# Energetic variational approaches for non-Newtonian fluid systems

## TL;DR

This paper develops energetic variational methods to derive generalized models for both compressible and incompressible non-Newtonian fluid systems, emphasizing thermodynamic principles.

## Contribution

It introduces a unified energetic variational framework for deriving non-Newtonian fluid equations, extending previous models with thermodynamic consistency.

## Key findings

- Derived generalized compressible non-Newtonian fluid system
- Derived generalized incompressible non-Newtonian fluid system
- Established energetic variational approach as a systematic derivation method

## Abstract

We consider the dominant equations for the motion of the non-Newtonian fluid in a domain from an energetic point of view. We apply our energetic variational approaches and the first law of thermodynamics to derive the generalized compressible non-Newtonian fluid system. We also derive the generalized incompressible non-Newtonian fluid system by using our energetic variational approaches.