0
TECHNICAL PAPERS: Micro/Nanoscale Heat Transfer

Temperature-Dependent Viscosity and Viscous Dissipation Effects in Simultaneously Developing Flows in Microchannels With Convective Boundary Conditions

[+] Author and Article Information
C. Nonino1

Dipartimento di Energetica e Macchine, Università degli Studi di Udine, Via delle Scienze 208, 33100 Udine, Italycarlo.nonino@uniud.it

S. Del Giudice, S. Savino

Dipartimento di Energetica e Macchine, Università degli Studi di Udine, Via delle Scienze 208, 33100 Udine, Italy

1

Corresponding author.

J. Heat Transfer 129(9), 1187-1194 (Dec 11, 2006) (8 pages) doi:10.1115/1.2740306 History: Received July 25, 2006; Revised December 11, 2006

The effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels are studied with reference to convective boundary conditions. Two different geometries, namely the circular tube and the parallel plate channel, are considered. Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. A finite element procedure, based on a projection algorithm, is employed for the step-by-step solution of the parabolized momentum and energy equations. Axial distributions of the local overall Nusselt number and of the apparent Fanning friction factor are presented with reference to both heating and cooling conditions for two different values of the Biot number. Examples of radial temperature profiles at different axial locations and of axial distributions of centerline velocity and temperature are also shown.

FIGURES IN THIS ARTICLE
<>
Copyright © 2007 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Axial distributions of the Nusselt number Nuc for thermally developing and hydrodynamically fully developed flows of constant property fluids in circular ducts with convective boundary conditions (Bi=4): comparisons of numerical results (solid lines) with analytical solutions by Lin (32) (diamonds) for different values of the Brinkman number.

Grahic Jump Location
Figure 2

Axial distribution of (fappRe)c for simultaneously developing flows of constant property fluids in circular ducts and parallel plate channels: comparisons of numerical results (solid line) with literature data (3) (squares).

Grahic Jump Location
Figure 3

Axial distributions of the local overall Nusselt number (Nuo)c for simultaneously developing flows of constant property fluids with Prm=5 in microchannels of circular cross section with different Brinkman numbers Brm: (a) Bi=5; and (b) Bi=20.

Grahic Jump Location
Figure 4

Axial distributions of the local overall Nusselt number (Nuo)c for simultaneously developing flows of constant property fluids with Prm=5 in flat microchannels with different Brinkman numbers Brm: (a) Bi=5; and (b) Bi=20.

Grahic Jump Location
Figure 5

Axial distributions of the ratio Nuo∕(Nuo)c for microchannels of circular cross section with Prm=5 and different Brinkman numbers Brm: (a) Bi=5; and (b) Bi=20.

Grahic Jump Location
Figure 6

Axial distributions of the ratio Nuo∕(Nuo)c for flat microchannels with Prm=5 and different Brinkman numbers Brm: (a) Bi=5; and (b) Bi=20.

Grahic Jump Location
Figure 7

Axial distributions of the ratio fappRem∕(fappRem)c for microchannels of circular cross section with Prm=5 and different Brinkman numbers Brm: (a) Bi=5; and (b) Bi=20.

Grahic Jump Location
Figure 8

Axial distributions of the ratio fappRem∕(fappRem)c for flat microchannels with Prm=5 and different Brinkman numbers Brm: (a) Bi=5; and (b) Bi=20.

Grahic Jump Location
Figure 9

Radial profiles of dimensionless temperature T at different axial locations for microchannels of circular cross section with Prm=5, ∣Brm∣=0.1, and Bi=5: (a) fluid heating; and (b) fluid cooling.

Grahic Jump Location
Figure 10

Transverse profiles of dimensionless temperature T at different axial locations for flat microchannels with Prm=5, ∣Brm∣=0.1, and Bi=5: (a) fluid heating; and (b) fluid cooling.

Grahic Jump Location
Figure 11

Axial distributions of dimensionless velocity and temperature at the center of the cross section of circular and flat microchannels with Prm=5 and ∣Brm∣=0.1: (a) U0′, and (b) T0.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In