Numerical Solution of Nonlinear Diff. Equations for Heat Transfer in Micropolar Fluids over a Stretching Domain
A numerical study based on finite difference approximation is attempted to analyze the bulk flow, micro spin flow and heat transfer phenomenon for micropolar fluids dynamics through Darcy porous medium. The fluid flow mechanism is considered over a moving permeable sheet. The heat transfer is associ...
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MDPI AG
2020-05-01
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| Series: | Mathematics |
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| author | Farooq Ahmad A. Othman Almatroud Sajjad Hussain Shan E. Farooq Roman Ullah |
| author_facet | Farooq Ahmad A. Othman Almatroud Sajjad Hussain Shan E. Farooq Roman Ullah |
| author_sort | Farooq Ahmad |
| collection | DOAJ |
| description | A numerical study based on finite difference approximation is attempted to analyze the bulk flow, micro spin flow and heat transfer phenomenon for micropolar fluids dynamics through Darcy porous medium. The fluid flow mechanism is considered over a moving permeable sheet. The heat transfer is associated with two different sets of boundary conditions, the isothermal wall and isoflux boundary. On the basis of porosity of medium, similarity functions are utilized to avail a set of ordinary differential equations. The non-linear coupled ODE’s have been solved with a very stable and reliable numerical scheme that involves Simpson’s Rule and Successive over Relaxation method. The accuracy of the results is improved by making iterations on three different grid sizes and higher order accuracy in the results is achieved by Richardson extrapolation. This study provides realistic and differentiated results with due considerations of micropolar fluid theory. The micropolar material parameters demonstrated reduction in the bulk fluid speed, thermal distribution and skin friction coefficient but increase in local heat transfer rate and couple stress. The spin behavior of microstructures is also exhibited through microrotation vector <inline-formula> <math display="inline"> <semantics> <mrow> <mi>N</mi> <mo stretchy="false">(</mo> <mi>η</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>. |
| first_indexed | 2024-03-10T19:36:39Z |
| format | Article |
| id | doaj.art-725ec5fe0cf04af5a4e16c94d6879ee7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T19:36:39Z |
| publishDate | 2020-05-01 |
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| spelling | doaj.art-725ec5fe0cf04af5a4e16c94d6879ee72023-11-20T01:37:16ZengMDPI AGMathematics2227-73902020-05-018585410.3390/math8050854Numerical Solution of Nonlinear Diff. Equations for Heat Transfer in Micropolar Fluids over a Stretching DomainFarooq Ahmad0A. Othman Almatroud1Sajjad Hussain2Shan E. Farooq3Roman Ullah4Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 55425, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Ha’il, Ha’il 55425, Saudi ArabiaSchool of Mechanical and Aerospace Engineering, NANYANG Technological University, Singapore 639897, SingaporeMathematics Department, Govt. College University, Lahore 54000, Punjab, PakistanDepartment of Computing, Muscat College, Muscat 113, OmanA numerical study based on finite difference approximation is attempted to analyze the bulk flow, micro spin flow and heat transfer phenomenon for micropolar fluids dynamics through Darcy porous medium. The fluid flow mechanism is considered over a moving permeable sheet. The heat transfer is associated with two different sets of boundary conditions, the isothermal wall and isoflux boundary. On the basis of porosity of medium, similarity functions are utilized to avail a set of ordinary differential equations. The non-linear coupled ODE’s have been solved with a very stable and reliable numerical scheme that involves Simpson’s Rule and Successive over Relaxation method. The accuracy of the results is improved by making iterations on three different grid sizes and higher order accuracy in the results is achieved by Richardson extrapolation. This study provides realistic and differentiated results with due considerations of micropolar fluid theory. The micropolar material parameters demonstrated reduction in the bulk fluid speed, thermal distribution and skin friction coefficient but increase in local heat transfer rate and couple stress. The spin behavior of microstructures is also exhibited through microrotation vector <inline-formula> <math display="inline"> <semantics> <mrow> <mi>N</mi> <mo stretchy="false">(</mo> <mi>η</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>.https://www.mdpi.com/2227-7390/8/5/854solution of nonlinear equationsmicropolar fluidssimilarity transformationsporous mediumheat transferpermeable stretching sheet |
| spellingShingle | Farooq Ahmad A. Othman Almatroud Sajjad Hussain Shan E. Farooq Roman Ullah Numerical Solution of Nonlinear Diff. Equations for Heat Transfer in Micropolar Fluids over a Stretching Domain Mathematics solution of nonlinear equations micropolar fluids similarity transformations porous medium heat transfer permeable stretching sheet |
| title | Numerical Solution of Nonlinear Diff. Equations for Heat Transfer in Micropolar Fluids over a Stretching Domain |
| title_full | Numerical Solution of Nonlinear Diff. Equations for Heat Transfer in Micropolar Fluids over a Stretching Domain |
| title_fullStr | Numerical Solution of Nonlinear Diff. Equations for Heat Transfer in Micropolar Fluids over a Stretching Domain |
| title_full_unstemmed | Numerical Solution of Nonlinear Diff. Equations for Heat Transfer in Micropolar Fluids over a Stretching Domain |
| title_short | Numerical Solution of Nonlinear Diff. Equations for Heat Transfer in Micropolar Fluids over a Stretching Domain |
| title_sort | numerical solution of nonlinear diff equations for heat transfer in micropolar fluids over a stretching domain |
| topic | solution of nonlinear equations micropolar fluids similarity transformations porous medium heat transfer permeable stretching sheet |
| url | https://www.mdpi.com/2227-7390/8/5/854 |
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