What is it about?
Viscoelastic fluids are complex substances exhibiting both viscous and elastic behaviour, and moreover, in practice their properties are highly sensitive to temperature. This work provides the first of its kind existence result for the differential equations that model the full thermodynamical evolution of such flows.
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Why is it important?
Comparing with real-world experiments, neglecting the temperature effects in modelling of viscoelastic materials is highly idealized. Instead, it turns out that the elastic mechanism of the fluid contributes significantly to the produced entropy. Proving unconditional solvability of the governing system of equations is the first step to amend this issue.
Perspectives
Relying on the positivity of the entropy production, we are able to guarantee solvability of the governing system that determines the evolution of the flow velocity, temperature distribution and also of all components of the elasticity tensor.
PhD Michal Bathory
Charles University
Read the Original
This page is a summary of: Coupling the Navier–Stokes–Fourier equations with the Johnson–Segalman stress-diffusive viscoelastic model: global-in-time and large-data analysis, Mathematical Models and Methods in Applied Sciences, November 2023, World Scientific Pub Co Pte Lt,
DOI: 10.1142/s0218202524500064.
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