How is the finite element method used to study heat transfer and fluid flow?

The finite element method (FEM) is a powerful numerical technique used to obtain approximate solutions for complex physical processes, including heat transfer and fluid flow, which are often governed by differential equations that are too complicated to solve explicitly.1

The core principle of FEM involves approximating a continuous surface, structure, or process by dividing it into a finite number of simple, interconnected elements. By breaking down a complex domain into these smaller, manageable pieces, engineers and mathematicians can apply numerical algorithms to model how heat propagates through a material or how a fluid moves through a system.1

In the context of fluid dynamics, FEM is essential for addressing problems that are otherwise intractable, such as the complex vortices and turbulence described by the Navier-Stokes equation. While the Navier-Stokes equations provide the theoretical framework for fluid motion, their practical application in three-dimensional flows relies heavily on such numerical analysis methods to approximate solutions.2