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Applied Mathematics and Mechanics

, Volume 28, Issue 1, pp 69–78 | Cite as

Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

  • K. HoomanEmail author
  • H. Gurgenci
Article

Abstract

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [12], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Raut [14].

Key words

entropy generation rate forced convection porous medium rectangular duct temperature-dependent viscosity 

Nomenclature

a

aspect ratio

A

coefficient defined by Eq. (17)

Be

Bejan number defined by Eq.(32)

Br

Brinkman number defined by Eq.(29)

cP

specific heat at constant pressure

DH

hydraulic diameter

Dn

coefficient defined by Eq.(14)

G

Negative of the applied pressure gradient

H

duct height

k

thermal conductivity

K

permeability

m

coefficient defined by Eq.(14)

S1, S2

series defined by Eq.(19b,c)

gen

entropy generation rate per unit volume

T*

temperature

Tw

wall temperature

Tm

bulk mean temperature

u*

filtration velocity

ū

mean velocity

û

normalized velocity u/ū

x,y,z

dimensionless coordinates

N

viscosity variation number

NFFI

fluid friction irreversibility

NHTI

heat transfer irreversibility

NS

dimensionless entropy generation number defined by Eq.(31)

Nu

Nusselt number defined by Eq.(20)

P2

viscosity variation parameter defined by Eq.(11)

Pe

Péclet number defined by Eq.(27a)

q

dimensionless wall heat flux by Eq.(27b)

q

wall heat flux

R

dimensionless parameter defined by Eq.(10)

x*,y*,z*

Cartesian coordinates

Greek symbols

ϑ

k T w T* / qH

μ

fluid viscosity

λn

Eigenvalues of the problem

ρ

fluid density

Subscripts

cp

constant property

w

wall

Chinese Library Classification

O357.3 

2000 Mathematics Subject Classification

76S05 

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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  1. 1.School of Engineeringthe University of QueenslandBrisbaneAustralia

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