# FEA or CFD for a Better Thermal Solution Accuracy?

Personalizing products conferring to the unique requirements of customer groups has instilled the need for multiple design models. Before prototyping these models, they are tested using Finite Element Analysis (FEA) and/ or Computational Fluid Dynamic (CFD) tools for their performance. During these tests, there are multiple instances when FEA tools are compared with CFD. It is to be noted that FEA is the analysis type using a numerical method, while CFD models fluid flow problems using one such numerical method. Numerical methods can deliver accurate solutions if used correctly or according to the application. Technical know-how and experience using both tools can help distinguish which tool suits the specific application. FEA and CFD can solve thermal problems, but there is a difference in the solution accuracy while solving different physics.

**Thermal Analysis Using CFD**

CFD tools are widely used for thermal analysis of fluid flow problems where convection and radiation heat transfer are analyzed in detail. While carrying out CFD analysis, the geometry is simplified to a great extent. The complicated features of the geometry are removed; only the surface around which the flow occurs is considered. Since fluid dynamics is all about fluid volume, the numerical method used in CFD analysis is the Finite Volume Method (FVM).

In FVM, the volume integrals of partial differential equations are converted to surface integrals using the divergence theorem. FVM is the volumetric analog of 1D or 2D finite difference methods; it is generally used with flow or flux problems, such as advection or diffusion in 3D. Moreover, the nonlinear convection term in the Navier-Stokes equation makes CFD solutions suitable for thermal problems involving fluid flow primarily because convection heat transfer takes place only in the presence of a fluid.

Using CFD tools, it is possible to analyze heat transfer between solid and fluid domains. This is referred to as Conjugate Heat Transfer (CHT). The CHT model is effectively used for cooling applications. In a heat exchanger, forced convection is used to cool the hot fluid inside a tube, separated by a wall where conduction is the mode of heat transfer between the outer and inner walls of the tube. Forced convection can help achieve a high heat transfer rate in a CHT model. Using the CHT approach, the heat transfer coefficients for the walls are directly calculated and are not simplified based on empirical formulas.

**Thermal Analysis Using FEA**

FEA uses the finite element method (FEM) and is primarily used to solve conduction heat transfer in a solid. From a thermal context, FEA considers convection and radiation effects in a simplified manner with a boundary condition for the heat transfer coefficient. The shortcoming of FEA is convergence and stability. In a non-self-adjoint 3D nonlinear system of partial differential equations, the FEA solution can become unstable and diverge from the true solution. This arises due to specific nonlinear terms in the governing equations. This makes FEA incompetent for fluid flow heat transfer problems.

FEA is predominantly used for structural analysis and complements CFD prototype testing towards a multidisciplinary system analysis. Thermal strain loading for stress analysis is an example where FEA is used for thermal analysis.

**Coupling FEA and CFD**

Most energy systems around us work with a combination of different energy forms, making it necessary to evaluate the system at different levels. For example, the thermomechanical behavior of an aircraft tire during cornering produces heat on the skid due to friction; this analysis helps study the relationship between lateral friction and heat dissipation to avoid thermal runaway.

To address problems at a multidisciplinary level, Cadence is constantly working towards developing and acquiring solutions that can enable system-level analysis. One such product is our in-house Celsius Thermal solver, which incorporates FEA and CFD tools to take care of the fluid flow and electrical-thermal aspects of PCB design. We have Fidelity CFD software for silo fluid flow solutions, and our recent investment in Cascade technologies also provides end-to-end CFD workflow.

More information about Cascade Technologies can be found on their website.

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