The nonparallel linear stability analysis of flow through a slowly diverging pipe undergoing viscous heating is considered. The pipe wall is maintained at constant temperatures and Nahme’s law is applied to model the temperature dependence of the fluid viscosity. A one-parameter family of velocity profiles for the basic state is obtained for small angles of divergence. The nonparallel stability equations for the disturbance velocity coupled to a linearized energy equation are derived and solved using a spectral collocation method. Our results indicate that increasing viscous heating, characterized by increasing Nahme number, is destabilizing. The Prandtl number has a negligible effect on the linear stability characteristics. The Grashof number stablizes the flow for , below which it has a negligible effect.
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July 2011
Research Papers
The Instability of Flow Through a Slowly Diverging Pipe With Viscous Heating
Kirti Chandra Sahu
e-mail: ksahu@iith.ac.in
Kirti Chandra Sahu
Department of Chemical Engineering, Indian Institute of Technology
Hyderabad, Yeddumailaram 502 205, Andhra Pradesh, India
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Kirti Chandra Sahu
Department of Chemical Engineering, Indian Institute of Technology
Hyderabad, Yeddumailaram 502 205, Andhra Pradesh, India
e-mail: ksahu@iith.ac.in
J. Fluids Eng. Jul 2011, 133(7): 071201 (8 pages)
Published Online: July 5, 2011
Article history
Received:
October 31, 2010
Accepted:
May 19, 2011
Online:
July 5, 2011
Published:
July 5, 2011
Citation
Chandra Sahu, K. (July 5, 2011). "The Instability of Flow Through a Slowly Diverging Pipe With Viscous Heating." ASME. J. Fluids Eng. July 2011; 133(7): 071201. https://doi.org/10.1115/1.4004299
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