Natural convection far downstream of a heat source on a solid wall

1998 ◽  
Vol 361 ◽  
pp. 25-39 ◽  
Author(s):  
F. J. HIGUERA ◽  
P. D. WEIDMAN
Keyword(s):  
Natural Convection ◽  
Heat Source ◽  
Numerical Solutions ◽  
Solid Wall ◽  
Nonlinear Eigenvalue Problem ◽  
Vertical Wall ◽  
Heat Sources ◽  
Two Dimensional ◽  
Localized Source ◽  
Self Similar

An analysis is presented of some steady natural convection flows at large distances downstream of point heat sources on solid walls. These asymptotic self-similar flows depend only on the Prandtl number of the fluid. The flow induced by a localized source on an adiabatic wall that is vertical or facing downwards is described numerically, whereas the flow due to a localized source on a wall facing upwards separates and leads to a self-similar plume. When the wall is held at the same temperature as the ambient fluid far from the source, the flow is described by a self-similar solution of the second kind, with the algebraic decay of the temperature excess above the ambient temperature determined by a nonlinear eigenvalue problem. Numerical solutions of this problem are presented for two-dimensional and localized heat sources on a vertical wall, whereas the problem for a localized heat source under an inclined isothermal downwards-facing wall turns out to capture the Rayleigh–Taylor instability of the flow and could not be solved by the methods used in this paper. The analogous flows in fluid-saturated porous media are found to be the solutions of parameter-free problems. A conservation law similar to the one holding for a wall jet is found in the case of a two-dimensional source on an isothermal wall and numerical solutions are presented for the other cases.

Turbulent Natural Convection Flow on a Heated Vertical Wall Immersed in a Stratified Atmosphere

1989 ◽  
Vol 111 (2) ◽  
pp. 378-384 ◽  
Author(s):  
A. K. Kulkarni ◽  
S. L. Chou
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Leading Edge ◽  
Transitional Flow ◽  
Convection Flow ◽  
Ambient Atmosphere ◽  
Ambient Conditions ◽  
Natural Convection Flow ◽  
Turbulent Natural Convection

This paper presents a comprehensive mathematical model and numerical solutions for a natural convection flow over an isothermal, heated, vertical wall immersed in an ambient atmosphere that is thermally stratified. The model assumes a laminar flow near the leading edge, which then becomes a transitional flow, and finally becomes fully turbulent away from the leading edge. Effects of several typical cases of ambient stratification on heat transfer to the wall, peak velocity, and temperature are examined. It is found that the velocity field is affected more significantly by the “memory” of upstream ambient conditions than the temperature field.

Laminar Natural Convection in a Discretely Heated Cavity: I—Assessment of Three-Dimensional Effects

1995 ◽  
Vol 117 (4) ◽  
pp. 902-909 ◽  
Author(s):  
T. J. Heindel ◽  
S. Ramadhyani ◽  
F. P. Incropera
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Nusselt Numbers ◽  
Aspect Ratios ◽  
Laminar Natural Convection

Two and three-dimensional calculations have been performed for laminar natural convection induced by a 3 × 3 array of discrete heat sources flush-mounted to one vertical wall of a rectangular cavity whose opposite wall was isothermally cooled. Edge effects predicted by the three-dimensional model yielded local and average Nusselt numbers that exceeded those obtained from the two-dimensional model, as well as average surface temperatures that were smaller than the two-dimensional predictions. For heater aspect ratios Ahtr ≲ 3, average Nusselt numbers increased with decreasing Ahtr. However, for Ahtr ≳ 3, the two and three-dimensional predictions were within 5 percent of each other and results were approximately independent of Ahtr. In a companion paper (Heindel et al., 1995a), predictions are compared with experimental results and heat transfer correlations are developed.

Natural Convection in Two-Dimensional Horizontal Channel With Heat Sources

2003 ◽  
Author(s):  
Tito Dias ◽  
Luiz Fernando Milanez
Keyword(s):  
Natural Convection ◽  
Flux Ratio ◽  
Horizontal Channel ◽  
Maximum Temperature ◽  
Computational Domain ◽  
Heat Sources ◽  
Two Dimensional ◽  
Temperature Excess ◽  
Fluid Properties ◽  
Laminar Natural Convection

Laminar natural convection in a two-dimensional horizontal channel is very important in laptop design, since optimizing the utilization of the cooler saves energy from the battery. In this work, this configuration has been numerically studied. Three cases were studied according to the position of the heat sources in the lower wall, upper wall and both. The computational domain consisted of two adiabatic walls where the heat sources were positioned, and two open boundaries, where the manometric pressure and normal gradient of velocity were zero. Ambient temperature was prescribed for the entering fluid and zero normal gradient for the exiting fluid. Fluid properties were assumed constant except for the density change with temperature on the buoyancy term. The influence of the modified Rayleigh number, position of the heat sources and heat flux ratio between the sources were analyzed for Prandtl number of 0.7. The maximum temperature excess on the heat source is lower for the case with two heat sources and Ra = 104. This preliminary study showed the existence of a minimum value of the excess temperature for the studies aspect ratio (0.1).

Natural Convection Ventilation in Fully Open Enclosures

2010 ◽  
Author(s):  
Morteza Nateghi ◽  
Steven W. Armfield
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Full Range ◽  
Vertical Wall ◽  
Staggered Grid ◽  
Finite Volume Scheme ◽  
Full Development ◽  
Prandtl Numbers ◽  
Rayleigh Numbers

The present study is concerned with natural convection ventilation in a two dimensional fully open enclosure (cavity) with thermally stratified ambient for both transient and steady-state flow. The left hand vertical wall of the enclosure is heated and the right hand facing boundary is open, with the top and bottom boundaries insulated. The numerical solutions will be obtained by solving the Navier-Stokes equations and the temperature transport equation on a non-staggered grid using an unsteady second-order finite-volume scheme with a pressure correction equation used to simultaneously provide an update for the pressure field and enforce the divergence free condition. Results will be presented for Rayleigh numbers in the range 1 × 105 to 1 × 1010 with Prandtl numbers in the range 0.2 to 1.0. It will be shown that the flow transits from steady to unsteady, at full development, with increasing Rayleigh number for Pr <= 1.0, as observed for the similar closed enclosure flow. For higher Prandtl numbers the flow is steady at full development for the full range of Rayleigh numbers considered, again as for the similar fully closed enclosure. Streamline and temperature contour plots will be presented to illustrate the basic flow behaviours and to demonstrate the effect of the Prandtl number.

Mixed Convection Heat Transfer From Thermal Sources Mounted on Horizontal and Vertical Surfaces

1990 ◽  
Vol 112 (4) ◽  
pp. 975-987 ◽  
Author(s):  
S. S. Tewari ◽  
Y. Jaluria
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Source ◽  
Mixed Convection ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Finite Width ◽  
Heat Sources ◽  
Wide Range ◽  
Thermal Sources

An experimental study is carried out on the fundamental aspects of the conjugate, mixed convective heat transfer from two finite width heat sources, which are of negligible thickness, have a uniform heat flux input at the surface, and are located on a flat plate in the horizontal or the vertical orientation. The heat sources are wide in the transverse direction and, therefore, a two-dimensional flow circumstance is simulated. The mixed convection parameter is varied over a fairly wide range to include the buoyancy-dominated and the mixed convection regimes. The circumstances of pure natural convection are also investigated. The convective mechanisms have been studied in detail by measuring the surface temperatures and determining the heat transfer coefficients for the two heated strips, which represent isolated thermal sources. Experimental results indicate that a stronger upstream heat source causes an increase in the surface temperature of a relatively weaker heat source, located downstream, by reducing its convective heat transfer coefficient. The influence of the upstream source is found to be strongly dependent on the surface orientation, especially in the pure natural convection and the buoyancy dominated regimes. The two heat sources are found to be essentially independent of each other, in terms of thermal effects, at a separation distance of more than about three strip widths for both the orientations. The results obtained are relevant to many engineering applications, such as the cooling of electronic systems, positioning of heating elements in furnaces, and safety considerations in enclosure fires.

Heat Transfer in Discretely Heated Side-Vented Compact Enclosures by Combined Conduction, Natural Convection, and Radiation

1999 ◽  
Vol 121 (4) ◽  
pp. 1002-1010 ◽  
Author(s):  
E. Yu ◽  
Y. K. Joshi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Radiative Heating ◽  
Computational Domain ◽  
Flow Recirculation ◽  
Discrete Heat Source ◽  
Rayleigh Numbers

A three-dimensional investigation of combined conduction, natural convection, and radiation in a side-vented compact enclosure is carried out. The focus of the study is on the enhancement of overall heat transfer through the opening, and the roles of the various modes in achieving it. A discrete heat source, flush-mounted centrally on a vertical substrate, is placed in the enclosure with a single rectangular opening on the opposite vertical wall. Steady-state computations are carried out for Rayleigh numbers, Ra, at 2.6 × 106 and 2.0 × 107. The results show that radiation plays a significant role in the overall heat transfer, and the radiative transport is even more pronounced for lower Ra. It is found that natural convection is weakened by radiation, however, contrary to the existing studies on top vented enclosures, the overall heat transfer is enhanced when radiation is included in the computations. Flow recirculation by radiative heating of enclosure walls is predicted, and is also observed experimentally. Heat spreading in the substrate is found to effect both convection and radiation. The numerical solutions on an extended computational domain are found in good agreement with the experimental data, when the conjugate effects are accounted for.

Two-dimensional viscous gravity currents flowing over a deep porous medium

2001 ◽  
Vol 440 ◽  
pp. 359-380 ◽  
Author(s):  
JAMES M. ACTON ◽  
HERBERT E. HUPPERT ◽  
M. GRAE WORSTER
Keyword(s):  
Porous Medium ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Constant Volume ◽  
Two Dimensional ◽  
Theoretical Predictions ◽  
Self Similar ◽  
Coefficient Of Viscosity ◽  
Good Agreement

The spreading of a two-dimensional, viscous gravity current propagating over and draining into a deep porous substrate is considered both theoretically and experimentally. We first determine analytically the rate of drainage of a one-dimensional layer of fluid into a porous bed and find that the theoretical predictions for the downward rate of migration of the fluid front are in excellent agreement with our laboratory experiments. The experiments suggest a rapid and simple technique for the determination of the permeability of a porous medium. We then combine the relationships for the drainage of liquid from the current through the underlying medium with a formalism for its forward motion driven by the pressure gradient arising from the slope of its free surface. For the situation in which the volume of fluid V fed to the current increases at a rate proportional to t3, where t is the time since its initiation, the shape of the current takes a self-similar form for all time and its length is proportional to t2. When the volume increases less rapidly, in particular for a constant volume, the front of the gravity current comes to rest in finite time as the effects of fluid drainage into the underlying porous medium become dominant. In this case, the runout length is independent of the coefficient of viscosity of the current, which sets the time scale of the motion. We present numerical solutions of the governing partial differential equations for the constant-volume case and find good agreement with our experimental data obtained from the flow of glycerine over a deep layer of spherical beads in air.

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