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Journal of Fusion Energy

, Volume 25, Issue 3–4, pp 165–173 | Cite as

Thermodynamic’s Second Law Analysis for Laminar Non-Newtonian Fluid Flow

  • H. G. Langeroudi
  • C. Aghanajafi
Article

Abstract

In this paper, the entropy generation of a non-Newtonian fluid such as Tho2 inside a circular channel with constant surface temperature has been investigated. The pressure gradient along the pipe line, the difference between the dimensionless inlet wall temperature and fluid temperature and modified Stanton number are the key elements to calculate the entropy generation for three different non-Newtonian fluids. Also the variation of the dimensionless entropy generation and the pumping power to heat transfer rate ratio is calculated for two different cases, the first case involves fixed pipe length and variable inlet temperature and the second case considers fixed fluid inlet temperature and variable pipe length.

Keywords

Non-Newtonian fluid dimensionless entropy generation pressure gradient pumping power 

NOMENCLATURE

Cp

specific heat capacity (J/kg K)

R

pipe radius (m)

Ec

Eckert number [ \(\bar{U}^2/[C_{p} (T_{\rm w} -T_0 )\)]]

f

friction factor

\(\bar {h}\)

average heat transfer coefficient (W/m2 K)

\(\bar{h}_{\rm c.p}\)

constant property average heat transfer coefficient (W/m2 K)

k

thermal conductivity (W/m K)

l

length of the pipe (m)

\(\dot{m}\)

mass flow rate (kg/s)

P

pressure (N/m2)

τ0

yield

μ0

viscosity yield shear stress (Ns/m2)

τR

shear stress in R radius (N/m2)

T0

inlet fluid temperature (K)

Rp

ratio of the plug radius to pipe radius =  \(({r_{\rm p}}/{R})\)

Q

flow flux m3/s

Re

Reynolds number \(\rho \bar {U}D/\mu]\)

s

entropy (J/kg K)

\(\dot{S}_{\rm gen}\)

entropy generation (W/K)

St

Stanton number \([\bar{h}/(\rho \bar {U}(C_{p} )]\)

T

temperature (K)

Tref

reference temperature (=293 K)

Tw

wall temperature the pipe (K)

\(\bar {U}\)

fluid bulk velocity (m/s)

Pr

pumping power to heat transfer rate ratio

Ψ

dimensionless entropy generation [ \(\dot {S}_{\rm gen}/[\dot{Q}/ (T_{\rm w} -T_0)\)]

D

Pipe diameter (m)

λ

dimensionless axial distance [l/D]

Π1

modified Stanton number [St λ]

Π2

dimensionless group [Ec/(St Re)]

ρ

density (kg/m3)

τ

dimensionless inlet wall-to-fluid

μb

viscosity of fluid at bulk temperature (N s/ m2)

x

axial distance (m)

ΔT

increase of fluid temperature (K)

μ

viscosity (N s/ m2)

r0

plug radius for Bingham fluid (m)

rp

plug radius for Casson model (m)

Vz

velocity along the pipe for Bingham model (m/s)

n

the degree of non-Newtonian fluid for power-law model

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringK.N.T. University of TechnologyTehranIran

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