Free Convection of a Bingham Fluid in a Differentially-Heated Porous Cavity: The Effect of a Square Grid Microstructure
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 w...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Physics |
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| Online Access: | https://www.mdpi.com/2624-8174/4/1/15 |
| _version_ | 1797443450757447680 |
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| author | D. Andrew S. Rees |
| author_facet | D. Andrew S. Rees |
| author_sort | D. Andrew S. Rees |
| collection | DOAJ |
| description | 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, <i>A</i>, are obtained. |
| first_indexed | 2024-03-09T12:56:15Z |
| format | Article |
| id | doaj.art-c2734c9228a34ed7ad47e2a009293a9e |
| institution | Directory Open Access Journal |
| issn | 2624-8174 |
| language | English |
| last_indexed | 2024-03-09T12:56:15Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Physics |
| spelling | doaj.art-c2734c9228a34ed7ad47e2a009293a9e2023-11-30T21:59:54ZengMDPI AGPhysics2624-81742022-02-014120221610.3390/physics4010015Free Convection of a Bingham Fluid in a Differentially-Heated Porous Cavity: The Effect of a Square Grid MicrostructureD. Andrew S. Rees0Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UKWe 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, <i>A</i>, are obtained.https://www.mdpi.com/2624-8174/4/1/15Bingham fluidporous mediafree convectionanisotropic |
| spellingShingle | D. Andrew S. Rees Free Convection of a Bingham Fluid in a Differentially-Heated Porous Cavity: The Effect of a Square Grid Microstructure Physics Bingham fluid porous media free convection anisotropic |
| title | Free Convection of a Bingham Fluid in a Differentially-Heated Porous Cavity: The Effect of a Square Grid Microstructure |
| title_full | Free Convection of a Bingham Fluid in a Differentially-Heated Porous Cavity: The Effect of a Square Grid Microstructure |
| title_fullStr | Free Convection of a Bingham Fluid in a Differentially-Heated Porous Cavity: The Effect of a Square Grid Microstructure |
| title_full_unstemmed | Free Convection of a Bingham Fluid in a Differentially-Heated Porous Cavity: The Effect of a Square Grid Microstructure |
| title_short | Free Convection of a Bingham Fluid in a Differentially-Heated Porous Cavity: The Effect of a Square Grid Microstructure |
| title_sort | free convection of a bingham fluid in a differentially heated porous cavity the effect of a square grid microstructure |
| topic | Bingham fluid porous media free convection anisotropic |
| url | https://www.mdpi.com/2624-8174/4/1/15 |
| work_keys_str_mv | AT dandrewsrees freeconvectionofabinghamfluidinadifferentiallyheatedporouscavitytheeffectofasquaregridmicrostructure |