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Heat and Mass Transfer

, Volume 41, Issue 9, pp 799–809 | Cite as

Numerical simulation of three-dimensional natural convection inside a heat generating anisotropic porous medium

  • Ch. S. Y. Suresh
  • Y. Vamsee Krishna
  • T. Sundararajan
  • Sarit K. DasEmail author
Original

Abstract

Natural convection in anisotropic heat generating porous medium enclosed inside a rectangular cavity has been studied. A 3D finite volume based code is developed using the Darcy approximation and validated using experimental results of natural convection around an enclosed rod bundle. Subsequently, detailed simulation is carried out for a cavity, filled with orthotropic porous medium. The effects of heat generation, geometry and anisotropy are studied. Anisotropy is found to be of significant importance for both maximum value and distribution of temperature.

Keywords

Porous Medium Natural Convection Rayleigh Number Rectangular Cavity Permeability Ratio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

A

Aspect ratio \( \left( {\frac{{L_z }} {L}} \right) \)

g

Acceleration due to gravity, m s−2

k

Thermal conductivity, W m−1 K−1

K

Permeability, m2

K*

Permeability ratio \( \left( {\frac{{K_z }} {{K_x }}} \right) \)

L

Length in x-direction, m

p

Pressure, N m−2

P

Non-dimensional pressure, \( P = \frac{p} {{\mu \alpha _x /K_x }} \)

\( q''' \)

Internal heat generation rate, W m−3

Ra*

Modified Rayleigh number, \({\text{Ra}}^* = {\text{ }}\frac{{\rho g\beta \left( {q'''L^2 /k_x } \right)K_z L}} {{\nu \alpha _x }}\)

T

Temperature, K

Tcw

Temperature of cold wall, K

Tf, \( T_\infty \)

Constant cooling fluid (air) temperature, K

u

Velocity in x-direction, m s−1

v

Velocity in y-direction, m s−1

w

Velocity in z-direction, m s−1

U

Non-dimensional velocity in X-direction, \( U = \frac{u} {{\alpha _x /L}}, \)

V

Non-dimensional velocity in Y-direction, \( V = \frac{v} {{\alpha _x /L}}, \)

W

Non-dimensional velocity in W-direction, \( W = \frac{w} {{\alpha _x /L}} \)

x, y, z

Co-ordinates in dimensional form, m

X, Y, Z

Co-ordinates in non-dimensional form \( \left( {X = \frac{x} {L},\,Y = \frac{y} {L},\,Z = \frac{z} {L}} \right) \)

Greek Symbols

K*

Permeability ratio \( \left( {\frac{{K_z }} {{K_x }}} \right) \)

λ

Thermal conductivity ratio \( \left( {\frac{{k_z }} {{k_x }}} \right) \)

ρ

Density, kg m−3

α

Thermal diffusivity, m2 s−1

β

Coefficient of thermal expansion, K–1

μ

Viscosity of fluid, N s m−2

ν

Kinematic viscosity, m2 s−1

θ

Non-dimensional temperature \( \left( {\theta = \frac{{T - T_f }} {{q^{'''} L^2 /k_x }}} \right) \)

References

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    Prasad V (1985) Thermal convection of a heat generating porous medium in a rectangular cavity, heat transfer in porous media and particulate flows. ASME HTD 46:209–216Google Scholar
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    Suresh ChSY, Vamsee Krishna Y, Sateesh G, Deepak Philip Thomas, Harichandan M, Dhanasekaran MR, Murali K (2003) Theoretical and experimental investigation of heat transfer from totally blocked fuel subassembly of a liquid metal fast breeder reactor. A project report submitted to IGCAR, Kalpakkam. Department of Mechanical Engineering, Indian Institute of Technology Madras, ChennaiGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Ch. S. Y. Suresh
    • 1
  • Y. Vamsee Krishna
    • 1
  • T. Sundararajan
    • 1
  • Sarit K. Das
    • 1
    Email author
  1. 1.Heat Transfer and Thermal Power Laboratory, Department of Mechanical EngineeringIndian Institute of Technology MadrasChennaiIndia

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