On various models describing behaviour of thermoviscoelastic rate-type fluids

TL;DR

This paper develops a thermodynamically consistent model for heat-conducting viscoelastic rate-type fluids and proves the existence of global weak solutions in two dimensions, accounting for thermal effects and material properties.

Contribution

It introduces a new model integrating thermal effects into viscoelastic fluids and establishes global existence results under natural energy and entropy conditions.

Findings

Existence of global weak solutions in 2D

Model accounts for heat conduction and temperature-dependent properties

Provides a mathematical foundation for thermoviscoelastic fluids

Abstract

Viscoelastic rate-type fluid models are essential for describing the behavior of a wide range of complex materials, with applications in fields such as engineering, biomaterials, and medicine. These models are particularly useful for understanding the rheological properties of materials that exhibit both elastic and viscous behavior under deformation. However, many real-world applications involve significant thermal effects, where heat conduction and the temperature dependence of material properties must also be considered. In this paper, we introduce a thermodynamically consistent model for heat-conducting viscoelastic rate-type fluids and establish the existence of a global weak solution in a two-dimensional setting. The result holds under the condition that the initial energy and entropy are controlled in appropriate natural norms.