Conference Proceeding

Mathematics in Space and Applied Sciences (ICMSAS-2023)
ICMSAS-2023

Subject Area: Mathematics
Pages: 331
Published On: 03-Mar-2023
Online Since: 04-Mar-2023

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Author(s): Sweta Sharma, Sunil, Poonam Sharma

Email(s): Email ID Not Available

Address: Sweta Sharma1, Sunil1, Poonam Sharma2 1Department of Mathematics and Scientific Computing, National Institute of Technology Hamirpur, Hamirpur, (H.P.) – 177005, India. 2Department of Mathematics, NSCBM Govt. College Hamirpur, Hamirpur, (H.P.) –177005, India. *Corresponding Author

Published In:   Conference Proceeding, Mathematics in Space and Applied Sciences (ICMSAS-2023)

Year of Publication:  March, 2023

Online since:  March 04, 2023

DOI: Not Available

ABSTRACT:
In the present work, we show that the global stability threshold for thermal convection in a Navier-Stokes-Voigt fluid layer with free-free, free-rigid and rigid-rigid boundaries is exactly the same as the linear instability boundary. This optimal result is important because linearized instability theory has captured completely the physics of the onset of convection. The eigen value problem is formed by using normal mode analysis for linear analysis and using energy method for nonlinear analysis. The critical Rayleigh number is found to be exactly same using both linear and nonlinear analysis for different boundary cases. It ensures the absence of any sub-critical instability. An important role of a Kelvin-Voigt parameter has been seen in an energy decay for nonlinear stability whereas it doesn’t affect the value of Rayleigh number.


Cite this article:
Sweta Sharma, Sunil, Poonam Sharma. Global stability for thermal convection in a Navier-Stokes-Voigt fluid. Proceedings of 2nd International Conference on Mathematics in Space and Applied Sciences. 2023;1:158-165.


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Author/Editor Information

Dr. Sanjay Kango

Department of Mathematics, Neta Ji Subhash Chander Bose Memorial, Government Post Graduate College, Hamirpur Himachal Pradesh-177 005, INDIA