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Unsteady and chaotic characteristics of natural convection field in vertical slots at large Prandtl number

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Abstract

In this study we examined the unsteady and chaotic characteristics of the natural convection field in vertical slots at large Prandtl number. In the computation, temperature dependence of viscosity was partially taken into consideration. As a result we discovered that the spatial region where a significant temperature fluctuation is detected corresponds to the spatial region where the secondary cells exist. The largest Lyapunov exponents calculated from the temperature on the center line have a local maximum at the lower region of the enclosure when the viscosity change was considered. These characteristics agree well with the experimental ones that have been observed by authors (Ishida, Kure and Kimoto 2001).

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Abbreviations

a :

Thermal diffusivity (m2/s)

L :

Representative length (width of enclosure) (m)

Nu:

Surface-averaged Nusselt number

\(\overline{{\text{Nu}}}\) :

Time- and surface-averaged Nusselt number

t :

Dimensionless time, (t*a m)/L 2

T :

Dimensional temperature

T m :

Reference (mean) temperature, (T h + T c)/2 (°C)

Gr:

The Grashof number based on L and Θ at the reference temperature

Pr:

The Prandtl number at the reference temperature

Ra:

Rayleigh number, Pr×Gr

x :

Dimensionless component of x coordinate, x */L

y :

Dimensionless component of y coordinate, y */L

α:

Aspect ratio of enclosure

β:

Thermal expansion coefficient (1/°C)

δ:

Length scale of boundary layer

φ:

Dimensionless stream function, ϕ*/a m

λ:

The largest Lyapunov (Liapunov) exponent

μ:

Dimensionless dynamic viscosity, μ*(T)/μ*m

θ:

Dimensionless temperature, (T−T c)/Θ

Θ:

Representative temperature difference, T h−T c

τ:

Time scale at which auto-correlation function becomes 1/e

ζ:

Dimensionless vorticity, (L 2ζ*)/a m

*:

Dimensional quantity

c:

Cold surface or critical number

h:

Hot surface

m:

Mean (reference) temperature

1–5:

The definition point on the center line of the enclosure

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Authors and Affiliations

  1. Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka, 560-8531, Japan

    Hideshi Ishida, Kazunari Momose & Hideo Kimoto

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  1. Hideshi Ishida
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  2. Kazunari Momose
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  3. Hideo Kimoto
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Correspondence to Hideshi Ishida.

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Ishida, H., Momose, K. & Kimoto, H. Unsteady and chaotic characteristics of natural convection field in vertical slots at large Prandtl number. Heat Mass Transfer 42, 645–651 (2006). https://doi.org/10.1007/s00231-005-0039-9

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  • DOI: https://doi.org/10.1007/s00231-005-0039-9

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