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Porous Media

# Numerical Investigation of Forced Convective Heat Transfer Around and Through a Porous Circular Cylinder With Internal Heat Generation

[+] Author and Article Information

School of Mechanical Engineering,  Semnan University,3519645399 Semnan, Iranmsvalipour@semnan.ac.ir

J. Heat Transfer 134(6), 062601 (Apr 26, 2012) (7 pages) doi:10.1115/1.4005741 History: Received July 02, 2010; Revised October 23, 2011; Published April 26, 2012; Online April 26, 2012

## Abstract

In this study, convective heat transfer around and through a porous circular cylinder together with internal heat generation has been investigated numerically. Governing equations containing continuity, momentum, and energy equations have been developed in polar coordinate system in both porous and nonporous media based on single-domain approach. However, governing equations in porous medium are derived using intrinsic volume averaging method. The equations are solved numerically based on finite volume method over staggered grid arrangement. Also, pressure correction-based iterative algorithm, SIMPLE, is applied for solving the pressure linked equations. Reynolds and Peclet numbers (based on cylinder diameter and velocity of free stream) are from 1 to 40. Also, Darcy number (Da) varies within the range of $10-6≤Da≤10-2$ and porosity is considered 0.9 for all calculations. The influence of Da and Re numbers on local and average Nu numbers has been investigated. It is found that the local and average Nu numbers increase with any increase in Da number. Two correlations of average Nu number are presented for high and low Da numbers.

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## Figures

Figure 1

Schematic configuration of computational domain and coordinate system

Figure 2

A typical grid distribution inside and around the porous cylinder

Figure 3

Comparison of local Nu number for forced convective heat transfer around a solid circular cylinder with the results of Bharti [5]

Figure 4

Local Nu number variation on the surface of the porous cylinder at different Da for (a) Re=10, (b) Re=20, and (c) Re=40

Figure 5

Variation of average Nusselt number on the surface of the porous cylinder versus Da for different Re numbers

Figure 6

Nondimensional temperature profile on symmetry line at different Da for: (a) Re=10, (b) Re=20, and (c) Re=40

Figure 7

The position of maximum dimensionless temperature on symmetry axis as a function of Da for different Re

Figure 8

Isothermal contours inside and around porous cylinder at Re = 10 for: (a) Da=10-2 (b) Da=10-6

Figure 9

Isothermal contours inside and around porous cylinder at Re = 20 for: (a) Da=10-2 (b) Da=10-6

Figure 10

Isothermal contours inside and around porous cylinder at Re = 40 for: (a) Da=10-2 (b) Da=10-6

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