Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Closed-form Exact Solution for the Heat Transfer Due to a Second Grade Fluid over a Shrinking Sheet

Closed-form Exact Solution for the Heat Transfer Due to a Second Grade Fluid over a Shrinking Sheet Abstract 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Engineering de Gruyter

Closed-form Exact Solution for the Heat Transfer Due to a Second Grade Fluid over a Shrinking Sheet

Loading next page...
 
/lp/de-gruyter/closed-form-exact-solution-for-the-heat-transfer-due-to-a-second-grade-xNh0aP03Fx
Publisher
de Gruyter
Copyright
Copyright © 2013 by the
ISSN
2192-8029
eISSN
2192-8010
DOI
10.1515/nleng-2013-0016
Publisher site
See Article on Publisher Site

Abstract

Abstract 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.

Journal

Nonlinear Engineeringde Gruyter

Published: Dec 1, 2013

There are no references for this article.