Analysis of the weak formulation of a coupled nonlinear parabolic system modeling a heat exchanger

TL;DR

This paper rigorously analyzes a complex coupled nonlinear parabolic system modeling heat exchange, establishing existence, uniqueness, and regularity of weak solutions with realistic boundary conditions and heterogeneous coefficients.

Contribution

It introduces a tailored Faedo-Galerkin method for coupled systems, providing new insights into the regularity and well-posedness of heat exchanger models.

Findings

Proved existence and uniqueness of weak solutions.

Established enhanced regularity in time and space.

Addressed realistic boundary conditions and interfacial dynamics.

Abstract

This paper establishes the existence, uniqueness and time-space regularity of the weak solution to a nonlinear coupled parabolic system modeling temperature evolution in a coaxial heat exchanger with source terms and spatially varying coefficients. The system is formulated in a weak sense and the analysis relies on a Faedo-Galerkin method tailored to handle the nonlinear coupling and heterogeneous domains. Under suitable assumptions on the initial data and source terms, enhanced regularity in both time and space is obtained. In contrast with classical scalar models, the study addresses a multi-component system with realistic boundary conditions and complex interfacial dynamics.