# Mathematical analysis and numerical resolution of a heat transfer problem arising in water recirculation

## TL;DR

This paper presents a mathematical model combining heat transfer and fluid dynamics for water recirculation, proves solution existence, and offers a numerical algorithm validated with realistic examples.

## Contribution

It introduces a novel coupled heat transfer and Navier-Stokes model with turbulence, providing theoretical analysis and a computational algorithm.

## Key findings

- Proved existence of solutions for the coupled model
- Developed a numerical algorithm for simulation
- Validated with realistic water recirculation examples

## Abstract

This work is devoted to the analysis and resolution of a well-posed mathematical model for several processes involved in the artificial circulation of water in a large waterbody. This novel formulation couples the convective heat transfer equation with the modified Navier-Stokes system following a Smagorinsky turbulence model, completed with a suitable set of mixed, nonhomogeneous boundary conditions of diffusive, convective and radiative type. We prove several theoretical results related to existence of solution, and propose a full algorithm for its computation, illustrated with some realistic numerical examples.