| 000 -LEADER |
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| fixed length control field |
03940nam a22001577a 4500 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
621 |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Khan, Ghani |
| 245 ## - TITLE STATEMENT |
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| Title |
Symmetry Analysis and Analytic Solutions for Unsteady Flows on a Stretching Surface in the Presence of Magnetic Field, Internal Heat Source and Thermocapillary Effects / |
| Statement of responsibility, etc. |
Ghani Khan |
| 264 ## - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
Islamabad : |
| Name of producer, publisher, distributor, manufacturer |
SMME- NUST; |
| Date of production, publication, distribution, manufacture, or copyright notice |
2023. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
89p. ; |
| Other physical details |
Soft Copy |
| Dimensions |
30cm. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
This study employs Lie point symmetry analysis to investigate the unsteady flow on a stretching<br/>surface. Such flows are common in various manufacturing processes such as extrusion, meltspinning, and coating. Three cases have been discussed i.e. unsteady flow on a stretching surface<br/>in the presence of a variable magnetic field, its 1-dimensional optimal system, and unsteady flow<br/>on a stretching surface in the presence of thermocapillarity, an internal source or sink, and a variable<br/>magnetic field.<br/>For unsteady flow on a stretching surface in the presence of a variable magnetic field, a general<br/>linear combination of all admitted translational and scaling Lie point symmetries has been used to<br/>obtain the system invariants and general forms of the velocity, temperature, and concentration at<br/>the stretching surface. The deduced invariants provide a new generalized class of similarity<br/>transformations that convert the governing boundary layer equations into a system of non-linear<br/>ODEs. Analytic series solutions have been obtained for the resulting system of ODEs using<br/>Homotopy Analysis Method (HAM) and the effect of different parameters such as unsteadiness,<br/>magnetic parameter, Prandtl number, Schmidt number, and coefficients of the Lie point symmetries<br/>has been depicted graphically. It has been found that coefficients of the translational symmetries<br/>do not play any role in the solution while coefficients of the scaling symmetries can control the<br/>temperature and concentration fields. Secondly, a 1-dimensional optimal system of this flow is<br/>obtained which provides 22 new classes of similarity transformations that reduce the governing<br/>boundary layer equations into 22 news classes of ODEs, thus providing multiple new solutions of<br/>heat and mass transfer.<br/>Similarly, the hydrodynamics and thermal characteristics of the flow induced by the unsteady<br/>stretching of a sheet in the presence of thermocapillarity, internal heat source or sink, and variable<br/>magnetic field are investigated using Lie point analysis. The linear combinations of Lie point<br/>symmetries is again a Lie point symmetry. It is admitted by all boundary conditions while leave<br/>the stretching sheet velocity and temperature as a function of both distance and time. We utilize<br/>such a linear combination to develop Lie transformations that reduce the governing momentum and<br/>energy equations into a system of coupled non-linear ODEs. The resulting five-parameter problem<br/>namely, unsteadiness term 𝑆, magnetic parameter 𝑀𝑎, Prandtl number 𝑃𝑟, temperature-dependent<br/>heat source or sink term 𝐺<br/>and the thermocapillarity parameter 𝑀, is solved using Homotopy<br/>Perturbation Method (HPM). It has been found that thermocapillary forces drag the free surface of<br/>the fluid in the direction of the stretching sheet, due to which a local velocity minimum forms in<br/>the fluid. Thermocapillarity thickens the fluid film resulting in the increase of free surface velocity,<br/>temperature, and heat flux from the sheet while reducing the friction between the sheet and the<br/>fluid film. The temperature-dependent heat source or sink term and the magnetic parameter greatly<br/>affect the variation of the temperature across the fluid and can be useful in speeding up the cooling<br/>or heating of the fluid. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
MS Mechanical Engineering |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Supervisor : Dr Muhammad Safdar |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="http://10.250.8.41:8080/xmlui/handle/123456789/34079">http://10.250.8.41:8080/xmlui/handle/123456789/34079</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
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| Koha item type |
Thesis |
