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Research Papers: Fundamental Issues and Canonical Flows

# Analysis of Forced Convection in a Circular Tube Filled With a Darcy–Brinkman–Forchheimer Porous Medium Using Spectral Homotopy Analysis Method

[+] Author and Article Information

Saeid Abbasbandy

Department of Mathematics, Science and Research Branch,  Islamic Azad University, Tehran, Iran

J. Fluids Eng 133(10), 101207 (Oct 05, 2011) (9 pages) doi:10.1115/1.4004998 History: Received February 15, 2011; Revised August 30, 2011; Published October 05, 2011; Online October 05, 2011

## Abstract

This paper provides a fresh analytical solution for fully developed forced convection through a Darcy–Brinkman–Forchheimer porous medium imbedded inside a circular tube, with imposed uniform heat flux at walls. A spectral homotopy analysis method is applied to present a solution which spans a wide range of the main parameters (the Darcy number (Da), viscosity ratio (M), and Forchheimer number (F)). The analytical results are compared with data available in the literature, and excellent agreement is found. The paper is capable of addressing the problem in a general porous medium for which both inertial and boundary-friction effects affect the flow and heat transfer physics. In order to serve this aim, the influence of Da, M, and F on the dimensionless velocity and temperature profiles, as well as Nusselt number, are investigated.

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## Figures

Figure 6

Comparison between normalized velocity of the present work with experimental and numerical results of Ref [26]

Figure 7

Effect of Darcy number on the dimensionless velocity profile

Figure 1

Schematic of the problem

Figure 2

(a)–(c) h curves for the tenth order of approximation

Figure 3

(a)–(f) Residual error of the tenth order of approximation versus h

Figure 4

Comparison between normalized velocities of the present work with those of Ref. [13]

Figure 5

Comparison between dimensionless temperature distributions of the present work with those of Ref. [13]

Figure 8

Effect of viscosity ratio on the dimensionless velocity profile

Figure 9

(a)–(e) Effect of form drag term on the dimensionless velocity profile in different values of Da

Figure 10

Effect of Darcy number on the dimensionless temperature distribution

Figure 11

Effect of viscosity ratio on the dimensionless temperature distribution

Figure 12

(a), (b) Effect of form drag term on the dimensionless temperature distribution

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