Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase Model
In this study, the free convection of nanofluids between a rectangular enclosure and a sinusoidal cylinder is numerically analyzed using the finite element method (FEM). Two-phase Buongiorno’s formulation was used to model the fluid layer, and Brinkman-Forchheimer equation was used to formulate the...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2023/8426825 |
| _version_ | 1797840075355062272 |
|---|---|
| author | Abeer Alhashash Habibis Saleh |
| author_facet | Abeer Alhashash Habibis Saleh |
| author_sort | Abeer Alhashash |
| collection | DOAJ |
| description | In this study, the free convection of nanofluids between a rectangular enclosure and a sinusoidal cylinder is numerically analyzed using the finite element method (FEM). Two-phase Buongiorno’s formulation was used to model the fluid layer, and Brinkman-Forchheimer equation was used to formulate the porous layer. The enclosure has a low temperature, while the cylinder is maintained at a high temperature. The governing equations are expressed in PDEs and converted into weak formulations (Galerkin FEM). In numerical simulations, the average concentration, the amplitude of undulated cylinder, the number of undulated, and the Rayleigh number are investigated. It is observed that the homogeneous nanofluid model could be valid for low heating intensity with higher waviness frequency and/or higher amplitude. The higher the alumina concentration, the higher the heat transfer rate. The heat transfer rate can be boosted by up to 13% by suspending 1% alumina particles. The heat transfer enhancement decreases with increasing the amplitude and/or increasing the waviness number. |
| first_indexed | 2024-04-09T16:08:36Z |
| format | Article |
| id | doaj.art-61182bced4cd4adb897a760732bc6552 |
| institution | Directory Open Access Journal |
| issn | 1687-9139 |
| language | English |
| last_indexed | 2024-04-09T16:08:36Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj.art-61182bced4cd4adb897a760732bc65522023-04-25T00:00:14ZengHindawi LimitedAdvances in Mathematical Physics1687-91392023-01-01202310.1155/2023/8426825Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase ModelAbeer Alhashash0Habibis Saleh1Department of MathematicsMathematics Education DepartmentIn this study, the free convection of nanofluids between a rectangular enclosure and a sinusoidal cylinder is numerically analyzed using the finite element method (FEM). Two-phase Buongiorno’s formulation was used to model the fluid layer, and Brinkman-Forchheimer equation was used to formulate the porous layer. The enclosure has a low temperature, while the cylinder is maintained at a high temperature. The governing equations are expressed in PDEs and converted into weak formulations (Galerkin FEM). In numerical simulations, the average concentration, the amplitude of undulated cylinder, the number of undulated, and the Rayleigh number are investigated. It is observed that the homogeneous nanofluid model could be valid for low heating intensity with higher waviness frequency and/or higher amplitude. The higher the alumina concentration, the higher the heat transfer rate. The heat transfer rate can be boosted by up to 13% by suspending 1% alumina particles. The heat transfer enhancement decreases with increasing the amplitude and/or increasing the waviness number.http://dx.doi.org/10.1155/2023/8426825 |
| spellingShingle | Abeer Alhashash Habibis Saleh Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase Model Advances in Mathematical Physics |
| title | Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase Model |
| title_full | Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase Model |
| title_fullStr | Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase Model |
| title_full_unstemmed | Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase Model |
| title_short | Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase Model |
| title_sort | use of finite element method for free convection of nanofluids between a rectangular enclosure and a sinusoidal cylinder using buongiorno s two phase model |
| url | http://dx.doi.org/10.1155/2023/8426825 |
| work_keys_str_mv | AT abeeralhashash useoffiniteelementmethodforfreeconvectionofnanofluidsbetweenarectangularenclosureandasinusoidalcylinderusingbuongiornostwophasemodel AT habibissaleh useoffiniteelementmethodforfreeconvectionofnanofluidsbetweenarectangularenclosureandasinusoidalcylinderusingbuongiornostwophasemodel |