Natural convection of power law fluids in inclined cavities

Abstract Steady two-dimensional natural convection in rectangular two-dimensional cavities filled with non-Newtonian power law-Boussinesq fluids is numerically investigated. The conservation equations of mass, momentum and energy are solved using the finite volume method for varying inclination angles between 0° and 90° and two cavity height based Rayleigh numbers, Ra = 104 and 105, a Prandtl number of Pr = 102 and three cavity aspect ratios of 1, 4 and 8. For the vertical inclination of 90°, computations were performed for two Rayleigh numbers Ra = 104 and 105 and three Prandtl numbers of Pr = 102, 103 and 104. In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side walls and the inclination angle is varied. A comprehensive comparison between the Newtonian and the non-Newtonian cases is presented based on the dependence of the average Nusselt number N u ¯ on the angle of inclination together with the Rayleigh number, Prandtl number, power law index n and aspect ratio dependent flow configurations which undergo several exchange of stability as the angle of inclination ɸ is gradually increased from the horizontal resulting in a rather sudden drop in the heat transfer rate triggered by the last loss of stability and transition to a single cell configuration. A correlation relating N u ¯ to the power law index n for vertically heated cavities for the range 104 ≤ Ra ≤ 105 and 102 ≤ Pr ≤ 104 and valid for aspect ratios 4 ≤ AR ≤ 8 is given.

[1]  Abdul Jabbar N. Khalifa.  Natural convective heat transfer coefficient – a review: II. Surfaces in two- and three-dimensional enclosures , 2001 .

[2]  Frank P. Incropera,et al.  Fundamentals of Heat and Mass Transfer , 1981 .

[3]  E. Obata,et al.  A NUMERICAL STUDY ON NATURAL CONVECTIVE HEAT TRANSFER OF PSEUDOPLASTIC FLUIDS IN A SQUARE CAVITY , 2002 .

[4]  Massimo Corcione,et al.  Effects of the thermal boundary conditions at the sidewalls upon natural convection in rectangular enclosures heated from below and cooled from above , 2003 .

[5]  W. Minkowycz,et al.  Natural convection in a porous cavity saturated with a non-Newtonian fluid , 1996 .

[6]  J. Hartnett,et al.  Natural convection in power-law fluids , 1986 .

[7]  J. F. Richardson,et al.  An experimental study of heat transfer by laminar natural convection between an electrically-heated vertical plate and both Newtonian and non-Newtonian fluids , 1999 .

[8]  M. Hasnaoui,et al.  Natural Convection in a Tilted Rectangular Slot Containing Non-Newtonian Power-Law Fluids and Subject to a Longitudinal Thermal Gradient , 2006 .

[9]  T. Chi,et al.  Thermal instability of a horizontal layer of non-Newtonian fluid heated from below , 1969 .

[10]  Chuanshan Dai,et al.  Natural convection heat transfer of microemulsion phase-change-material slurry in rectangular cavities heated from below and cooled from above , 2003 .

[11]  Jae Min Hyun,et al.  Transient buoyant convection of a power-law non-Newtonian fluid in an enclosure , 2003 .

[12]  D. Edwards,et al.  Experimental Investigation of Natural Convection in Inclined Rectangular Regions of Differing Aspect Ratios , 1976 .

[13]  A. Emery,et al.  The Free Convection of Heat from a Vertical Plate to Several Non-Newtonian “Pseudoplastic” Fluids , 1972 .

[14]  Bahgat Sammakia,et al.  Buoyancy-Induced Flows and Transport , 1988 .

[15]  M. Hamed,et al.  Flow mode-transition of natural convection in inclined rectangular enclosures subjected to bidirectional temperature gradients , 2006 .

[16]  Stuart W. Churchill,et al.  NATURAL CONVECTION IN AN INCLINED SQUARE CHANNEL , 1974 .

[17]  Portonovo S. Ayyaswamy,et al.  Natural convection flow in a finite, rectangular slot arbitrarily oriented with respect to the gravity vector , 1974 .

[18]  Andreas Acrivos,et al.  A theoretical analysis of laminar natural convection heat transfer to non‐Newtonian fluids , 1960 .

[19]  Simon Ostrach,et al.  Natural convection in enclosures , 1988 .

[20]  Hiroyuki Ozoe,et al.  Hydrodynamic stability and natural convection in Ostwald‐de Waele and Ellis fluids: The development of a numerical solution , 1972 .

[21]  A. Emery,et al.  Free Convection Through Vertical Plane Layers of Non-Newtonian Power Law Fluids , 1971 .

[22]  D. Siginer,et al.  Natural convection in inclined two dimensional rectangular cavities , 2012 .

[23]  Hayatoshi Sayama,et al.  NATURAL CONVECTION IN AN INCLINED RECTANGULAR CHANNEL AT VARIOUS ASPECT RATIOS AND ANGLES-EXPERIMENTAL MEASUREMENTS , 1975 .

[24]  C. Y. Soong,et al.  Numerical study on mode-transition of natural convection in differentially heated inclined enclosures , 1996 .