Free Convection of a Bingham Fluid in a Differentially-Heated Porous Cavity: The Effect of a Square Grid Microstructure

Research output: Contribution to journalArticlepeer-review

2 Citations (SciVal)
56 Downloads (Pure)

Abstract

We examine how a square-grid microstructure affects the manner in which a Bingham fluid is convected in a sidewall-heated rectangular porous cavity. When the porous microstructure is isotropic, flow arises only when the Darcy–Rayleigh number is higher than a critical value, and this corresponds to when buoyancy forces are sufficient to overcome the yield threshold of the Bingham fluid. In such cases, the flow domain consists of a flowing region and stagnant regions within which there is no flow. Here, we consider a special case where the constituent pores form a square grid pattern. First, we use a network model to write down the appropriate macroscopic momentum equations as a Darcy–Bingham law for this microstructure. Then detailed computations are used to determine strongly nonlinear states. It is found that the flow splits naturally into four different regions: (i) full flow, (ii) no-flow, (iii) flow solely in the horizontal direction and (iv) flow solely in the vertical direction. The variations in the rate of heat transfer and the strength of the flow with the three governing parameters, the Darcy–Rayleigh number, Ra, the Rees–Bingham number, Rb, and the aspect ratio, A, are obtained.
Original languageEnglish
Pages (from-to)202-216
Number of pages15
JournalPhysics
Volume4
Issue number1
Early online date10 Feb 2022
DOIs
Publication statusPublished - 31 Mar 2022

Keywords

  • Anisotropic
  • Bingham fluid
  • Free convection
  • Porous media

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Fingerprint

Dive into the research topics of 'Free Convection of a Bingham Fluid in a Differentially-Heated Porous Cavity: The Effect of a Square Grid Microstructure'. Together they form a unique fingerprint.

Cite this