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Research Papers

Temperature Dependent Viscosity and Thermal Conductivity Effects on the Laminar Forced Convection in Straight Microchannels

[+] Author and Article Information
Stefano Del Giudice

Professor
e-mail: stefano.delgiudice@uniud.it

Stefano Savino

Research Assistant
e-mail: stefano.savino@uniud.it

Carlo Nonino

Professor
e-mail: carlo.nonino@uniud.it
Dipartimento di Ingegneria Elettrica,
Gestionale e Meccanica,
Università degli Studi di Udine,
Via delle Scienze 208,
Udine 33100, Italy

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received May 31, 2012; final manuscript received September 4, 2012; published online September 11, 2013. Assoc. Editor: Sushanta K. Mitra.

J. Heat Transfer 135(10), 101003 (Sep 11, 2013) (8 pages) Paper No: HT-12-1262; doi: 10.1115/1.4024496 History: Received May 31, 2012; Revised September 04, 2012

A parametric investigation is carried out on the effects of temperature dependent viscosity and thermal conductivity and of viscous dissipation in simultaneously developing laminar flows of liquids in straight microchannels of constant cross sections. Uniform heat flux boundary conditions are specified at the heated walls. A superposition method is proved to be applicable in order to predict the value of the Nusselt number by considering separately the effects of temperature dependent viscosity and those of temperature dependent thermal conductivity. In addition, it is found that the influence of the temperature dependence of thermal conductivity on the value of the Nusselt number is independent of the value of the Brinkman number, i.e., it is the same no matter whether viscous dissipation is negligible or not. Finally, it is demonstrated that, in liquid flows, the main effects on pressure drop of temperature dependent fluid properties can be retained even if only viscosity is allowed to vary with temperature, the other properties being assumed constant. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries are considered, corresponding to both axisymmetric (circular) and three-dimensional (square) microchannel geometries. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the viscosity and thermal conductivity Pearson numbers and of the Brinkman number.

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References

Figures

Grahic Jump Location
Fig. 1

Axial distributions of the ratio Nuμ,k/Nuc,0 for simultaneously developing laminar flows in circular microchannels with Pre = 5, different values of Pnk and Br, and (a) Pnμ = 0.5, (b) Pnμ = 1, and (c) Pnμ = 2

Grahic Jump Location
Fig. 2

Axial distributions of the ratio Nuμ,k/Nuc,0 for simultaneously developing laminar flows in square microchannels with Pre = 5, different values of Pnk and Br, and (a) Pnμ = 0.5, (b) Pnμ = 1, and (c) Pnμ = 2

Grahic Jump Location
Fig. 3

Comparison of axial distributions of the ratios Nuμ,k/Nuc,0 and (Nuμ,k/Nuc,0)' for simultaneously developing laminar flows in circular microchannels with Pre = 5,Br = 0.01,Pnμ = 2 and different values of Pnk

Grahic Jump Location
Fig. 4

Comparison of axial distributions of the ratios Nuμ,k/Nuc,0 and (Nuμ,k/Nuc,0)' for simultaneously developing laminar flows in square microchannels with Pre = 5,Br = 0.01,Pnμ=2 and different values of Pnk

Grahic Jump Location
Fig. 5

Comparison of axial distributions of the ratios Nuk,0/Nuc,0 and (Nuk,0/Nuc,0)' = k¯k,0/ke for simultaneously developing laminar flows in circular microchannels with Pre = 5 and different values of Pnk

Grahic Jump Location
Fig. 6

Comparison of axial distributions of the ratios Nuk,0/Nuc,0 and (Nuk,0/Nuc,0)' = k¯k,0/ke for simultaneously developing laminar flows in square microchannels with Pre = 5 and different values of Pnk

Grahic Jump Location
Fig. 7

Axial distributions of the ratio (faPee)μ,k/(faPee)μ for simultaneously developing laminar flows in circular microchannels with Pre = 5,Pnμ = 2,Br = 0 and 0.01, and different values of Pnk

Grahic Jump Location
Fig. 8

Axial distributions of the ratio (faPee)μ,k/(faPee)μ for simultaneously developing laminar flows in square microchannels with Pre = 5,Pnμ = 2,Br = 0 and 0.01, and different values of Pnk

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