoparticle Suspensions (Nanofluids) , 2010 .

[9]  O. V. Trevisan,et al.  Natural convection with combined heat and mass transfer buoyancy effects in a porous medium , 1985 .

[10]  Stephen U. S. Choi.  Enhancing thermal conductivity of fluids with nano-particles , 1995 .

[11]  C. Chon,et al.  Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement , 2005 .

[12]  I. Catton,et al.  NATURAL CONVECTION IN ENCLOSURES , 1978 .

[13]  M. Hasnaoui,et al.  On numerical stability analysis of double-diffusive convection in confined enclosures , 2001, Journal of Fluid Mechanics.

[14]  W. Roetzel,et al.  Natural convection of nano-fluids , 2003 .

[15]  Niladri Chakraborty,et al.  Study of heat transfer augmentation in a differentially heated square cavity using copper–water nanofluid , 2008 .

[16]  A. Bahloul,et al.  Double-diffusive and Soret-induced convection in a shallow horizontal porous layer , 2003, Journal of Fluid Mechanics.

[17]  A. F. Mills,et al.  Natural convection of microparticle suspensions in thin enclosures , 2008 .

[18]  Ching-Jenq Ho,et al.  Numerical simulation of natural convection of nanofluid in a square enclosure: Effects due to uncertainties of viscosity and thermal conductivity , 2008 .

[19]  O. K. Crosser,et al.  Thermal Conductivity of Heterogeneous Two-Component Systems , 1962 .

[20]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[21]  L. Robillard,et al.  Convection of a binary fluid saturating a shallow porous cavity subjected to cross heat fluxes , 2007, Journal of Fluid Mechanics.

[22]  H. Brinkman.  The Viscosity of Concentrated Suspensions and Solutions , 1952 .

[23]  Ziyad N. Masoud,et al.  Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids , 2008 .

[24]  H. Oztop,et al.  Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids , 2008 .

[25]  Sheng-Chung Tzeng,et al.  Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures , 2006 .

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

[27]  K. Khanafer,et al.  BUOYANCY-DRIVEN HEAT TRANSFER ENHANCEMENT IN A TWO-DIMENSIONAL ENCLOSURE UTILIZING NANOFLUIDS , 2003 .