Skip to main content
SpringerLink
Log in

Heat Transfer Characteristics of Reciprocating Flows in Channels Partially Filled with Porous Medium

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

This paper presents the effect of introducing a porous medium on the flow regime and heat transfer of a two-dimensional channel through which the flow is reciprocating. The channel is discretely heated from above and is insulated in the bottom which can simulate a cooling mechanism for compact circuit boards. In this ideal geometry, a fully developed reciprocating flow is established via oscillating pressure gradient. In side boundaries, velocity and temperature are assumed to be periodic. A certain volume of this channel is occupied by a porous medium which is shown to be an effecting tool for augmentation of heat transfer. At first, Momentum equations of the domain are solved analytically (Brinkman-extended Darcy model is used for porous region) and then the energy equation is solved numerically using alternating direction implicit (ADI) method. Finally a case study is investigated for a high-porous and high-conductive medium (Aluminum alloy T-6201) and the enhancing effect and optimization criteria are discussed in the result section.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

A :

Dimensionless pressure gradient amplitude

B :

Constant defined by Eq.24

C:

Constant defined by Eq.24

c p :

Specific heat capacity (J/kg)

D:

Constant defined by Eq.29

Da :

Darcy number

E:

Constant defined by Eq.29

f :

Frequency (s−1)

H :

Dimensionless channel height

K :

Permeability (m2)

k :

Conductivity (W/mK)

L :

Dimensionless channel length

P :

Dimensionless pressure

Pr :

Prandtl number

Pe :

Peclet number

q :

Dimensionless heat transfer per unit area

\({\Re}\) :

Real Part of a complex number

S :

Dimensionless distance of porous layer from channel line

T :

Dimensionless temperature of the field

u :

Dimensionless velocity

α :

Womersley number

γ :

Oscillation resistance

ε :

Porosity

μ :

Dynamic viscosity (Pa s)

υ :

Kinematic viscosity (m2/s)

\({\phi}\) :

Complex velocity (m/s)

ω :

Angular frequency (rad/s)

*:

Dimensional quantity

0:

Wall Parameter

eff:

Porous property

f:

Fluid property

p:

Porous property

opt:

Optimum

References

  • Alazmi B.K., Vafai K.: Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer. Int. J. Heat Mass Transf. 44, 1735–1749 (2001)

    Article  Google Scholar 

  • Beavers G.S., Joseph D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207 (1967)

    Article  Google Scholar 

  • Beckmann C., Viskanta R.S., Ramadhyani S.: Natural convection in vertical enclosures containing simultaneously fluid and porous layers. J. Fluid Mech. 186, 257–284 (1988)

    Article  Google Scholar 

  • Bhattacharya A., Mahajan R.L.: Finned metal foam heat sinks for electronics cooling in forced convection. J. Electron. Packag. 124, 155–163 (2002)

    Article  Google Scholar 

  • Bhattacharya A., Calmidi V.V., Mahajan R.L.: Thermo-physical properties of high porosity metal foams. Int. J. Heat Mass Transf. 45, 1017–1031 (2002)

    Article  Google Scholar 

  • Byun S.Y., Ro S.T., Shin J.Y., Son Y.S., Lee D.Y.: Transient thermal behavior of porous media under oscillating flow condition. Int. J. Heat Mass Transf. 49, 5081–5085 (2006)

    Article  Google Scholar 

  • Chung T.J.: Computational fluid dynamics, 1st ed, pp. 72–73. Cambridge University Press, Cambridge (2002)

    Book  Google Scholar 

  • Cooper W.L., Nee V.W., Yang K.T.: An experimental investigation of convective heat transfer from the heated floor of a rectangular duct to a low frequency large tidal displacement oscillatory flow. Int. J. Heat Mass Transf. 37, 581–592 (1994)

    Article  Google Scholar 

  • Hwang G., Chao C.: Heat transfer measurement and analysis for sintered porous channels. J. Heat Transf. 116, 456–464 (1994)

    Article  Google Scholar 

  • Incropera F.P., DeWitt D.P., Bergman T.L., Lavine A.S.: Fundamentals of heat and mass transfer, chap. 9, 6th ed, pp. 574–579. Wiley, New York (2006)

    Google Scholar 

  • Jen T.C., Yan T.Z.: Developing fluid flow and heat transfer in a channel partially filled with porous medium. Int. J. Heat Mass Transf. 48, 3995–4009 (2005)

    Article  Google Scholar 

  • Khodadadi J.M.: Oscillatory fluid flow through a porous medium channel bounded by two impermeable parallel plates. J. Fluids Eng. 113, 509–511 (1991)

    Article  Google Scholar 

  • Kuznetsov A.V., Nield D.A.: Forced convection with laminar pulsating flow in a saturated porous channel or tube. Transp. Porous Med. 65, 505–523 (2006)

    Article  Google Scholar 

  • Leong K.C., Jin L.W.: An experimental study of heat transfer in oscillating flow through a channel filled with an aluminum foam. Int. J. Heat Mass Transf. 48, 243–253 (2005)

    Article  Google Scholar 

  • Leong K.C., Jin L.W.: Effect of oscillatory frequency on heat transfer in metal foam heat sinks of various pore densities. Int. J. Heat Mass Transf. 49, 671–681 (2006)

    Article  Google Scholar 

  • Liao Q.D., Yang K.T., Nee V.W.: Microprocessor chip cooling by channeled zero-mean oscillatory air flow. Adv Electron. Packag. 10(2), 789–794 (1995)

    Google Scholar 

  • Mathews J.H., Howell R.W.: Complex Analysis for Mathematics and Engineering, 4th ed, pp. 7–38. Jones & Bartlett Pub, Sudbury, MA (2000)

    Google Scholar 

  • Nield D.A., Kuznetsov A.V.: Forced convection with laminar pulsating flow in a channel or tube. Int. J. Therm. Sci. 46, 551–560 (2007)

    Article  Google Scholar 

  • Poulikakos D., Kazmierczak M.: Forced convection in a duct partially filled with a porous material. J. Heat Transf. 109, 653–662 (1987)

    Article  Google Scholar 

  • Rachedi R.S., Chikh S.: Enhancement of electronic cooling by insertion of foam materials. Heat Mass Transf. 37, 371–378 (2001)

    Article  Google Scholar 

  • Richardson E.G., Tyler E.: The transverse velocity gradient near the mouths of pipes in which an alternating or continuous flow of air is established. Proc. Phys. Soc. Lond. 42, 1–15 (1929)

    Article  Google Scholar 

  • Sert C., Beskok A.: Numerical simulation of reciprocating flow forced convection in two-dimensional channels. J. Heat Transf. 125, 403–412 (2003)

    Article  Google Scholar 

  • Siegel R.: Influence of oscillation-induced diffusion on heat transfer in uniformly heated channel. J. Heat Transf. 109, 244–247 (1987)

    Article  Google Scholar 

  • Somerton C.W., Catton I.: On the thermal instability of superimposed porous and fluid layers. J. Heat Transf. 104, 160–165 (1982)

    Article  Google Scholar 

  • Vafai K., Kim S.J.: Analysis of surface enhancement by a porous substrate. J. Heat Transf. 112, 700–706 (1990)

    Article  Google Scholar 

  • Vafai K., Thiyagaraja R.: Analysis of flow and heat transfer at the interface region of a porous medium. Int. J. Heat Mass Transf. 30, 1391–1405 (1987)

    Article  Google Scholar 

  • Zhao T., Cheng P.: A numerical solution of laminar forced convection in a pipe subjected to a reciprocating flow. Int. J. Heat Mass Transf. 38, 3011–3022 (1995)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Aeroacoustics Lab, Mechanical Engineering Department, McGill University, Room 256, McDonald Eng. Build., 817 Sherbrooke St. West, Montreal, QC, Canada

    Kaveh Habibi

  2. Mechanical Engineering Department, McGill University, Montreal, QC, Canada

    Ali Mosahebi

  3. School of Mechanical Engineering, University of Tehran, Tehran, Iran

    Hossein Shokouhmand

Authors
  1. Kaveh Habibi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Mosahebi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hossein Shokouhmand
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kaveh Habibi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Habibi, K., Mosahebi, A. & Shokouhmand, H. Heat Transfer Characteristics of Reciprocating Flows in Channels Partially Filled with Porous Medium. Transp Porous Med 89, 139–153 (2011). https://doi.org/10.1007/s11242-011-9759-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-011-9759-0

Keywords

Search

Navigation