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.

Onset of thermal convection in a horizontal fluid layer under ramp heating

2002 ◽  
Author(s):  
Dae Jun Yang ◽  
Jake Kim ◽  
Chang Kyun Choi ◽  
In Gook Hwang
Keyword(s):  
Thermal Convection ◽  
Fluid Layer ◽  
Horizontal Fluid Layer

The effect of heating rate on the stability of stationary fluids

1967 ◽  
Vol 29 (2) ◽  
pp. 337-347 ◽  
Author(s):  
I. G. Currie
Keyword(s):  
Rayleigh Number ◽  
Surface Temperature ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Lower Surface ◽  
Published Data ◽  
Heating Rates ◽  
Lower Surface Temperature ◽  
The Stability ◽  
Horizontal Fluid Layer

A horizontal fluid layer whose lower surface temperature is made to vary with time is considered. The stability analysis for this situation shows that the criterion for the onset of instability in a fluid layer which is being heated from below, depends on both the method and the rate of heating. For a fluid layer with two rigid boundaries, the minimum Rayleigh number corresponding to the onset of instability is found to be 1340. For slower heating rates the critical Rayleigh number increases to a maximum value of 1707·8, while for faster heating rates the critical Rayleigh number increases without limit.Two specific types of heating are investigated in detail, constant flux heating and linearly varying surface temperature. These cases correspond closely to situations for which published data exist. The results are in good qualitative agreement.

Temporal evolution of thermal convection in an initially stably-stratified horizontal fluid layer

2004 ◽  
Vol 43 (8) ◽  
pp. 817-823 ◽  
Author(s):  
Chang Kyun Choi ◽  
Joung Hwan Park ◽  
Hee Kwan Park ◽  
Hong Je Cho ◽  
Tae Joon Chung ◽  
...  
Keyword(s):  
Thermal Convection ◽  
Temporal Evolution ◽  
Fluid Layer ◽  
Horizontal Fluid Layer

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.

A Numerical Investigation of Thermal Convection in a Heat-Generating Fluid Layer

1980 ◽  
Vol 102 (3) ◽  
pp. 531-537 ◽  
Author(s):  
A. A. Emara ◽  
F. A. Kulacki
Keyword(s):  
Thermal Convection ◽  
Large Scale ◽  
Fluid Layer ◽  
Lower Surface ◽  
Rectangular Domain ◽  
Temperature Fields ◽  
Free Boundaries ◽  
Low Velocity ◽  
Nusselt Numbers ◽  
Rayleigh Numbers

Finite difference solutions of the equations governing thermal convection driven by uniform volumetric energy sources are presented for two-dimensional flows in a rectangular domain. The boundary conditions are a rigid, (i.e., zero slip), zero heat-flux lower surface, rigid adiabatic sides, and either a rigid or free (i.e., zero shear) isothermal upper surface. Computations are carried out for Prandtl numbers from 0.05 to 20 and Rayleigh numbers from 5 × 104 to 5 × 108. Nusselt numbers and average temperature profiles within the layer are in good agreement with experimental data for rigid-rigid boundaries. For rigid-free boundaries, Nusselt numbers are larger than in the former case. The structure of the flow and temperature fields in both cases is dominated by rolls, except at larger Rayleigh numbers where large-scale eddy transport occurs. Generally, low velocity upflows over broad regions of the layer are balanced by higher velocity downflows when the flow exhibits a cellular structure. The hydrodynamic constraint at the upper surface and the Prandtl number are found to influence only the detailed nature of flow and temperature fields. No truly steady velocity and temperature fields are found despite the fact that average Nusselt numbers reach steady values.

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