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Thermal boundary layer and the characteristic length on natural convection over a horizontal plate

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Abstract

Thickness of the thermal boundary layer on natural convection from a horizontal plate was experimentally measured and expressed as a function of Rayleigh number both in laminar and turbulent regimes. Several parametric equations expressing the Nusselt number as a function of Rayleigh number were developed combining experimental data by other authors with the ones obtained in this work. The characteristic length was taken as the thickness of the thermal boundary layer in one equation and as the ratio of the area to the perimeter in another one. Both characteristic lengths correlated the data precisely in wide ranges of Rayleigh numbers.

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Notes

  1. In a recent review Khalifa [10] showed that large discrepancies could occur among the natural convective heat transfer coefficients given by different authors for horizontal surfaces. The effect of the geometry of the horizontal plate on free convection heat transfer continues to be of interest of the cientific community; Baskaya and Kanli [2] studied the influence of the plate length while Radziemska and Lewandowski [17] presented their experimental results as a function of the plate width.

  2. Martorell et al. [14] also took attention to the thermal plume rising near the center of the plate.

  3. Figure 4 shows the temperature distributions for another experiment where the adverse temperature gradient is not big enough to create convection regime since the intensity of radiation is low.

Abbreviations

A :

Area of the surface (m2)

g :

Gravitational acceleration (m/s2)

h :

Convection coefficient (W/m2 °C)

I 0 :

Intensity of radiation (W/m2)

k :

Thermal conductivity (W/m °C)

L :

Characteristic dimension (m)

P :

Perimeter of the plate (m)

T :

Temperature (°C)

T 0 :

Initial temperature (°C)

t :

Time (s)

z :

Vertical distance (m)

α :

Thermal diffusivity (m2/s)

β :

Thermal expansion coefficient (1/K)

δ :

Thickness of the thermal boundary layer (m)

ν :

Kinematic viscosity (m2/s)

Nu :

Nusselt number (hL/k)

Nu δ :

Nusselt number (hδ/k)

Ra :

Rayleigh number (gβΔT L 3/να)

Ra δ :

Rayleigh number in thermal instability (gβΔT δ 3/να)

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Authors and Affiliations

  1. Mechanical Engineering Department, Universidad de las Americas, Puebla, 72820, Sta. Catarina Martir, Cholula, Puebla, Mexico

    Bulent Kozanoglu & Jorge Lopez

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  1. Bulent Kozanoglu
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  2. Jorge Lopez
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Correspondence to Bulent Kozanoglu.

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Kozanoglu, B., Lopez, J. Thermal boundary layer and the characteristic length on natural convection over a horizontal plate. Heat Mass Transfer 43, 333–339 (2007). https://doi.org/10.1007/s00231-006-0114-x

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