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The effect of blowing or suction on laminar free convective heat transfer on flat horizontal plates

Der Einfluß von Ausblasung oder Absaugung auf den Wärmeübergang an ebenen horizontalen Platten bei laminarer freier Konvektion

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Abstract

In the present paper laminar free convective heat transfer on flat permeable horizontal plates is investigated. To assess the effect of surface suction or injection on heat transfer a correction factor, provided by the film model (or “film theory”), is applied. Comparing the film model predictions with numerical results of previous boundary layer analyses yields good agreement for a wide range of dimensionless transpiration levels.

Zusammenfassung

In der Arbeit wird der Wärmeübergang an ebene stoffdurchlässige horizontale Platten bei laminarer freier Konvektion untersucht. Zur Abschätzung des Einflusses von Absaugung oder Ausblasung auf den Wärmeübergang wird ein aus der Filmtheorie entnommener Korrekturfaktor herangezogen. Ein Vergleich der Voraussagen nach dem Filmmodell mit vorliegenden numerischen Ergebnissen nach dem Grenzschichtmodell ergab gute Übereinstimmungen in einem weiten Bereich des dimensionslosen Transpirationsgrades.

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Abbreviations

C :

dimensionless mass flux

c p :

specific heat [J kg −1 K−1]

E :

relative difference between literature and film model, Eq. (13)

f w :

dimensionless mass flux

Gr x :

Grashof number,g β (T w−T ∞)x 3/ν 2

g :

gravitational acceleration [ms−2]

h x :

local heat transfer coefficient, Eq. (4) [Wm−2 K−1]

K :

constants

k :

thermal conductivity [Wm−1 K−1]

L :

plate length [m]

Nu x :

local Nusselt number, Eq. (8)

n :

power-law coefficient

Pr :

Prandtl number,ν c p ϱ/k

q :

heat flux [Wm−2]

T :

temperature [K]

ν :

component of velocity in they-direction [ms−1]

x :

coordinate along the plate [m]

y :

coordinate normal to the plate [m]

β :

coefficient of thermal expansion [K−1]

η :

dimensionless similarity variable, Eq. (6)

Θ t :

ratio of actual heat transfer and impermeable plate heat transfer

Θ :

dimensionless temperature, Eq. (5)

ν :

inematic viscosity [m2 s−1]

ϱ :

density [kg m−3]

ϕ t :

dimensionless wall mass flux, Eq. (3)

film:

pertaining to film model

num:

pertaining to numerical solution

w :

wall

∞:

ambient fluid

*:

pertaining to impermeable plate

′:

differentiation with respect toη

-:

mean

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  1. Dept. of Civil Engineering & Management, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    H. J. H. Brouwers

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Brouwers, H.J.H. The effect of blowing or suction on laminar free convective heat transfer on flat horizontal plates. Wärme- und Stoffübertragung 28, 341–344 (1993). https://doi.org/10.1007/BF01539531

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