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Free convention heat transfer from an isothermal horizontal thin strip: The influence of the Prandtl number

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Abstract

Simultaneous free convection above and below a uniformly heated horizontal plate has been widely investigated, both in the case of an isothermal surface, and of a uniformly heated surface, but always assuming only air as fluid (Pr=0.7). Nevertheless, there are works dealing with horizontal plates whose results show that the Nu dependence on Pr may not be simply expressed by a power law with the same exponent of the Gr one. So it was considered useful to study the Prandtl number influence in the case of the isothermal horizontal strip. Results show that, while for the lower surface of the strip the Nu dependence in Gr can be expressed by a power law with an exponent close to the Gr one, for the upper surface the exponent is sensibly different. Correlating equations related to the investigated situations are proposed.

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Abbreviations

a,b :

major and minor axes of an ellipse

f 1 , f 2 :

functions defined in the text

g:

gravitational acceleration

Nu:

Nusselt number

Pr:

Prandtl number

Gr:

Grashof number

Ra:

Rayleigh number

T:

temperature

u:

velocity component in x direction

v:

velocity component in y direction

p:

pressure

W:

strip width

cP :

constant pressure specific heat of the fluid

L:

width of the integration domain

H1:

height of the integration domain over the strip

H2:

height of the integration domain under the strip

λ :

heat conductivity of the fluid

γ :

fluid density of the fluid

β :

thermal expansion coefficient of the fluid

µ:

dynamic viscosity of the fluid

gv :

kinematic viscosity of the fluid

η :

relative error

φ :

angle

\(\bar A\) :

average value of A

und :

relative to the lower face

ov :

relative to the upper face

w :

relative to the strip surface max maximum value

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Authors and Affiliations

  1. Dipartimento di Architettura, Università degli Studi Roma Tre, via Madonna dei Monti, 40 00184, Roma, Italy

    Lucia Fontana

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  1. Lucia Fontana
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Fontana, L. Free convention heat transfer from an isothermal horizontal thin strip: The influence of the Prandtl number. J. Therm. Sci. 23, 586–592 (2014). https://doi.org/10.1007/s11630-014-0745-z

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  • DOI: https://doi.org/10.1007/s11630-014-0745-z

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