0
Research Papers

Conjugated Convection-Conduction Analysis in Microchannels With Axial Diffusion Effects and a Single Domain Formulation

[+] Author and Article Information
Renato M. Cotta

e-mail: cotta@mecanica.coppe.ufrj.br
Laboratory of Transmission and Technology of Heat, LTTC,
Mechanical Engineering Department—POLI and COPPE, UFRJ,
Universidade Federal do Rio de Janeiro, Cidade Universitária,
Cx. Postal 68503,
Rio de Janeiro, RJ, CEP 21945-970, Brazil

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received June 26, 2012; final manuscript received February 18, 2013; published online July 26, 2013. Guest Editors: G. P. “Bud” Peterson and Zhuomin Zhang.

J. Heat Transfer 135(9), 091401 (Jul 26, 2013) (10 pages) Paper No: HT-12-1313; doi: 10.1115/1.4024425 History: Received June 26, 2012; Revised February 18, 2013

An extension of a recently proposed single domain formulation of conjugated conduction–convection heat transfer problems is presented, taking into account the axial diffusion effects at both the walls and fluid regions, which are often of relevance in microchannels flows. The single domain formulation simultaneously models the heat transfer phenomena at both the fluid stream and the channel walls, by making use of coefficients represented as space variable functions, with abrupt transitions occurring at the fluid-wall interface. The generalized integral transform technique (GITT) is then employed in the hybrid numerical–analytical solution of the resulting convection–diffusion problem with variable coefficients. With axial diffusion included in the formulation, a nonclassical eigenvalue problem may be preferred in the solution procedure, which is itself handled with the GITT. To allow for critical comparisons against the results obtained by means of this alternative solution path, we have also proposed a more direct solution involving a pseudotransient term, but with the aid of a classical Sturm-Liouville eigenvalue problem. The fully converged results confirm the adequacy of this single domain approach in handling conjugated heat transfer problems in microchannels, when axial diffusion effects must be accounted for.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Schematic representation of the conjugated heat transfer problem in a microchannel

Grahic Jump Location
Fig. 3

Convergence behavior of the 25th eigenfunction of the problem defined in Eq. (4), for different truncation orders of the auxiliary algebraic eigenvalue problem, Eqs. (8), INC,aux = 30, 35, 40, 45, and 50. Pe = 0.5.

Grahic Jump Location
Fig. 2

Representation of the space variable coefficients with the abrupt transition occurring at the interface fluid–solid wall: (a) U(Y) and (b) K(Y)

Grahic Jump Location
Fig. 8

Fluid bulk temperature along the microchannel length for Pe = 0.75, 1.5, and 3

Grahic Jump Location
Fig. 9

Local Nusselt number along the microchannel length for (a) Pe = 0.75; (b) Pe = 1.5; and (c) Pe = 3

Grahic Jump Location
Fig. 4

Transversal temperature profiles calculated using the single domain formulation via the nonclassical eigenvalue problem (Sec. 2.2) (solid curves) in comparison with the partial integral transformation solution (Sec. 2.3) (dashed curves) for Pe = 0.5

Grahic Jump Location
Fig. 5

Temperature evolution along Z for different transversal positions, Y = 0 (centerline), 0.3, 0.5, 0.7, and 0.9, using the single domain formulation via the nonclassical eigenvalue problem (Sec. 2.2) (solid curves) in comparison with the partial integral transformation solution (Sec. 2.3) (dashed curves) for Pe = 0.5

Grahic Jump Location
Fig. 6

Temperature evolution at the centerline of the channel (Y = 0) for different Péclet numbers, Pe = 0.05, 0.5, 1.25, 2.5, 3.75, and 5, using the single domain formulation via the nonclassical eigenvalue problem (Sec. 2.2) (solid curves) in comparison with the partial integral transformation solution (Sec. 2.3) (dashed curves)

Grahic Jump Location
Fig. 7

Temperature contours along the microchannel cross-section, including the fluid stream, from Y = − 0.5 to 0.5 and the channel walls, from Y = −1.0 to −0.5 and from Y = 0.5 to 1.0 with Pe = 0.5

Grahic Jump Location
Fig. 10

Pe = 30: (a) fluid bulk temperature along the microchannel length and (b) local Nusselt number along the microchannel length

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