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Forced Convection

Convective Heat Transfer in Microchannels of Noncircular Cross Sections: An Analytical Approach

[+] Author and Article Information
S. Shahsavari1

Laboratory for Alternative Energy Conversion, Mechatronic Systems Engineering, School of Engineering Science,  Simon Fraser University, BC V3T 0A3, Canada

A. Tamayol, E. Kjeang, M. Bahrami

Laboratory for Alternative Energy Conversion, Mechatronic Systems Engineering, School of Engineering Science,  Simon Fraser University, BC V3T 0A3, Canada

1

Corresponding author.

J. Heat Transfer 134(9), 091701 (Jun 25, 2012) (10 pages) doi:10.1115/1.4006207 History: Received May 02, 2011; Revised February 03, 2012; Published June 25, 2012; Online June 25, 2012

Analytical solutions are presented for velocity and temperature distributions of laminar fully developed flow of Newtonian, constant property fluids in micro/minichannels of hyperelliptical and regular polygonal cross sections. The considered geometries cover several common shapes such as ellipse, rectangle, rectangle with round corners, rhombus, star-shape, and all regular polygons. The analysis is carried out under the conditions of constant axial wall heat flux with uniform peripheral heat flux at a given cross section. A linear least squares point matching technique is used to minimize the residual between the actual and the predicted values on the boundary of the channel. Hydrodynamic and thermal characteristics of the flow are derived; these include pressure drop and local and average Nusselt numbers. The proposed results are successfully verified with existing analytical and numerical solutions from the literature for a variety of cross sections. The present study provides analytical-based compact solutions for velocity and temperature fields that are essential for basic designs, parametric studies, and optimization analyses required for many thermofluidic applications.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 4

Dimensionless velocity and temperature contours in a star-shaped channel with = 0.5 and = 1, using (a) Eq. 8 and (b) Eq. 23

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Figure 5

Dimensionless velocity and temperature contours in a square with round corners duct, = 4, using (a) Eq. 8 and (b) Eq. 23

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Figure 6

Comparison of the values of Poiseuille number in channels of hyperelliptical cross section calculated using the present model with numerical results of Shah [23]

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Figure 7

Comparison of the values of Nusselt number in channels of hyperelliptical cross section calculated using the present model with numerical results of Shah [23]

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Figure 8

Comparison of the values of Poiseuille number and Nusselt number in channels of polygonal cross section calculated using the present model with numerical results of Shah [23]

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Figure 9

Variation of the local Nusselt number in channels of hyperelliptical cross section, ɛ = 1

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Figure 3

Considered geometry for modeling (a) hyperelliptical and (b) regular polygonal cross section and the applied boundary conditions

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Figure 2

Regular polygons with different number of sides

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Figure 1

Hyperelliptical cross sections for ɛ=1

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