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Technical Briefs

Analytical Solution for Forced Convection in a Sector Duct Filled With a Porous Medium

[+] Author and Article Information
C. Y. Wang

Departments of Mathematics and Mechanical Engineering, Michigan State University, East Lansing, MI 48824cywang@mth.msu.edu

J. Heat Transfer 132(8), 084502 (Jun 04, 2010) (4 pages) doi:10.1115/1.4001102 History: Received August 25, 2009; Revised January 06, 2010; Published June 04, 2010; Online June 04, 2010

Abstract

The fully developed viscous flow through a sector duct filled with a porous medium is studied. The Darcy–Brinkman and energy equations are solved analytically by series expansions in Bessel functions of the first kind. The problem is governed by a porous medium parameter $s$, which is proportional to the inverse square root of the permeability. For large $s$ there exists a boundary layer on the walls, and the resistance increases greatly. The Nusselt number for the H1 heat transfer problem also increases. If the apex angle is acute, the local velocity and heat transfer are very low. If the apex angle is obtuse, the local shear and heat transfer are large. Tables for the friction factor-Reynolds number products and Nusselt numbers are determined for various $s$ and apex angles.

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Figures

Figure 1

Cross section of the sector duct

Figure 2

The case when s=10 and β=π: (a) constant velocity lines Δw=0.002; (b) constant temperature lines Δτ=−0.00025

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