Analysis of Mixed Convection on Two-Phase Nanofluid Flow Past a Vertical Plate in Brinkman-Extended Darcy Porous Medium with Nield Conditions
The rapid advancement in technology in recent years has shown that nanofluids are very vital to further development in science and technology. Moreover, many industrial specifications cannot be met by allowing natural convection only, hence the need to incorporate forced convection and natural conve...
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MDPI AG
2022-10-01
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| author | Hatem Gasmi Umair Khan Aurang Zaib Anuar Ishak Sayed M. Eldin Zehba Raizah |
| author_facet | Hatem Gasmi Umair Khan Aurang Zaib Anuar Ishak Sayed M. Eldin Zehba Raizah |
| author_sort | Hatem Gasmi |
| collection | DOAJ |
| description | The rapid advancement in technology in recent years has shown that nanofluids are very vital to further development in science and technology. Moreover, many industrial specifications cannot be met by allowing natural convection only, hence the need to incorporate forced convection and natural convection into a single flow regime. The research aims to quantify the mixed convective two-phase flow past a vertical permeable surface in a Brinkman-Extended Darcy porous medium (BEDPM) induced by nanofluid, with heat and mass transfer. In addition, the Nield condition is also incorporated. The model of the problem was initially constructed in the vital form of leading governing equations (LGEs). These LGEs are specifically called partial differential equations (PDEs) (because of two or more independent variables) which were later converted into a set of the single independent variable of ordinary differential equations (ODEs) by implementing the similarity transformations. The set of single independent ODEs was numerically solved via the boundary value problem of fourth-order (bvp4c) technique. The bvp4c is one of the most frequently recommended built-in MATLAB subroutines based on the three-stage Labatto formula. The impact of several physically embedded influential parameters on the fluid flow, along with mass and thermal properties of the nanofluid in a Brinkman-Extended Darcy porous medium for the cases of buoyancy assisting flow (BAF) and buoyancy opposing flow (BOF), were investigated and argued. The numerical outcomes clarify that the porosity parameter reduces the velocity, whereas the concentration and the temperature enhance in the case of the buoyancy assisting and buoyancy opposing flows. In addition, the wall drag force elevates for the larger value of the dimensionless permeability parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>K</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> and the buoyancy ratio parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>N</mi></semantics></math></inline-formula>, while it declines for the modified porosity parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ε</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-09T19:51:48Z |
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| id | doaj.art-0478509afe774ae2a288326fa9591483 |
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| last_indexed | 2024-03-09T19:51:48Z |
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| spelling | doaj.art-0478509afe774ae2a288326fa95914832023-11-24T01:08:36ZengMDPI AGMathematics2227-73902022-10-011020391810.3390/math10203918Analysis of Mixed Convection on Two-Phase Nanofluid Flow Past a Vertical Plate in Brinkman-Extended Darcy Porous Medium with Nield ConditionsHatem Gasmi0Umair Khan1Aurang Zaib2Anuar Ishak3Sayed M. Eldin4Zehba Raizah5Department of Civil Engineering, College of Engineering, University of Ha’il, Hail 81451, Saudi ArabiaDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM, Bangi 43600, MalaysiaDepartment of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology, Gulshan-e-Iqbal, Karachi 75300, PakistanDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM, Bangi 43600, MalaysiaCenter of Research, Faculty of Engineering, Future University in Egypt, New Cairo 11835, EgyptDepartment of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi ArabiaThe rapid advancement in technology in recent years has shown that nanofluids are very vital to further development in science and technology. Moreover, many industrial specifications cannot be met by allowing natural convection only, hence the need to incorporate forced convection and natural convection into a single flow regime. The research aims to quantify the mixed convective two-phase flow past a vertical permeable surface in a Brinkman-Extended Darcy porous medium (BEDPM) induced by nanofluid, with heat and mass transfer. In addition, the Nield condition is also incorporated. The model of the problem was initially constructed in the vital form of leading governing equations (LGEs). These LGEs are specifically called partial differential equations (PDEs) (because of two or more independent variables) which were later converted into a set of the single independent variable of ordinary differential equations (ODEs) by implementing the similarity transformations. The set of single independent ODEs was numerically solved via the boundary value problem of fourth-order (bvp4c) technique. The bvp4c is one of the most frequently recommended built-in MATLAB subroutines based on the three-stage Labatto formula. The impact of several physically embedded influential parameters on the fluid flow, along with mass and thermal properties of the nanofluid in a Brinkman-Extended Darcy porous medium for the cases of buoyancy assisting flow (BAF) and buoyancy opposing flow (BOF), were investigated and argued. The numerical outcomes clarify that the porosity parameter reduces the velocity, whereas the concentration and the temperature enhance in the case of the buoyancy assisting and buoyancy opposing flows. In addition, the wall drag force elevates for the larger value of the dimensionless permeability parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>K</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> and the buoyancy ratio parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>N</mi></semantics></math></inline-formula>, while it declines for the modified porosity parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ε</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2227-7390/10/20/3918nanofluidporous mediumbuoyancy impactNield condition |
| spellingShingle | Hatem Gasmi Umair Khan Aurang Zaib Anuar Ishak Sayed M. Eldin Zehba Raizah Analysis of Mixed Convection on Two-Phase Nanofluid Flow Past a Vertical Plate in Brinkman-Extended Darcy Porous Medium with Nield Conditions Mathematics nanofluid porous medium buoyancy impact Nield condition |
| title | Analysis of Mixed Convection on Two-Phase Nanofluid Flow Past a Vertical Plate in Brinkman-Extended Darcy Porous Medium with Nield Conditions |
| title_full | Analysis of Mixed Convection on Two-Phase Nanofluid Flow Past a Vertical Plate in Brinkman-Extended Darcy Porous Medium with Nield Conditions |
| title_fullStr | Analysis of Mixed Convection on Two-Phase Nanofluid Flow Past a Vertical Plate in Brinkman-Extended Darcy Porous Medium with Nield Conditions |
| title_full_unstemmed | Analysis of Mixed Convection on Two-Phase Nanofluid Flow Past a Vertical Plate in Brinkman-Extended Darcy Porous Medium with Nield Conditions |
| title_short | Analysis of Mixed Convection on Two-Phase Nanofluid Flow Past a Vertical Plate in Brinkman-Extended Darcy Porous Medium with Nield Conditions |
| title_sort | analysis of mixed convection on two phase nanofluid flow past a vertical plate in brinkman extended darcy porous medium with nield conditions |
| topic | nanofluid porous medium buoyancy impact Nield condition |
| url | https://www.mdpi.com/2227-7390/10/20/3918 |
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