A special case of Falkner–Skan flows past stretching boundaries is considered when the momentum and thermal slip boundary conditions are allowed at the boundary. Exact analytical solutions are found for the converging channel (wedge nozzle). The solutions are shown to be unique, double, or triple depending on the slip parameter and wall moving parameter. The provided closed-form analytical solutions are rare class of exact solutions for the Falkner–Skan flow equations. Thresholds of existence of multiple solutions are determined. For each flow solutions, the corresponding energy equation is also exactly solved when the internal heat generated by viscous dissipation can be neglected or numerically integrated when the viscous dissipation is significant. Analytic and numeric values of the rate of heat transfer affected by the presence of a surface temperature jump are also worked out. The possibility of realistic physical solution out of multiple solutions is finally discussed.
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Exact Multiple Solutions for the Slip Flow and Heat Transfer in a Converging Channel
Mustafa Turkyilmazoglu
Mustafa Turkyilmazoglu
1
Department of Mathematics,
e-mail: turkyilm@hacettepe.edu.tr
Hacettepe University
,Beytepe
,Ankara 06532
, Turkey
e-mail: turkyilm@hacettepe.edu.tr
1Corresponding author.
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Mustafa Turkyilmazoglu
Department of Mathematics,
e-mail: turkyilm@hacettepe.edu.tr
Hacettepe University
,Beytepe
,Ankara 06532
, Turkey
e-mail: turkyilm@hacettepe.edu.tr
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 16, 2014; final manuscript received March 22, 2015; published online June 2, 2015. Assoc. Editor: Peter Vadasz.
J. Heat Transfer. Oct 2015, 137(10): 101301 (8 pages)
Published Online: October 1, 2015
Article history
Received:
June 16, 2014
Revision Received:
March 22, 2015
Online:
June 2, 2015
Citation
Turkyilmazoglu, M. (October 1, 2015). "Exact Multiple Solutions for the Slip Flow and Heat Transfer in a Converging Channel." ASME. J. Heat Transfer. October 2015; 137(10): 101301. https://doi.org/10.1115/1.4030307
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