Solving Navier-Stokes equations coupled with a heat transfer equation using Bagarello's approach and the Hankel transform

TL;DR

This paper presents a novel analytical method combining Bagarello's non-commutative approach and the Hankel transform to solve coupled Navier-Stokes and heat transfer equations for incompressible fluid dynamics.

Contribution

It introduces a new analytical technique that leverages non-commutative operator theory and the Hankel transform to solve complex coupled PDEs in fluid mechanics.

Findings

Derived explicit solutions for the coupled equations.

Demonstrated the effectiveness of the method on the fluid dynamics model.

Provided a new analytical framework for similar PDE systems.

Abstract

In this paper, the dynamics of an incompressible fluid in a bounded connected domain, described by Navier-Stokes equations coupled with a heat transfer equation, is investigated by a method inspired from the non-commutative strategy developed by Bagarello, (see Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394).The solution of involved systems of partial differential equations is derived with the help of the unbounded self-adjoint densely defined Hamiltonian operator of the physical model and the Hankel transform.