Closed-form Exact Solution for the Heat Transfer Due to a Second Grade Fluid over a Shrinking Sheet
| Autor: | Singh V., Agarwal Shweta, Van Gorder Robert A. |
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| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Nonlinear Engineering, Vol 2, Iss 3-4, Pp 113-119 (2013) |
| Druh dokumentu: | article |
| ISSN: | 2192-8010 2192-8029 |
| DOI: | 10.1515/nleng-2013-0016 |
| Popis: | In the present work, we present a systematic study of the MHD heat transfer of a second grade fluid over a shrinking sheet. We are able to obtain an exact solution for the heat transfer problem in closed form, even for various values of the viscoelastic parameter. Such exact solutions are a rarity, and are useful for comparison with numerical solutions. The exact solutions strongly depend on the exact solutions for the flow field which were studied. Indeed, we obtain dual solutions for some parameter regimes, and no solutions for others. The exact solution method allows us to give the Nusselt number in terms of the model parameters, in closed analytic form. For parameter regimes where the exact solution may not be well-behaved (such as when two solutions branch apart), we also give a numerical method for comparison. This allows for the study of dual solutions, which are shown to exist in some parameter regimes. Results for the dimensionless velocity and temperature profiles, as well as for the Nusselt number, are obtained and displayed through tables and graphs. It is observed that an increase in the magnitude of the viscoelastic parameter increases the thermal boundary layer thickness for both upper and lower branch solutions. |
| Databáze: | Directory of Open Access Journals |
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