Thermodynamics of Viscous Flows on Surfaces

TL;DR

This paper develops a thermodynamic framework for viscous flows on surfaces, extending phase space with deformation and stress tensors to describe state equations and co-existence conditions.

Contribution

It introduces a novel thermodynamic description for viscous media on manifolds, incorporating deformation and stress tensors into the phase space.

Findings

Derived thermodynamic state equations for flows on surfaces.

Characterized co-existence manifolds in extended phase space.

Provided a mathematical framework for viscous flow thermodynamics on manifolds.

Abstract

In this paper, thermodynamics of a moving medium is considered. Main goal of this paper is to describe thermodynamics state equations and equations of co-existence manifolds of media on two- and three-dimensional manifolds. To this end the phase space of a medium is extended with the deformation tensor and the stress tensor.