Transport in Porous Media

, 89:421 | Cite as

Control of Flow and Heat Transfer in a Porous Enclosure due to an Adiabatic Thin fin on the Hot Wall

  • M. SathiyamoorthyEmail author
  • S. Narasimman


Natural convection flow in a differentially heated square enclosure filled with porous matrix with a solid adiabatic thin fin attached at the hot left wall is studied numerically. The Brinkman–Forchheimer-extended Darcy model is used to solve the momentum equations, in the porous medium. The numerical investigation is done through streamlines, isotherms, and heat transfer rates. A parametric study is carried out using the following parameters: Darcy number (Da) from 10−4 to 10−2, dimensionless thin fin lengths (L p) 0.3, 0.5, and 0.7, dimensionless positions (S p) 0.25, 0.5, and 0.75 with Prandtl numbers (Pr) 0.7 and 100 for Ra = 106. For Da = 10−3 and Pr = 0.7, it is observed that there is a counter clock-wise secondary flow formation around the tip of the fin for S p = 0.5 for all lengths of L p. Moreover when Da = 10−2 the secondary circulation behavior has been observed for S p = 0.25 and 0.75 and there is another circulation between the top wall and the fin that is separated from the primary circulation. However, these secondary circulations features are not observed for Pr = 100. It is also found that the average Nusselt number decreases as the length of the fin increases for all locations. However, the rate of decrease of average Nusselt number becomes slower as the location of fin moves from the bottom wall to the top wall. The overall heat transfer rate can be controlled with a suitable selection of the fin location and length.


Natural convection Non-Darcy flow Thin fin Square cavity 

List of Symbols


Acceleration due to gravity, m s−2


Darcy number


Forchheimer number


Permeability of the porous medium


Length of the fin, m


Position of the fin at the bottom wall, m


Length of the square cavity, m


Dimensionless length of the fin, = l p/L


Dimensionless position of fin at the left wall, = s p/L


The normal direction on a enclosure wall


Total number of nodes


Local Nusselt number


Local Nusselt number at the side wall

\({\overline {Nu}}\)

Average Nusselt number

\({\overline {Nu_{\rm s}}}\)

Average Nusselt number at the side wall


Pressure, Pa


Dimensionless fluid pressure


Prandtl number


Rayleigh number


Fluid temperature, K


Temperature of cold right wall, K


Temperature of hot left wall, K


x component of velocity


x component of dimensionless velocity


y component of velocity


y component of dimensionless velocity


Dimensionless distance along x coordinate


Dimensionless distance along y coordinate

Greek Symbols


Thermal diffusivity, m2 s−1


Volume expansion coefficient, K−1


Penalty parameter


Dimensionless temperature


Stream function





Left wall


Right wall


Side wall


Partition or fin


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsGovernment Thirumagal Mills CollegeGudiyathamIndia
  2. 2.Department of MathematicsSSN College of EngineeringChennaiIndia

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