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Research Papers: Natural and Mixed Convection

Gaseous Slip Flow Mixed Convection in Vertical Microducts With Constant Axial Energy Input

[+] Author and Article Information
Arman Sadeghi

School of Mechanical Engineering,
Sharif University of Technology,
P.O. Box 11155-9567,
Tehran, Iran
e-mail: armansadeghi@mech.sharif.edu

Mostafa Baghani

School of Mechanical Engineering,
College of Engineering,
University of Tehran,
P.O. Box 11155-4563,
Tehran, Iran
e-mail: baghani@ut.ac.ir

Mohammad Hassan Saidi

School of Mechanical Engineering,
Sharif University of Technology,
P.O. Box 11155-9567,
Tehran, Iran
e-mail: saman@sharif.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 9, 2012; final manuscript received October 27, 2013; published online December 23, 2013. Assoc. Editor: Oronzio Manca.

J. Heat Transfer 136(3), 032501 (Dec 23, 2013) (13 pages) Paper No: HT-12-1490; doi: 10.1115/1.4025919 History: Received September 09, 2012; Revised October 27, 2013

The present investigation is devoted to the fully developed slip flow mixed convection in vertical microducts of two different cross sections, namely, polygon, with circle as a limiting case, and rectangle. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The velocity and temperature discontinuities at the boundary are incorporated into the solutions using the first-order slip boundary conditions. The method considered is mainly analytical in which the governing equations in cylindrical coordinates along with the symmetry conditions and finiteness of the flow parameter at the origin are exactly satisfied. The first-order slip boundary conditions are then applied to the solution using the point matching technique. The results show that both the Nusselt number and the pressure drop parameter are increasing functions of the Grashof to Reynolds ratio. It is also found that, with the exception of the H2 Nusselt number of the triangular duct, which shows an opposite trend, both the Nusselt number and the pressure drop are decreased by increasing the Knudsen number. Furthermore, the pressure drop of the H2 case is found to be higher than that obtained by assuming an H1 thermal boundary condition.

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Figures

Grahic Jump Location
Fig. 1

Geometries of the ducts being considered along with the coordinate system; the bold dot shows the origin of the coordinate system for each geometry

Grahic Jump Location
Fig. 2

Dimensionless velocity distribution for H1 case with Kn = 0.012 at different values of Gr/Re (a) triangular channel and (b) rectangular channel with α = 0.5

Grahic Jump Location
Fig. 3

Dimensionless temperature distribution for H1 case with Kn = 0.012 at different values of Gr/Re (a) triangular channel and (b) rectangular channel with α = 0.5

Grahic Jump Location
Fig. 4

Distributions of u* and T* for a square duct with H2 thermal boundary conditions at different Knudsen numbers and angular positions while keeping Gr/Re = 40 (a) u* and (b) T*

Grahic Jump Location
Fig. 5

Heat flux ratio as a function of normalized angular coordinate for a triangular duct with H1 thermal boundary conditions at different values of Gr/Re and Kn

Grahic Jump Location
Fig. 6

Nusselt number versus Gr/Re for polygonal duct (a) M = 3, (b) M = 4, (c) M = 5, and (d) M = 6

Grahic Jump Location
Fig. 7

Nusselt number versus Gr/Re for rectangular duct (a) α = 0.4, (b) α = 0.6, (c) α = 0.8, and (d) α = 1

Grahic Jump Location
Fig. 8

Pressure drop parameter versus Gr/Re for polygonal duct (a) M = 3, (b) M = 4, (c) M = 5, and (d) M = 6

Grahic Jump Location
Fig. 9

Pressure drop parameter versus Gr/Re for rectangular duct (a) α = 0.4, (b) α = 0.6, (c) α = 0.8, and (d) α = 1

Grahic Jump Location
Fig. 10

Nusselt number and pressure drop parameter as functions of Gr/Re for circular duct

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