Mathematical Modeling of Mixed Convection Boundary Layer Flows over a Stretching Sheet with Viscous Dissipation in Presence of Suction and Injection
The variational principle, developed by Gyarmati, embodying the principles of thermodynamics of irreversible processes is employed to study the mixed convection flows near the stagnation point of an incompressible viscous fluid with suction, injection and viscous dissipation effects towards a vertic...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-10-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/11/1754 |
| _version_ | 1797550130475302912 |
|---|---|
| author | Chandrasekar Muthukumaran Kalidoss Bathrinathan |
| author_facet | Chandrasekar Muthukumaran Kalidoss Bathrinathan |
| author_sort | Chandrasekar Muthukumaran |
| collection | DOAJ |
| description | The variational principle, developed by Gyarmati, embodying the principles of thermodynamics of irreversible processes is employed to study the mixed convection flows near the stagnation point of an incompressible viscous fluid with suction, injection and viscous dissipation effects towards a vertical stretching sheet. The velocity and temperature of the stretching sheet are considered to vary linearly proportional to the distance from the stagnation point. In this analysis, two equal and opposite forces are applied on the stretching sheet by keeping the origin fixed in a viscous fluid with constant free-stream temperature. The velocity and temperature distributions are assumed as simple polynomial functions and then the variational principle has been formulated. The corresponding Euler–Lagrange equations of the variational principle have been transformed into coupled polynomial equations in terms of hydro-dynamical and thermal boundary layer thicknesses. These equations are solvable for any combinations of Prandtl number, suction and injection parameter, Eckert number and buoyancy parameter. The obtained results are compared with known numerical results for assisting and opposing flows, and the comparison reveals that the accuracy is quite acceptable and found to be in good agreement. |
| first_indexed | 2024-03-10T15:25:08Z |
| format | Article |
| id | doaj.art-eedacedd78e040fabf5a431503897f45 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T15:25:08Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-eedacedd78e040fabf5a431503897f452023-11-20T18:09:25ZengMDPI AGSymmetry2073-89942020-10-011211175410.3390/sym12111754Mathematical Modeling of Mixed Convection Boundary Layer Flows over a Stretching Sheet with Viscous Dissipation in Presence of Suction and InjectionChandrasekar Muthukumaran0Kalidoss Bathrinathan1Department of Mathematics, Anna University, Chennai 600 025, IndiaDepartment of Mathematics, Anna University, Chennai 600 025, IndiaThe variational principle, developed by Gyarmati, embodying the principles of thermodynamics of irreversible processes is employed to study the mixed convection flows near the stagnation point of an incompressible viscous fluid with suction, injection and viscous dissipation effects towards a vertical stretching sheet. The velocity and temperature of the stretching sheet are considered to vary linearly proportional to the distance from the stagnation point. In this analysis, two equal and opposite forces are applied on the stretching sheet by keeping the origin fixed in a viscous fluid with constant free-stream temperature. The velocity and temperature distributions are assumed as simple polynomial functions and then the variational principle has been formulated. The corresponding Euler–Lagrange equations of the variational principle have been transformed into coupled polynomial equations in terms of hydro-dynamical and thermal boundary layer thicknesses. These equations are solvable for any combinations of Prandtl number, suction and injection parameter, Eckert number and buoyancy parameter. The obtained results are compared with known numerical results for assisting and opposing flows, and the comparison reveals that the accuracy is quite acceptable and found to be in good agreement.https://www.mdpi.com/2073-8994/12/11/1754stagnation point flowheat transferboundary layer flowsstretching sheetnon-equilibrium thermodynamicsviscous dissipation effects |
| spellingShingle | Chandrasekar Muthukumaran Kalidoss Bathrinathan Mathematical Modeling of Mixed Convection Boundary Layer Flows over a Stretching Sheet with Viscous Dissipation in Presence of Suction and Injection Symmetry stagnation point flow heat transfer boundary layer flows stretching sheet non-equilibrium thermodynamics viscous dissipation effects |
| title | Mathematical Modeling of Mixed Convection Boundary Layer Flows over a Stretching Sheet with Viscous Dissipation in Presence of Suction and Injection |
| title_full | Mathematical Modeling of Mixed Convection Boundary Layer Flows over a Stretching Sheet with Viscous Dissipation in Presence of Suction and Injection |
| title_fullStr | Mathematical Modeling of Mixed Convection Boundary Layer Flows over a Stretching Sheet with Viscous Dissipation in Presence of Suction and Injection |
| title_full_unstemmed | Mathematical Modeling of Mixed Convection Boundary Layer Flows over a Stretching Sheet with Viscous Dissipation in Presence of Suction and Injection |
| title_short | Mathematical Modeling of Mixed Convection Boundary Layer Flows over a Stretching Sheet with Viscous Dissipation in Presence of Suction and Injection |
| title_sort | mathematical modeling of mixed convection boundary layer flows over a stretching sheet with viscous dissipation in presence of suction and injection |
| topic | stagnation point flow heat transfer boundary layer flows stretching sheet non-equilibrium thermodynamics viscous dissipation effects |
| url | https://www.mdpi.com/2073-8994/12/11/1754 |
| work_keys_str_mv | AT chandrasekarmuthukumaran mathematicalmodelingofmixedconvectionboundarylayerflowsoverastretchingsheetwithviscousdissipationinpresenceofsuctionandinjection AT kalidossbathrinathan mathematicalmodelingofmixedconvectionboundarylayerflowsoverastretchingsheetwithviscousdissipationinpresenceofsuctionandinjection |