International Journal of Emerging Multidisciplinaries: Mathematics

Corresponding Author

Nusrat Rehman

Document Type

Research Article

Subject Areas

Numerical Analysis and Differential Equations


Finite Element Method, Non‐Newtonian fluid, Oscillating lid-driven cavity, Power law.


Fluid flows in cavities has been one of the important benchmark problems in Computational Fluid Dynamics to test and validate open source and commercial codes. Fluid mixing plays a pivotal role in Chemical and Process engineering research. Cavities have emerged as valuable assets in facilitating mixing processes. Enhancement of mixing within cavities can be achieved through various means, including the installation of baffles within the domain, utilization of stirrers, and implementation of an oscillating lid. We focus on oscillating lid driven flows in cavities in this thesis including the non-Newtonian fluid (Power law model). Numerical simulations are performed for top wall oscillations for different values of power law index (), later on the simulations are carried out to explore the vortex behavior for the cases of parallel wall oscillations (both top and bottom walls moving in the same direction) and anti-parallel wall oscillations (both top and bottom walls moving in the opposite direction). An approach based on finite elements has been used to solve the governing equations. Specifically, the discretization process of the governing non-dimensional equations of continuity and momentum is accomplished using the stable finite element pair of quadratic and linear (/) approximations on the hybrid grid. Velocity and streamline effects of all three shear regimes (thinning, thickening and Newtonian) are investigated numerical simulations with single and double wall oscillations have been performed. The impact of various involved parameters including the consistency index and Reynolds number have been discussed in great detail.

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Mathematics Commons