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Analysis and Optimization Laminar Viscous Flow Through a Channel

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Abstract

Optimizing of laminar viscous flow through a pipe by two dimensionless values is investigated analytically. Dimensionless entropy generation and pumping power to heat transfer rate ratio are used as basis for constant viscous and the temperature dependence on the viscosity. For this matter we calculate entropy generation and pumping power for a fully developed in a pipe subjected to constant wall temperature for either constant viscosity and the variable viscosity. The variation entropy generation increase along the pipe length for viscous fluid is drawn, either the variation summation dimensionless entropy generation and the pumping power to heat transfer rate ratio are varying the fluid inlet temperature for fixed pipe length and are varying pipe length for fixed fluid inlet temperature are drawn. For low heat transfer conditions the entropy generation due to viscosity friction becomes dominant and the dependence of viscosity with the temperature becomes essentially important to be considered.

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Abbreviations

C p :

specific heat capacity (J/kg K)

D :

diameter (m)

Ec :

Eckert number \([\overline {U}^2/[C_p(T_{\rm w}-T_0)]]\)

f :

friction factor

\(\bar {h}\) :

average heat transfer coefficient (W/m2 K)

\(\bar {h}_{c\cdot p}\) :

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)

P r :

pumping power to heat transfer rate ratio

\(\dot{Q}\) :

total heat transfer rate (W)

Re :

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

s :

entropy (J/kg K)

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

entropy generation (W/K)

St :

Stanton number [ \(\bar {h}/(\rho\overline {U}(C_p)\)]

T :

temperature (K)

T 0 :

inlet fluid temperature (K)

T ref :

reference temperature (=293 K)

T w :

wall temperature the pipe (K)

\(\overline {U}\) :

fluid bulk velocity (m/s)

x :

axial distance (m)

ΔT :

increase of fluid temperature (K)

μ:

viscosity (N/s m2)

μb :

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

μw :

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

λ:

dimensionless axial distance [l/D]

Π1 :

modified Stanton number [St λ]

Π2 :

dimensionless group [Ec/(St Re)]

Ψ:

dimensionless entropy generation [ \(\dot {S}_{\rm gen}/\)[ \(\dot {Q}\)/(T w − T 0)]

Ψ′:

modified dimensionless entropy generation [ \(\dot {S}_{\rm gen}/\)[ \(\dot {Q}\)/(ΔT)]

ρ:

density (kg/m3)

τ:

dimensionless inlet wall-to-fluid temperature difference [(T w − T 0)/T w]

θ:

dimensionless temperature [(T − T w)/(T 0 − T w)]]

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Authors and Affiliations

  1. Department of mechanical engineering, K.N.T University of Technology, Tehran, Iran

    H. G. Langeroudi & C. Aghanajafi

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  1. H. G. Langeroudi
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  2. C. Aghanajafi
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Correspondence to H. G. Langeroudi.

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Langeroudi, H.G., Aghanajafi, C. Analysis and Optimization Laminar Viscous Flow Through a Channel. J Fusion Energ 25, 155–164 (2006). https://doi.org/10.1007/s10894-006-9012-y

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  • DOI: https://doi.org/10.1007/s10894-006-9012-y

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