Non-Newtonian Fluid Dynamics Analysis

₹600-1500 INR

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Posted about 2 months ago

₹600-1500 INR

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We consider a thin film of a power-law liquid flowing down an inclined wall with sinusoidal topography. Based on the von Kármán–Pohlhausen method an integral boundary-layer model for the film thickness and the flow rate is derived. This allows us to study the influence of the non-Newtonian properties on the steady free surface deformation. For weakly undulated walls we solve the governing equation analyt- ically by a perturbation approach and find a resonant interaction of the free surface with the wavy bot- tom. Furthermore, the analytical approximation is validated by numerical simulations. Increasing the steepness of the wall reveals that nonlinear effects like the resonance of higher harmonics grow in impor- tance. We find that shear-thickening flows lead to a decrease while shear thinning flows lead to an ampli- fication of the steady free surface. A linear stability analysis of the steady state shows that the bottom undulation has in most cases a stabilizing influence on the free surface. Shear thickening fluids enhance this effect. The open questions which occurred in the linear analysis are then clarified by a nonlinear sta- bility analysis. Finally, we show the important role of capillarity and discuss its influence on the steady solution and on the stability.

Computational Fluid Dynamics

Engineering Mathematics

Mathematics

Matlab and Mathematica

Mechanical Engineering

Engineering

Project ID: 40248974

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@khattab25

I read your project description regarding the thin film flow of power-law liquids over wavy topography. It is a fascinating application of the von Kármán–Pohlhausen method, especially regarding how shear-thinning and shear-thickening properties affect surface resonance. While I am not a research academic, I specialize in Physics-Informed Machine Learning (PIML). I noticed that as the wall becomes steeper, the nonlinear effects and higher harmonics become much harder to solve with traditional math. I can help by building a Neural Network that "learns" the physics of your equations. Instead of using standard numerical simulations which can be slow or limited, my approach: -Embeds your equations (like the boundary-layer model) directly into the AI's learning process. -Handles non-Newtonian variables (the power-law index ) much faster than traditional solvers. -Provides smooth solutions for the steady free surface deformation, even in the "nonlinear resonance" zones you mentioned. Essentially, you provide the physics, and I provide a high-performance, machine-learning-based solver to get the results, of course with visualization of all graphs in the way you like.

₹2,500 INR in 2 days