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The onset of natural convection and heat transfer correlation in horizontal fluid layer heated uniformly from below

  • Thermal Engineering · Fluid Engineering · Energy and Power Engineering
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Abstract

The critical condition of the onset of buoyancy-driven convective motion of uniformly heated horizontal fluid layer was analysed by the propagation theory which transforms the disturbance quantities similarly. The dimensionless critical time,τ c , is obtained as a function of the Rayleigh number and the Prandtl number. Based on the stability criteria and the boundary-layer instability model, a new heat transfer correlation which can cover whole range of Rayleigh number was derived. Our theoretical results predict the experimental results quite reasonably.

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Abbreviations

a:

Horizontal wave number [−]

d:

Fluid depth [m]

g:

Gravitational acceleration [m/s2]

k:

Thermal conductivity [J/mK]

Nu:

Nusselt number (=qw/kΔT) [−]

P:

Pressure [Pa]

Pr:

Prandtl number (=ν/α) [−]

Ra:

Rayleigh number (=gβΔTd3/αν) [−]

Raq :

Rayleigh number based on the heat flux (=gβqwd4/kαν) [−]

qw :

Wall heat flux [J/m2]

T:

Temperature [K]

t:

Time [s]

\(\overrightarrow U \) :

Velocity vector [m/s]

w:

Dimensionless vertical velocity [−]

X, Y, Z:

Space in Cartesian coordinate [m]

α:

Thermal diffusivity [m2/s]

β:

Thermal expansion coefficient [1/K]

ΔT:

Temperature difference [K]

ζ:

Similarity variable [−]

θ:

Dimensionless temperature [−]

μ:

Viscosity [Pa s]

ν:

Kinematic viscosity [m2/s]

ρ:

Density [kg/m3]

τ:

Dimensionless time [−]

0:

Basic quantity

1:

Disturbed quantity

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Authors and Affiliations

  1. Department of Chemical Engineering, Cheju National University, 690-756, Cheju-do, Korea

    Min Chan Kim

  2. Department of Nuclear and Energy Engineering, Cheju National University, 690-756, Cheju-do, Korea

    Sin Kim

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  1. Min Chan Kim
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  2. Sin Kim
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Correspondence to Sin Kim.

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Kim, M.C., Kim, S. The onset of natural convection and heat transfer correlation in horizontal fluid layer heated uniformly from below. KSME International Journal 15, 1451–1460 (2001). https://doi.org/10.1007/BF03185687

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  • DOI: https://doi.org/10.1007/BF03185687

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