KSME International Journal

, Volume 15, Issue 10, pp 1451–1460 | Cite as

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

  • Min Chan Kim
  • Sin Kim
Thermal Engineering · Fluid Engineering · Energy and Power Engineering


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.

Key words

Buoyancy Effect Stability Analysis Heat Transfer Correlation Propagation Theory 



Horizontal wave number [−]


Fluid depth [m]


Gravitational acceleration [m/s2]


Thermal conductivity [J/mK]


Nusselt number (=qw/kΔT) [−]


Pressure [Pa]


Prandtl number (=ν/α) [−]


Rayleigh number (=gβΔTd3/αν) [−]


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


Wall heat flux [J/m2]


Temperature [K]


Time [s]

\(\overrightarrow U \)

Velocity vector [m/s]


Dimensionless vertical velocity [−]

X, Y, Z

Space in Cartesian coordinate [m]



Thermal diffusivity [m2/s]


Thermal expansion coefficient [1/K]


Temperature difference [K]


Similarity variable [−]


Dimensionless temperature [−]


Viscosity [Pa s]


Kinematic viscosity [m2/s]


Density [kg/m3]


Dimensionless time [−]



Basic quantity


Disturbed quantity


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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2001

Authors and Affiliations

  1. 1.Department of Chemical EngineeringCheju National UniversityCheju-doKorea
  2. 2.Department of Nuclear and Energy EngineeringCheju National UniversityCheju-doKorea

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