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Research Papers: Natural and Mixed Convection

Thermal Convection of a Non-Fourier Fluid in a Vertical Slot

[+] Author and Article Information
Mohammad Niknami

Department of Mechanical and
Material Engineering,
University of Western Ontario,
London, ON N6A 5B9, Canada

Roger E. Khayat

Department of Mechanical and
Material Engineering,
University of Western Ontario,
London, ON N6A 5B9, Canada
e-mail: rkhayat@uwo.ca

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 6, 2015; final manuscript received November 15, 2015; published online January 27, 2016. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 138(5), 052501 (Jan 27, 2016) (8 pages) Paper No: HT-15-1174; doi: 10.1115/1.4032309 History: Received March 06, 2015; Revised November 15, 2015

The instability of steady natural convection of a non-Fourier fluid of the single-phase lagging (SPL) type between two vertical surfaces maintained at different temperatures is studied. SPL fluids possess a relaxation time, which reflects the delay in the response of the heat flux and the temperature gradient. The SPL model is particularly relevant to low-temperature liquids, ultrafast processes, and nanofluids (with a retardation time added in this case). Linear stability analysis is employed to obtain the critical state parameters, such as critical Grashof numbers. For intermediate Prandtl numbers (Pr = 7.5), when non-Fourier level exceeds a certain value, the neutral stability curve comprises a Fourier branch and an oscillatory branch. In this case, oscillatory convection increasingly becomes the mode of preference, compared to both conduction and stationary convection. Critical Grashof number decreases for fluids with higher non-Fourier levels.

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Figures

Grahic Jump Location
Fig. 1

(a) Base flow velocity and temperature and (b) base flow heat flux in the y-direction (Gr = 1000)

Grahic Jump Location
Fig. 2

Influence of the Cattaneo number on the marginal stability curves in the Gr-a plane (Pr = 1 and C = 0–0.01)

Grahic Jump Location
Fig. 3

Influence of the Cattaneo number on the marginal stability curves in the Gr-a plane (Pr = 1 and C = 0.02)

Grahic Jump Location
Fig. 4

Influence of the Cattaneo number on the marginal stability curves in the Gr-a plane (Pr = 1 and C = 0.05)

Grahic Jump Location
Fig. 5

Influence of the Cattaneo number on the critical Grashof number and wavenumber (Pr = 1)

Grahic Jump Location
Fig. 6

Influence of the Cattaneo number on the marginal stability curves in the Gr-a plane (Pr = 7.5 and C = 0–0.005)

Grahic Jump Location
Fig. 7

Influence of the Cattaneo number on the critical Grashof number and wavenumber (Pr = 7.5)

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