Experiments on Transient Thermal Convection With Internal Heating—Large Time Results

1983 ◽  
Vol 105 (2) ◽  
pp. 261-266 ◽  
Author(s):  
M. Keyhani ◽  
F. A. Kulacki
Keyword(s):  
Boundary Layer ◽  
Thermal Convection ◽  
Lower Boundary ◽  
Horizontal Layer ◽  
Step Change ◽  
Boundary Layer Theory ◽  
Approximate Theory ◽  
Fourier Number ◽  
Final State ◽  
Volumetric Heating

Experimental data and correlations are presented for the time scales of developing and decaying thermal convection with volumetric heating in a horizontal layer. The layer is bounded by rigid surfaces, with an insulated lower boundary and an isothermal upper boundary. The time for complete flow development/decay, as a result of a step change in volumetric heat generation, is simply parameterized in terms of the Fourier number for the layer, the step change in Rayleigh number, ΔRa, and the initial/final dimensionless maximum core temperature. For developing flows, ΔRa > 0, results are in good agreement with existing experiments and an approximate boundary layer theory. In decaying flows, Fourier numbers are larger than those of previously reported experiments for a motionless final state. Data for turbulent-to-turbulent transitions when ΔRa < 0 suggests that the approximate boundary layer theory underestimates the Fourier number. Experimental uncertainties on measured Fourier numbers are generally well within the limits of uncertainty allowed by the approximate theory.

Thermal Convection in Porous Media at High Rayleigh Numbers

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Daniel J. Keene ◽  
R. J. Goldstein
Keyword(s):  
Boundary Layer ◽  
Porous Media ◽  
Thermal Convection ◽  
Thermal Boundary Layer ◽  
Packed Bed ◽  
Horizontal Layer ◽  
Homogeneous Fluid ◽  
Fluid Systems ◽  
Dimensionless Groups ◽  
Rayleigh Numbers

An experimental study of thermal convection in a porous medium investigates the heat transfer across a horizontal layer heated from below at high Rayleigh number. Using a packed bed of polypropylene spheres in a cubic enclosure saturated with compressed argon, the pressure was varied between 5.6 bar and 77 bar to obtain fluid Rayleigh numbers between 1.68 × 109 and 3.86 × 1011, corresponding to Rayleigh–Darcy numbers between 7.47 × 103 and 2.03 × 106. From the present and earlier studies of Rayleigh–Benard convection in both porous media and homogeneous fluid systems, the existence and importance of a thin thermal boundary layer are clearly demonstrated. In addition to identifying the governing role of the thermal boundary layer at high Rayleigh numbers, the successful correlation of data using homogeneous fluid dimensionless groups when the thermal boundary layer thickness becomes smaller than the length scale associated with the pore features is shown.

Correlation Equations for Turbulent Thermal Convection in a Horizontal Fluid Layer Heated Internally and from Below

1978 ◽  
Vol 100 (3) ◽  
pp. 416-422 ◽  
Author(s):  
F. B. Cheung
Keyword(s):  
Boundary Layer ◽  
Thermal Convection ◽  
Fluid Layer ◽  
Lower Surface ◽  
Rate Variation ◽  
Correlation Equations ◽  
Volumetric Heating ◽  
Local Boundary ◽  
Simple Boundary ◽  
Horizontal Fluid Layer

High Rayleigh number thermal convection in a horizontal fluid layer with uniform volumetric energy sources and a constant rate of bottom heating is studied analytically by a simple boundary layer approach. Heat transfer characteristics of the layer are defined in terms of local boundary-layer variables. Correlation equations are derived for the upper and the lower surface Nusselt numbers as functions of two independent Rayleigh numbers, based respectively on the surface to surface temperature difference and the volumetric heating rate. Variation of the turbulent core temperature, which so far has not been determined successfully by existing analytical methods, is obtained. This is found to depend on a single dimensionless parameter which measures the relative rates of internal and external heating. Results of this study are presented with available experimental data.

scholarly journals The global characteristics of the three-dimensional thermal convection inside a spherical shell

1997 ◽  
Vol 4 (1) ◽  
pp. 19-27 ◽  
Author(s):  
J. Arkani-Hamed
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Spherical Shell ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Horizontal Layer ◽  
Boundary Layer Theory ◽  
Physical Parameters ◽  
Rayleigh Numbers

Abstract. The Rayleigh number-Nusselt number, and the Rayleigh number-thermal boundary layer thickness relationships are determined for the three-dimensional convection in a spherical shell of constant physical parameters. Several models are considered with Rayleigh numbers ranging from 1.1 x 102 to 2.1 x 105 times the critical Rayleigh number. At lower Rayleigh numbers the Nusselt number of the three-dimensional convection is greater than that predicted from the boundary layer theory of a horizontal layer but agrees well with the results of an axisymmetric convection in a spherical shell. At high Rayleigh numbers of about 105 times the critical value, which are the characteristics of the mantle convection in terrestrial planets, the Nusselt number of the three-dimensional convection is in good agreement with that of the boundary layer theory. At even higher Rayleigh numbers, the Nusselt number of the three-dimensional convection becomes less than those obtained from the boundary layer theory. The thicknesses of the thermal boundary layers of the spherical shell are not identical, unlike those of the horizontal layer. The inner thermal boundary is thinner than the outer one, by about 30- 40%. Also, the temperature drop across the inner boundary layer is greater than that across the outer boundary layer.

scholarly journals Plume generation in natural thermal convection at high Rayleigh and Prandtl numbers

2001 ◽  
Vol 434 ◽  
pp. 1-21 ◽  
Author(s):  
C. LITHGOW-BERTELLONI ◽  
M. A. RICHARDS ◽  
C. P. CONRAD ◽  
R. W. GRIFFITHS
Keyword(s):  
Boundary Layer ◽  
Thermal Convection ◽  
Large Scale ◽  
Lower Boundary ◽  
Secular Change ◽  
Scaling Analysis ◽  
Temperature Dependent Viscosity ◽  
Earth’S Mantle ◽  
Dependent Viscosity ◽  
Rayleigh Numbers

We study natural thermal convection of a fluid (corn syrup) with a large Prandtl number (103–107) and temperature-dependent viscosity. The experimental tank (1 × 1 × 0.3m) is heated from below with insulating top and side boundaries, so that the fluid experiences secular heating as experiments proceed. This setup allows a focused study of thermal plumes from the bottom boundary layer over a range of Rayleigh numbers relevant to convective plumes in the deep interior of the Earth's mantle. The effective value of Ra, based on the viscosity of the fluid at the interior temperature, varies from 105 at the beginning to almost 108 toward the end of the experiments. Thermals (plumes) from the lower boundary layer are trailed by continuous conduits with long residence times. Plumes dominate flow in the tank, although there is a weaker large-scale circulation induced by material cooling at the imperfectly insulating top and sidewalls. At large Ra convection is extremely time-dependent and exhibits episodic bursts of plumes, separated by periods of quiescence. This bursting behaviour probably results from the inability of the structure of the thermal boundary layer and its instabilities to keep pace with the rate of secular change in the value of Ra. The frequency of plumes increases and their size decreases with increasing Ra, and we characterize these changes via in situ thermocouple measurements, shadowgraph videos, and videos of liquid crystal films recorded during several experiments. A scaling analysis predicts observed changes in plume head and tail radii with increasing Ra. Since inertial effects are largely absent no transition to ‘hard’ thermal turbulence is observed, in contrast to a previous conclusion from numerical calculations at similar Rayleigh numbers. We suggest that bursting behaviour similar to that observed may occur in the Earth's mantle as it undergoes secular cooling on the billion-year time scale.

An approximate theory for incompressible viscous flow past two-dimensional bluff bodies in the intermediate Reynolds number regime O(1) < Re < O(102)

1976 ◽  
Vol 77 (1) ◽  
pp. 129-152 ◽  
Author(s):  
Sheldon Weinbaum ◽  
Michael S. Kolansky ◽  
Michael J. Gluckman ◽  
Robert Pfeffer
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layer Theory ◽  
Navier Stokes ◽  
Bluff Bodies ◽  
Approximate Theory ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past

A new approximate theory is proposed for treating the flow past smoothly contoured two-dimensional bluff bodies in the intermediate Reynolds number rangeO(1) <Re< 0(102), where the displacement effect of the thick viscous layer near the surface of the body is large and a steady laminar wake is present. The theory is based on a new pressure hypothesis which enables one to take account of the displacement interaction and centrifugal effects in thick viscous layers using conventional first-order boundary-layer equations. The basic question asked is how the wall pressure gradient in ordinary boundary -layer theory must be modified if the pressure gradient along the displacement surface using the Prandtl pressure hypothesis is to be equal to the pressure gradient along this surface using a higher-order approximation to the Navier-Stokes equation in which centrifugal forces are considered. The inclusion of the normal pressure field with displacement interaction is shown to be equivalent to stretching the streamwise body co-ordinate in first-order boundary-layer theory such that the streamwise pressure gradient as a function of distance along the original and displacement body surfaces are equal.While the new theory is of a non-rigorous nature, it yields results for the location of separation and detailed surface pressure and vorticity distribution which are in remarkably good agreement with the large body of available numerical Navier-Stokes solutions. A novel feature of the new boundary-value problem is the development of a simple but accurate approximate method for determining the inviscid flow past an arbitrary two-dimensional displacement body with its wake.

Inertia and Energy Effects in the Developing Gas Film Between Two Parallel Flat Plates

1973 ◽  
Vol 95 (4) ◽  
pp. 524-532 ◽  
Author(s):  
H. G. Elrod ◽  
T. Y. Chu
Keyword(s):  
Boundary Layer ◽  
Temperature Effects ◽  
Boundary Layer Theory ◽  
Approximate Theory ◽  
Flat Plates ◽  
Entrance Flow

Inertia and temperature effects in entrance flow between parallel flat plates are investigated with the use of boundary-layer theory. In addition, an approximate theory is developed which is implemented by a “gas table” similar to that employed for conventional Fanno-line computations.

INVERSE PROBLEMS OF BOUNDARY LAYER THEORY

2018 ◽  
Vol 49 (8) ◽  
pp. 793-807
Author(s):  
Vladimir Efimovich Kovalev
Keyword(s):  
Boundary Layer ◽  
Inverse Problems ◽  
Boundary Layer Theory
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