Triple local similarity solutions of Darcy-Forchheimer Magnetohydrodynamic (MHD) flow of micropolar nanofluid over an exponential shrinking surface: stability analysis
In this paper, the MHD flow of a micropolar nanofluid on an exponential sheet in an Extended-Darcy-Forchheimer porous medium have been considered. Buongiorno's model is considered in order to formulate a mathematical model with different boundary conditions. The governing partial differential e...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019
|
| Subjects: | |
| Online Access: | https://repo.uum.edu.my/id/eprint/26534/1/C%2009%2000527%202019%201%2017.pdf |
| _version_ | 1803629143108091904 |
|---|---|
| author | Ali Lund, Liaquat Ching, Dennis Ling Chua Omar, Zurni Khan, Ilyas Nisar, Kottakkaran Sooppy |
| author_facet | Ali Lund, Liaquat Ching, Dennis Ling Chua Omar, Zurni Khan, Ilyas Nisar, Kottakkaran Sooppy |
| author_sort | Ali Lund, Liaquat |
| collection | UUM |
| description | In this paper, the MHD flow of a micropolar nanofluid on an exponential sheet in an Extended-Darcy-Forchheimer porous medium have been considered. Buongiorno's model is considered in order to formulate a mathematical model with different boundary conditions. The governing partial differential equations (PDEs) of the nanofluid flow are changed into a third order non-linear quasi-ordinary differential equation (ODE), using the pseudo-similarity variable. The resultant ODEs of the boundary value problems (BVPs) are renewed into initial value problems (IVPs) using a shooting method, and then the IVPs are solved by a fourth order Runge-Kutta (RK) method. The effects of various physical parameters on the profiles of velocity, temperature, microrotation velocity, concentration, skin friction, couple stress coefficients, heat, and concentration transfer are demonstrated graphically. The results reveal that triple solutions appear when S ≥ 2.0337 for K = 0.1 and S ≥ 2.7148 for K = 0.2. A stability analysis has been performed to show the stability of the solutions; only the first solution is stable and physically possible, whereas the remaining two solutions are not stable. |
| first_indexed | 2024-07-04T06:33:10Z |
| format | Article |
| id | uum-26534 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T06:33:10Z |
| publishDate | 2019 |
| publisher | MDPI AG |
| record_format | dspace |
| spelling | uum-265342019-10-29T01:43:38Z https://repo.uum.edu.my/id/eprint/26534/ Triple local similarity solutions of Darcy-Forchheimer Magnetohydrodynamic (MHD) flow of micropolar nanofluid over an exponential shrinking surface: stability analysis Ali Lund, Liaquat Ching, Dennis Ling Chua Omar, Zurni Khan, Ilyas Nisar, Kottakkaran Sooppy QA75 Electronic computers. Computer science In this paper, the MHD flow of a micropolar nanofluid on an exponential sheet in an Extended-Darcy-Forchheimer porous medium have been considered. Buongiorno's model is considered in order to formulate a mathematical model with different boundary conditions. The governing partial differential equations (PDEs) of the nanofluid flow are changed into a third order non-linear quasi-ordinary differential equation (ODE), using the pseudo-similarity variable. The resultant ODEs of the boundary value problems (BVPs) are renewed into initial value problems (IVPs) using a shooting method, and then the IVPs are solved by a fourth order Runge-Kutta (RK) method. The effects of various physical parameters on the profiles of velocity, temperature, microrotation velocity, concentration, skin friction, couple stress coefficients, heat, and concentration transfer are demonstrated graphically. The results reveal that triple solutions appear when S ≥ 2.0337 for K = 0.1 and S ≥ 2.7148 for K = 0.2. A stability analysis has been performed to show the stability of the solutions; only the first solution is stable and physically possible, whereas the remaining two solutions are not stable. MDPI AG 2019 Article PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/26534/1/C%2009%2000527%202019%201%2017.pdf Ali Lund, Liaquat and Ching, Dennis Ling Chua and Omar, Zurni and Khan, Ilyas and Nisar, Kottakkaran Sooppy (2019) Triple local similarity solutions of Darcy-Forchheimer Magnetohydrodynamic (MHD) flow of micropolar nanofluid over an exponential shrinking surface: stability analysis. Coatings, 9 (527). pp. 1-17. ISSN 2079-6412 http://doi.org/10.3390/coatings9080527 doi:10.3390/coatings9080527 doi:10.3390/coatings9080527 |
| spellingShingle | QA75 Electronic computers. Computer science Ali Lund, Liaquat Ching, Dennis Ling Chua Omar, Zurni Khan, Ilyas Nisar, Kottakkaran Sooppy Triple local similarity solutions of Darcy-Forchheimer Magnetohydrodynamic (MHD) flow of micropolar nanofluid over an exponential shrinking surface: stability analysis |
| title | Triple local similarity solutions of Darcy-Forchheimer Magnetohydrodynamic (MHD) flow of micropolar nanofluid over an exponential shrinking surface: stability analysis |
| title_full | Triple local similarity solutions of Darcy-Forchheimer Magnetohydrodynamic (MHD) flow of micropolar nanofluid over an exponential shrinking surface: stability analysis |
| title_fullStr | Triple local similarity solutions of Darcy-Forchheimer Magnetohydrodynamic (MHD) flow of micropolar nanofluid over an exponential shrinking surface: stability analysis |
| title_full_unstemmed | Triple local similarity solutions of Darcy-Forchheimer Magnetohydrodynamic (MHD) flow of micropolar nanofluid over an exponential shrinking surface: stability analysis |
| title_short | Triple local similarity solutions of Darcy-Forchheimer Magnetohydrodynamic (MHD) flow of micropolar nanofluid over an exponential shrinking surface: stability analysis |
| title_sort | triple local similarity solutions of darcy forchheimer magnetohydrodynamic mhd flow of micropolar nanofluid over an exponential shrinking surface stability analysis |
| topic | QA75 Electronic computers. Computer science |
| url | https://repo.uum.edu.my/id/eprint/26534/1/C%2009%2000527%202019%201%2017.pdf |
| work_keys_str_mv | AT alilundliaquat triplelocalsimilaritysolutionsofdarcyforchheimermagnetohydrodynamicmhdflowofmicropolarnanofluidoveranexponentialshrinkingsurfacestabilityanalysis AT chingdennislingchua triplelocalsimilaritysolutionsofdarcyforchheimermagnetohydrodynamicmhdflowofmicropolarnanofluidoveranexponentialshrinkingsurfacestabilityanalysis AT omarzurni triplelocalsimilaritysolutionsofdarcyforchheimermagnetohydrodynamicmhdflowofmicropolarnanofluidoveranexponentialshrinkingsurfacestabilityanalysis AT khanilyas triplelocalsimilaritysolutionsofdarcyforchheimermagnetohydrodynamicmhdflowofmicropolarnanofluidoveranexponentialshrinkingsurfacestabilityanalysis AT nisarkottakkaransooppy triplelocalsimilaritysolutionsofdarcyforchheimermagnetohydrodynamicmhdflowofmicropolarnanofluidoveranexponentialshrinkingsurfacestabilityanalysis |