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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

Shah, R. K., and London, A. L., 1978, Laminar Flow Forced Convection in Ducts, Academic Press, New York.
Kakaç, S., 1987, “The Effect of Temperature-Dependent Fluid Properties on Convective Heat Transfer,” Handbook of Single-Phase Convective Heat Transfer, S.Kakaç, R. K.Shah, W. Aung, eds., Wiley, New York, Chap. 18.
Herwig, H., 1985, “The Effect of Variable Properties on Momentum and Heat Transfer in a Tube With Constant Heat Flux Across the Wall,” Int. J. Heat Mass Transfer, 28, pp. 423–431. [CrossRef]
Herwig, H., Voigt, M., and Bauhaus, F. J., 1989, “The Effect of Variable Properties on Momentum and Heat Transfer in a Tube With Constant Wall Temperature,” Int. J. Heat Mass Transfer, 32, pp. 1907–1915. [CrossRef]
Herwig, H., and Mahulikar, S. P., 2006, “Variable Property Effects in Single-Phase Incompressible Flows Through Microchannels,” Int. J. Therm. Sci., 45, pp. 977–981. [CrossRef]
Mahulikar, S. P., and Hervig, H., 2006, “Physical Effects of Laminar Microconvection Due to Variations in Incompressible Fluid Properties,” Phys. Fluids, 18, p. 073601. [CrossRef]
Hooman, K., Hooman, F., and Famouri, M., 2009, “Scaling Effects for Flow in Micro-Channels: Variable Property, Viscous Heating, Velocity Slip, and Temperature Jump,” Int. Commun. Heat Mass Transfer, 36, pp. 192–196. [CrossRef]
Hooman, K., and Ejlali, A., 2010, “Effects of Viscous Heating, Fluid Property Variation, Velocity Slip, and Temperature Jump on Convection Through Parallel Plate and Circular Microchannels,” Int. Commun. Heat Mass Transfer, 37, pp. 34–38. [CrossRef]
Li, Z., Huai, X., Tao, Y., and Chen, H., 2007, “Effects of Thermal Property Variations on the Liquid Flow and Heat Transfer in Microchannel Heat Sinks,” Appl. Therm. Eng., 27, pp. 2803–2814. [CrossRef]
Liu, J., Peng, X., and Yan, W., 2007, “Numerical Study of Fluid Flow and Heat Transfer in Microchannel Cooling Passages,” Int. J. Heat Mass Transfer, 50, pp. 1855–1864. [CrossRef]
Nóbrega, J. M., Pinho, F. T., Oliveira, P. J., and Carneiro, O. S., 2004, “Accounting for Temperature Dependent Properties in Viscoelastic Duct Flows,” Int. J. Heat Mass Transfer, 47, pp. 1141–1158. [CrossRef]
Del Giudice, S., Nonino, C., and Savino, S., 2007, “Effects of Viscous Dissipation and Temperature Dependent Viscosity in Thermally and Simultaneously Developing Laminar Flows in Microchannels,” Int. J. Heat Fluid Flow, 28, pp. 15–27. [CrossRef]
Nonino, C., Del Giudice, S., and Savino, S., 2007, “Temperature-Dependent Viscosity and Viscous Dissipation Effects in Simultaneously Developing Flows in Microchannels With Convective Boundary Conditions,” ASME J. Heat Transfer. 129, pp. 1187–1194. [CrossRef]
Nonino, C., Del. Giudice, S., and Savino, S., 2010, “Temperature-Dependent Viscosity and Viscous Dissipation Effects in Microchannel Flows With Uniform Wall Heat Flux,” Heat Transfer Eng., 31(8), pp. 682–691. [CrossRef]
Nonino, C., Del Giudice, S., and Comini, G., 1988, “Laminar Forced Convection in Three-Dimensional Duct Flows,” Numer. Heat Transfer, 13, pp. 451–466. [CrossRef]
Del Giudice, S., Savino, S., and Nonino, C., 2010, Forced Convection in Laminar Duct Flows of Liquids With Temperature Dependent Properties: A Simplified Approach, in Proceedings of 28th UIT Heat Transfer Congress, UIT, pp. 231–236.
Shannon, R. L., and Depew, C. A., 1969, “Forced Laminar Flow Convection in a Horizontal Tube With Variable Viscosity and Free Convection Effects,” ASME J. Heat Transfer, 91, pp. 251–258. [CrossRef]
Joshi, S. D., and Bergles, A. E., 1980, “Analytical Study of Heat Transfer to Laminar In-Tube Flow of Non-Newtonian Fluids,” AIChE Symp. Ser., 76(199), pp. 270–281.
Lin, C. R., and Chen, C. K., 1994, “Effect of Temperature Dependent Viscosity on the Flow and Heat Transfer over an Accelerating Surface,” J. Phys. D: Appl. Phys., 27, pp. 29–36. [CrossRef]
Costa, A., and Macedonio, G., 2002, “Nonlinear Phenomena in Fluids With Temperature-Dependent Viscosity: An Hysteresis Model for Magma Flow in Conduits,” Geophys. Res. Lett., 29(10), pp. 40-1–40-4. [CrossRef]
Costa, A., and Macedonio, G., 2003, “Viscous Heating for Fluids With Temperature Dependent Viscosity: Implications for Magma Flows,” Nonlinear Process. Geophys., 10, pp. 545–555. [CrossRef]
Patankar, S. V., and Spalding, D. B., 1972, “A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows,” Int. J. Heat Mass Transfer, 15, pp. 1787–1806. [CrossRef]
Hirsh, C., 1988, Numerical Computation of Internal and External Flows, Vol. 1, Wiley, New York, p. 70.
Javeri, V., 1977, “Heat Transfer in Laminar Entrance Region of a Flat Channel for the Temperature Boundary Condition of the Third Kind,” Wärme- und Stoffübertragung, 10, pp. 137–144. [CrossRef]
Nonino, C., Del Giudice, S., and Savino, S., 2006, “Temperature Dependent Viscosity Effects on Laminar Forced Convection in the Entrance Region of Straight Ducts,” Int. J. Heat Mass Transfer, 49, pp. 4469–4481. [CrossRef]
Del Giudice, S., Savino, S., and Nonino, C., 2011, “Entrance and Temperature Dependent Viscosity Effects on Laminar Forced Convection in Straight Ducts With Uniform Wall Heat Flux,” ASME J. Heat Transfer, 133, p. 101702. [CrossRef]
Nonino, C., 2003, “A Simple Pressure Stabilization for a SIMPLE-Like Equal-Order FEM Algorithm,” Numer. Heat Transfer, Part B, 44, pp. 61–81. [CrossRef]

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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