On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders
Effects of the bounding solid walls are examined numerically for slow flow overregular, square arrays of circular cylinders between two parallel plates. A local magnitudeof the rate of entropy generation is used effectively to determine the flow region affected bythe presence of the solid boundary....
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| Format: | Article |
| Language: | English |
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MDPI AG
2007-09-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/9/3/118/ |
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| author | Uichiro Narusawa Prabhamani R. Patil Haidong Liu |
| author_facet | Uichiro Narusawa Prabhamani R. Patil Haidong Liu |
| author_sort | Uichiro Narusawa |
| collection | DOAJ |
| description | Effects of the bounding solid walls are examined numerically for slow flow overregular, square arrays of circular cylinders between two parallel plates. A local magnitudeof the rate of entropy generation is used effectively to determine the flow region affected bythe presence of the solid boundary. Computed axial pressure gradients are compared to thecorresponding solution based on the Darcy-Brinkman equation for porous media in whichthe effective viscosity appears as an additional property to be determined from the flowcharacteristics. Results indicate that, between two limits of the Darcian porous medium andthe viscous flow, the magnitude of μ (the ratio of the effective viscosity to the fluid ˆviscosity) needs to be close to unity in order to satisfy the non-slip boundary conditions atthe bounding walls. Although the study deals with a specific geometric pattern of the porousstructure, it suggests a restriction on the validity of the Darcy-Brinkman equation to modelhigh porosity porous media. The non-slip condition at the bounding solid walls may beaccounted for by introducing a thin porous layer with μ = 1 near the solid walls. ˆ |
| first_indexed | 2024-04-11T12:09:48Z |
| format | Article |
| id | doaj.art-a28d409156854de1b36265a067e8b55b |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:09:48Z |
| publishDate | 2007-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-a28d409156854de1b36265a067e8b55b2022-12-22T04:24:38ZengMDPI AGEntropy1099-43002007-09-019311813110.3390/e9030118On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of CylindersUichiro NarusawaPrabhamani R. PatilHaidong LiuEffects of the bounding solid walls are examined numerically for slow flow overregular, square arrays of circular cylinders between two parallel plates. A local magnitudeof the rate of entropy generation is used effectively to determine the flow region affected bythe presence of the solid boundary. Computed axial pressure gradients are compared to thecorresponding solution based on the Darcy-Brinkman equation for porous media in whichthe effective viscosity appears as an additional property to be determined from the flowcharacteristics. Results indicate that, between two limits of the Darcian porous medium andthe viscous flow, the magnitude of μ (the ratio of the effective viscosity to the fluid ˆviscosity) needs to be close to unity in order to satisfy the non-slip boundary conditions atthe bounding walls. Although the study deals with a specific geometric pattern of the porousstructure, it suggests a restriction on the validity of the Darcy-Brinkman equation to modelhigh porosity porous media. The non-slip condition at the bounding solid walls may beaccounted for by introducing a thin porous layer with μ = 1 near the solid walls. ˆhttp://www.mdpi.com/1099-4300/9/3/118/entropy generationporous mediaDarcy-Brinkman equationeffective viscosity. |
| spellingShingle | Uichiro Narusawa Prabhamani R. Patil Haidong Liu On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders Entropy entropy generation porous media Darcy-Brinkman equation effective viscosity. |
| title | On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders |
| title_full | On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders |
| title_fullStr | On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders |
| title_full_unstemmed | On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders |
| title_short | On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders |
| title_sort | on darcy brinkman equation viscous flow between two parallel plates packed with regular square arrays of cylinders |
| topic | entropy generation porous media Darcy-Brinkman equation effective viscosity. |
| url | http://www.mdpi.com/1099-4300/9/3/118/ |
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