Derivation and analysis of a Stokes-transport system in evolving vessels modeling thermoregulation in human skin

TL;DR

This paper develops a coupled mathematical model of blood flow and heat transfer in human skin, accounting for vessel dynamics driven by temperature, and proves the existence and uniqueness of solutions for this complex system.

Contribution

It introduces a novel coupled Stokes-transport model for thermoregulation in skin, including vessel evolution and nonlinear coupling analysis.

Findings

Proved existence and uniqueness of weak solutions.

Modeled temperature-dependent vessel dilation and constriction.

Captured the feedback between blood flow and heat transfer.

Abstract

We consider a Stokes flow coupled with advective-diffusive transport in an evolving domain with boundary conditions allowing for inflow and outflow. The evolution of the domain is induced by the transport process, leading to a fully coupled problem. Our aim is to model the thermal control of blood flow in human skin. To this end, the model takes into account the temperature-dependent production of biochemical substances, the subsequent dilation and constriction of blood vessels, and the resulting changes in convective heat transfer. We prove existence and uniqueness of weak solutions using a fixed point method that allows us to treat the nonlinear coupling.