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Research Papers: Natural and Mixed Convection

The Effect of Spatially Nonuniform Internal Heating on the Onset of Convection in a Horizontal Fluid Layer

[+] Author and Article Information
A. V. Kuznetsov

Department of Mechanical
and Aerospace Engineering,
North Carolina State University,
Campus Box 7910,
Raleigh, NC 27695-7910
e-mail: avkuznet@ncsu.edu

D. A. Nield

Department of Engineering Science,
University of Auckland,
Private Bag 92019,
Auckland 1142, New Zealand
e-mail: d.nield@auckland.ac.nz

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 17, 2015; final manuscript received January 25, 2016; published online March 22, 2016. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 138(6), 062503 (Mar 22, 2016) (9 pages) Paper No: HT-15-1604; doi: 10.1115/1.4032837 History: Received September 17, 2015; Revised January 25, 2016

In this paper, we investigated the onset of natural convection in a horizontal fluid layer due to nonuniform internal heat generation, which is relevant to a number of geophysical situations. We investigated a number of special cases, which we believe are paradigmatic. Those include linear, quadratic, concentrated, and exponential source strength distributions. Our results show that those situations that lead to a reduction/increase in the size of the region in which the basic temperature gradient is destabilizing lead to an increase/decrease in stability.

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References

Figures

Grahic Jump Location
Fig. 1

Plots of the critical internal Rayleigh number (a) and the corresponding critical wavenumber (b), for various values of the nonuniformity parameter, for Example 1. Case A: isothermal/isothermal boundaries, and case B: isoflux/isothermal boundaries.

Grahic Jump Location
Fig. 2

Plots of the critical internal Rayleigh number (a) and the corresponding critical wavenumber (b), for various values of the nonuniformity parameter, for Example 2. Case A: isothermal/isothermal boundaries, and case B: isoflux/isothermal boundaries.

Grahic Jump Location
Fig. 3

Plots of the critical internal Rayleigh number (a) and the corresponding critical wavenumber (b), for various values of the height of the position of the plane source, for Example 3. Case A: isothermal/isothermal boundaries, and case B: Isoflux/isothermal boundaries.

Grahic Jump Location
Fig. 4

Plots of the critical internal Rayleigh number (a) and the corresponding critical wavenumber (b), for various values of the nonuniformity parameter and exponential decay constant, for Example 4. Case (i) A: (boundary layer at the bottom) isothermal/isothermal boundaries.

Grahic Jump Location
Fig. 5

Plots of the critical internal Rayleigh number (a) and the corresponding critical wavenumber (b), for various values of the nonuniformity parameter and exponential decay constant, for Example 4. Case (i) B: (boundary layer at the bottom) isoflux/isothermal boundaries.

Grahic Jump Location
Fig. 6

Plots of the critical internal Rayleigh number (a) and the corresponding critical wavenumber (b), for various values of the nonuniformity parameter and exponential decay constant, for Example 4. Case (ii) A: (boundary layer at the top) isothermal/isothermal boundaries.

Grahic Jump Location
Fig. 7

Plots of the critical internal Rayleigh number (a) and the corresponding critical wavenumber (b), for various values of the nonuniformity parameter and exponential decay constant, for Example 4. Case (ii) B: (boundary layer at the top) isoflux/isothermal boundaries.

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