Natural convection in tilted rectangular enclosures with a vertically situated hot plate inside

Abstract A numerical study of laminar natural convection in tilted rectangular enclosures that contain a vertically situated hot plate is performed. The plate is very thin and isothermal on both lateral ends, and it acts as a heat source within the medium. Three surfaces of the rectangular enclosure are insulated while one lateral surface is cold. Navier–Stokes equations, continuity equation and the energy equation, along with the Boussinesq approximation, are expressed in the form of vorticity-transport equations. All the pertinent equations are solved using the finite volume method with SIMPLE algorithm. The Rayleigh numbers and the tilt angle of the enclosure are ranged from 105 to 107 and from 0° to 90°, respectively. The aspect ratios of the rectangular enclosures that are considered in this study are A = 1 and A = 2. The isotherms and streamlines are produced for various Rayleigh numbers and geometrical conditions, and steady-state Nusselt numbers are computed. The steady-state plate-surface-averaged Nusselt numbers are computed for each case as a function of Rayleigh number and other non-dimensional geometrical parameters and a correlation useful for practical problems was derived.

[1]  C. Tso,et al.  Flow pattern evolution in natural convection cooling from an array of discrete heat sources in a rectangular cavity at various orientations , 2004 .

[2]  Frank P. Incropera,et al.  Convection heat transfer in electronic equipment cooling , 1988 .

[3]  F. Penot,et al.  Electronic components cooling by natural convection in horizontal channel with slots , 2005 .

[4]  Theodore J. Heindel,et al.  Laminar Natural Convection in a Discretely Heated Cavity: II—Comparisons of Experimental and Theoretical Results , 1995 .

[5]  Ali Akbar Merrikh,et al.  Natural convection in an enclosure with disconnected and conducting solid blocks , 2005 .

[6]  Kadir Bilen,et al.  A Taguchi approach for investigation of heat transfer from a surface equipped with rectangular blocks , 2001 .

[7]  A. Fichera,et al.  Laminar natural convection in a vertical isothermal channel with symmetric surface-mounted rectangular ribs , 2002 .

[8]  Adrian Bejan,et al.  The Ra-Pr domain of laminar natural convection in an enclosure heated from the side , 1991 .

[9]  Rachid Bessaïh,et al.  Turbulent natural convection cooling of electronic components mounted on a vertical channel , 2000 .

[10]  Majid Keyhani,et al.  On the Natural Convection in a Cavity With a Cooled Top Wall and Multiple Protruding Heaters , 1995 .

[11]  Y. S. Sun,et al.  Effects of wall conduction, internal heat sources and an internal baffle on natural convection heat transfer in a rectangular enclosure , 1997 .

[12]  Y. Jaluria,et al.  Natural convection heat transfer characteristics of a protruding thermal source located on horizontal and vertical surfaces , 1990 .

[13]  Ihsan Dagtekin,et al.  Natural convection heat transfer by heated partitions within enclosure , 2001 .

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

[15]  A. Zebib,et al.  NATURAL CONVECTION AIR COOLING OF HEATED COMPONENTS MOUNTED ON A VERTICAL WALL , 1989 .

[16]  Theodore J. Heindel,et al.  Laminar Natural Convection in a Discretely Heated Cavity: I—Assessment of Three-Dimensional Effects , 1995 .

[17]  Douglas Probert,et al.  Simulation and numerical methods in heat transfer: By A. F. Emery. The American Society of Mechanical Engineers, United Engineering Center, New York. Available from the Institution of Mechanical Engineers, London, 1990. 108 pp. ISBN 0-7918-0697-2. Price: £29.00 , 1992 .