Heat and Mass Transfer

, Volume 41, Issue 3, pp 239–249

Natural convection of non-Newtonian power law fluids in a shallow horizontal rectangular cavity uniformly heated from below

Original

Abstract

Analytical and numerical study is conducted for two-dimensional steady-state buoyancy driven flow of a non-Newtonian power law fluid confined in a shallow rectangular horizontal cavity uniformly heated from below, while its short vertical rigid sides are considered adiabatic. The effect of the non-Newtonian behaviour on the onset of convection, fluid flow, temperature field, and heat transfer is examined. A closed approximate analytical solution is developed on the basis of the parallel flow assumption and the obtained results are validated numerically by solving the full governing equations.

List of symbols

A

aspect ratio of the enclosure Eq. 9

C

dimensionless temperature gradient in x-direction

g

acceleration due to gravity

H

height of the enclosure

k

consistency index for a power law fluid at the reference temperature

L

length of the enclosure

n

flow behaviour index for a power law fluid at the reference temperature

Nu

local Nusselt number Eq. 10

\( \overline{{Nu}} \)

mean Nusselt number Eq. 11

Pr

generalized Prandtl number Eq. 9

q

constant heat flux per unit area

Ra

generalized Rayleigh number Eq. 9

T

dimensionless temperature (T′−Tc)/ΔT*

Tc

reference temperature

ΔT*

characteristic temperature, qH′/λ

(u, v)

dimensionless axial and vertical velocities, (u′, v′)/(α/H′)

(x, y)

dimensionless axial and vertical coordinates, (x′, y′)/H′)

Greek symbols

α

thermal diffusivity at the reference temperature

β

thermal expansion coefficient at the reference temperature

λ

thermal conductivity at the reference temperature

μ

dynamic viscosity for a Newtonian fluid at the reference temperature

μa

dimensionless apparent viscosity for a non-Newtonian power law fluid Eq. 6

ρ

density of fluid at the reference temperature

Ω

dimensionless vorticity Ω′/(α/H2)

ψ

dimensionless stream function ψ′/α

Superscript

dimensional variables

Subscripts

c

critical value or value relative to the centre of the enclosure (x, y)=(A/2, 1/2)

max

maximum value

w

wall

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Faculté des Sciences et Techniques, Département de Physique, UFR de Chimie Appliquée et Sciences de l’Environnement, Equipe de Modélisation des Ecoulements et des Transferts (EMET)Université Cadi AyyadBéni-MellalMarocco
  2. 2.Faculté des Sciences Semlalia, Département de Physique, UFR de Thermique et Mécanique des Fluides, Laboratoire de Mécanique des Fluides et d’EnergétiqueUniversité Cadi AyyadMarrakechMaroccco

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