Effect of viscous dissipation on mixed convection flow of water near its density maximum in a rectangular enclosure with isothermal wall

Purpose – To investigate the effect of viscous dissipation on unsteady, combined convective heat transfer to water near its density maximum in a rectangular cavity.Design/methodology/approach – The upwind finite difference scheme along with successive over relaxation iteration technique is used to solve the governing equations for mixed convection flow of water with density maximum inversion in a rectangular cavity.Findings – The effect of viscous dissipation was to increase the fluid temperature and resulted in the formation of vortex motion near the lower part of the cavity in an opposite direction to the central vortex. An increase in the Eckert number and Reynolds number of the flow resulted in augmented surface heat transfer rates from the top heated surface.Research limitations/implication – The analysis is valid for unsteady, two dimensional laminar flow. Isothermal conditions are assumed for the top and bottom walls. An extension to unsteady three dimensional flow case is left for future work.Prac...

[1]  L. Robillard,et al.  Transient Natural Convection Heat Transfer of Water with Maximum Density Effect and Supercooling , 1981 .

[2]  Robert Schreiber,et al.  Spurious solutions in driven cavity calculations , 1983 .

[3]  D. Rees,et al.  Natural convection flow of water near its density maximum in a rectangular enclosure having isothermal walls with heat generation , 2005 .

[4]  M. K. Moallemi,et al.  Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity , 1992 .

[5]  Joseph C. Mollendorf,et al.  A new density relation for pure and saline water , 1977 .

[6]  Shigeho Noda,et al.  Numerical simulation of natural convection with density inversion in a square cavity , 2000 .

[7]  Hsiao-Tsung Lin,et al.  Similarity solutions for laminar forced convection heat transfer from wedges to fluids of any Prandtl number , 1987 .

[8]  Jae Min Hyun,et al.  Mixed convection in a driven cavity with a stable vertical temperature gradient , 1993 .

[9]  Lionel Alexander Bethune Pilkington,et al.  Review Lecture: The float glass process , 1969, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[10]  Michael Wilson,et al.  Natural convection flow in a fluid-saturated porous medium enclosed by non-isothermal walls with heat generation , 2002 .

[11]  G. Merker,et al.  Onset of convection in a horizontal water layer with maximum density effects , 1979 .

[12]  H. B. Keller,et al.  Driven cavity flows by efficient numerical techniques , 1983 .

[13]  M. Nansteel,et al.  Natural convection heat transfer in a square enclosure containing water near its density maximum , 1987 .

[14]  Ajay K. Prasad,et al.  Combined forced and natural convection heat transfer in a deep lid-driven cavity flow , 1996 .

[15]  S. Fukusako,et al.  Free convective heat transfer with density inversion in a confined rectangular vessel , 1978 .

[16]  J. Koster,et al.  Natural convection of water in a rectangular cavity including density inversion , 1993 .

[17]  A. Watson.  THE EFFECT OF THE INVERSION TEMPERATURE ON THE CONVECTION OF WATER IN AN ENCLOSED RECTANGULAR CAVITY , 1972 .

[18]  M. Morzynski,et al.  LAMINAR HEAT TRANSFER IN A TWO-DIMENSIONAL CAVITY COVERED BY A MOVING WALL , 1988 .

[19]  J. Ferziger,et al.  An adaptive multigrid technique for the incompressible Navier-Stokes equations , 1989 .

[20]  Vishwanath Prasad,et al.  Evaluation of correlations for stagnant thermal conductivity of liquid-saturated porous beds of spheres , 1989 .

[21]  Md. Anwar Hossain,et al.  Natural convection flow of a viscous incompressible fluid in a rectangular porous cavity heated from below with cold sidewalls , 2003 .

[22]  Kenneth E. Torrance,et al.  Cavity flows driven by buoyancy and shear , 1972, Journal of Fluid Mechanics.

[23]  Jörg Imberger,et al.  Dynamics of Lakes, Reservoirs, and Cooling Ponds , 1982 .

[24]  R. Agarwal,et al.  A third-order-accurate upwind scheme for Navier-Stokes solutions at high Reynolds numbers , 1981 .

[25]  Robert L. Street,et al.  The Lid-Driven Cavity Flow: A Synthesis of Qualitative and Quantitative Observations , 1984 .

[26]  D. Moore,et al.  Nonlinear penetrative convection , 1973, Journal of Fluid Mechanics.

[27]  F. Ideriah.  Prediction of Turbulent Cavity Flow Driven by Buoyancy and Shear , 1980 .

[28]  Orhan Aydm.  Aiding and opposing mechanisms of mixed convection in a shear- and buoyancy-driven cavity , 1999 .

[29]  Orhan Aydin,et al.  Aiding and opposing mechanisms of mixed convection in a shear- and buoyancy-driven cavity , 1999 .