FEM thermal analysis

Finite Element Method (FEM) thermal analysis is an advanced thermal simulation that enables engineers to predict temperature distributions in components and structures already at the design stage. By modelling heat flow within a material and evaluating phenomena such as conduction, convection, and radiation, thermal analysis reveals potential overheating areas and the resulting thermal stresses. In engineering practice, it can be just as important as traditional FEM strength calculations, which focus on mechanical loads—both approaches complement each other, providing a coupled analysis of a structure in terms of both strength and thermal resistance. This article explains what FEM thermal analysis involves, discusses the differences between steady-state and transient approaches, presents thermo-mechanical coupling, and shows application examples across various engineering industries.

What is thermal analysis using the finite element method?

Thermal FEA analysis involves digitally reproducing heat-transfer phenomena within a structural model. In the numerical model, the geometry is divided into a mesh of discrete finite elements, and then the heat-conduction equations are solved in those elements, taking into account the specified boundary conditions (e.g., surface temperatures, heat-flow modelling to the surroundings, heat sources within the material). The result of such a simulation is a temperature distribution across the entire structure under study—i.e., understanding what temperatures individual areas reach during device operation. This knowledge makes it possible, already at the design stage, to identify potential hot spots—areas that overheat—and introduce design changes (e.g., adding cooling fins, changing the material, or improving ventilation) before physical prototypes are built.

Importantly, an FEA thermal analysis can be carried out in two ways: as a steady-state analysis or a transient analysis. In the first case, we are interested in the established thermal equilibrium—for example, the maximum temperature of a component during continuous operation under constant ambient conditions. In the second case, we examine how temperature changes over time—e.g., how quickly a part heats up after the device is switched on, or how long it takes to cool down after it is switched off. In both approaches, the finite element method is used, but they differ in their assumptions and the data required, which is discussed in more detail in the next chapter.

Steady-State vs. Transient Thermal Analysis

Steady-state thermal analysis assumes that the system under study has reached thermal equilibrium and that temperatures no longer change over time. This refers to a situation where the amount of heat flowing into each point of the structure equals the amount of heat removed from it—in other words, dT/dt = 0 throughout the entire domain. In this type of analysis, the effect of the material’s heat capacity is neglected and there is no real time axis—we are interested only in the final, stabilized temperature distribution. The computational model therefore needs to account primarily for heat conduction properties (the thermal conductivity coefficient for each material), because these determine the temperature distribution under steady-state conditions. A steady-state thermal simulation therefore answers the question: what temperatures will the components of the structure reach over the long term, under constant conditions? This is useful, for example, for determining the maximum temperature of an electronic device enclosure during continuous operation.

Transient thermal analysis accounts for the passage of time and the storage of thermal energy in the material. In this approach, we examine how temperature changes over time at every point in the model. You must define not only thermal conductivity, but also material density and specific heat, because these properties determine the system’s thermal inertia (heat capacity). In addition, initial conditions are required (the initial temperature distribution at the start of the simulation), along with numerical parameters that define the time history of the analysis (simulation time and time step). Transient analysis makes it possible to answer questions such as: how quickly will the motor heat up to its operating temperature? or will local overheating occur during start-up before the system reaches steady state?. For example, a designer of an insulated tank knows that, ultimately, its contents will equalize in temperature with the surroundings (which is the steady-state result), but they are also interested in the rate at which the fluid cools over time—this requires transient analysis.

In practice, most thermal problems can be analyzed using either method, but the choice depends on whether the time history of the phenomenon matters. If you only care about the final result under steady conditions, steady-state analysis is faster and simpler—for example, determining the maximum temperature of a component during continuous operation. However, when transient thermal effects, changing conditions, or time-dependent phenomena are important (e.g., heating and cooling cycles, varying thermal loads), transient analysis becomes necessary. It is also worth noting that steady-state analysis may be insufficient in the presence of strong thermal nonlinearities, such as phase changes that require accounting for latent heat—in such cases, a transient approach is also required to correctly represent the physics of the phenomenon.

Coupling thermal analysis with structural analysis

From the perspective of a mechanical design engineer, the key point is that the temperature distribution within a structure affects its stress state and deformations. Most materials expand as temperature increases (they have a defined coefficient of thermal expansion). If, in a large assembly, one component heats up significantly and expands while another remains cooler (and expands less), thermal stresses may develop between them. Such stresses result from constrained thermal expansion—the hotter part “pushes” against the cooler part or against its mounting, leading to substantial internal forces. In many cases, thermal stresses prove critical to structural strength, potentially causing cracking, deformation, or accelerated material fatigue. That is why it is so important to couple thermal analyses with traditional strength analyses.

Coupled thermo-mechanical analysis (thermal-structural) involves combining two FEM simulations: first, a thermal analysis is performed to determine the temperature distribution in the model, and then those results are used as a load in a strength (mechanical) analysis. In practice, this is done, for example, by importing the temperature field as a thermal load into the structural model. The software then calculates additional strains in the elements caused by thermal expansion and the resulting stresses. This two-step process makes it possible to identify where dangerous stress concentrations arise in the structure due to temperature differences. For example, in electronic device structures, a coupled analysis will indicate whether heating components (such as a processor or transistors) cause deformation of the printed circuit board or solder joints that could, over time, lead to cracking. Another example is a steam turbine—thermal simulation provides information on the temperature distribution in the blades and turbine disc, and a strength analysis based on those results will show thermal stresses in the rotor and casing. This allows engineers to verify that under the most severe conditions (e.g., a cold start, a sudden thermal load) the design does not exceed allowable stresses.

In some cases, the coupling can be stronger and require an iterative approach: mechanical stresses, in turn, affect the temperature distribution (e.g., by changing air gaps, which reduces heat conduction, or through energy dissipation caused by deformation). In most engineering applications, however, thermo-mechanical coupling is handled in a one-way manner—first a thermal simulation, then a structural strength analysis—which is entirely sufficient to assess thermal stresses and predict how the structure will behave under thermal loads. From a tooling perspective, many CAE packages enable automatic transfer of thermal results to structural analysis, and even allow a coupled analysis to be run in a single pass. This allows the designer to comprehensively evaluate the product under near-real conditions—accounting for both mechanical and thermal loads at the same time.

Example applications across different industries

FEM thermal analyses are used wherever temperature affects the operation and strength of equipment. Below are a few examples from different industrial sectors:

• Elektronika: In electronic devices, a large share of failures results from component overheating. Thermal analysis makes it possible to predict the temperature distribution on PCBs, in integrated circuits, power converters, or batteries. This allows an engineer to design more effective cooling solutions—for example, the placement of heat sinks, ventilation openings, and the selection of materials with higher thermal conductivity—to ensure safe operating temperatures for components. Moreover, coupled analiza termiczno-wytrzymałościowa is useful, for example, for assessing deformation of the motherboard due to heating from a high-power processor, or for checking whether cyclic heating/cooling (e.g., during device power-on cycles) will not cause solder joint cracks or damage to the konstrukcji urządzeń elektronicznych. Thanks to thermal simulations, electronics manufacturers can increase the reliability of their products and prevent so-called thermal runaway—an uncontrolled temperature rise that leads to damage.
• Power and energy: In the energy sector, where equipment operates at high temperatures (e.g., in boilers, turbines, heat exchangers), thermal analyses are indispensable. They make it possible to assess how a boiler’s structural material will withstand continuous heating from hot flue gases or steam, as well as cooling during shutdowns. For example, in an analysis of a water-tube boiler, it is possible to simulate heat-flow modelling from hot gases through the tube walls and casing to determine the temperature distribution. Next, the calculated thermal stresses will indicate whether deformations or cracking may occur (e.g., at superheater hangers or at tube joints) during sudden changes in thermal load. In power plants, analyses also cover generator cooling, gas-turbine heating, and even thermal issues in high-power electrical systems. The aim is to prevent failures caused by component overheating, ensure long-term durability (e.g., avoiding material creep at high temperature), and optimise thermal insulation, which translates into better energy efficiency of the equipment.
• Machinery industry: In machines and mechanical equipment, thermal analysis helps design components exposed to friction, combustion, or other heat sources. For example, in internal combustion engines it is important to calculate how temperature is distributed in the cylinders, cylinder head, and exhaust system—in order to ensure effective cooling of these parts and avoid oil overheating or ignition of the mixture at the wrong moment. Engine thermal simulations make it possible to select suitable materials (e.g., aluminium alloys with additives that improve thermal conductivity) and to design the liquid-cooling system so that critical parts are kept within allowable temperatures. Another example is a machine or vehicle disc brake: during heavy braking, the discs and pads heat up to very high temperatures. Thermal analysis (often combined with airflow analysis—convective cooling) makes it possible to predict the disc’s maximum temperature and then assess the disc’s stresses and deformations after it cools down. This allows the designer to prevent deformation (warping) of brake discs or cracking due to thermal fatigue. In the machinery industry, heat-related manufacturing processes are also simulated, e.g., metal heat treatment and welding (introducing a large amount of heat locally)—to understand how the resulting temperature gradients translate into welding stresses and structural deformation.
• Aerospace industry: Aircraft structures must operate across extremely varied thermal conditions—from red-hot jet engines, through atmospheric friction at high speeds, to extreme cold at high altitude. FEA thermal analysis is used, for example, to design aircraft engine components: the high-pressure turbine in a jet engine is made from heat-resistant materials, yet it still requires intensive cooling. Thermal simulations of the turbine show the temperature distribution on the blades and disk during operation with aviation fuel combustion, enabling the design of cooling passages and the selection of materials for thermal-insulation coatings. At the same time, thermo-mechanical analysis verifies whether, at these temperatures, excessive stresses will occur that could lead to creep or cracking of components. In airframe design, the effects of aerodynamic heating are also considered (e.g., the leading edges of wings or the aircraft nose at supersonic speeds)—thermal analysis makes it possible to determine how much the skin temperature will rise and then assess whether thermal deformations could affect the airframe’s structural integrity. In the space industry (spacecraft, satellites), thermal simulations are in fact critical: for example, during atmospheric re-entry a return module experiences extreme heating, so thermal analysis of the ablative protection determines mission safety. In all these applications, the goal is to ensure that the structure can withstand the expected thermal loads with an appropriate safety margin.

Benefits of using FEM thermal analysis

Implementing FEM thermal analysis at the design stage delivers a range of tangible benefits for the design engineer and for the product’s final quality:

• Lower risk of structural failure: Simulations make it possible to identify potential issues related to overheating or thermal stresses at an early stage. The engineer can introduce preventive changes in advance, for example by redesigning a component exposed to excessively high temperatures or adding appropriate cooling. As a result, the final product offers higher reliability, and the risk of costly failures during operation is significantly reduced.
• Improved cooling and thermal optimisation: FEA analysis makes it possible to optimise the design for efficient heat dissipation. Based on the simulation results, the designer can improve the cooling system—for example, by increasing the surface area of heat sinks, changing fin geometry, ensuring better airflow, or using materials with higher thermal conductivity where needed. The result is a more even temperature distribution and lower peak temperatures, which benefits the device’s operation (e.g., electronics do not throttle power due to overheating, and the machine maintains operating parameters without downtime for cooling).
• Lower prototyping costs and faster development: The traditional approach to solving thermal issues relied on building successive prototypes and testing them under laboratory conditions—which is time-consuming and expensive. Thermal simulations make it possible to move a significant part of this work into the virtual space. An engineer can evaluate many design variants (different materials, different cooling configurations, insulation, etc.) without physically producing prototypes of every version. This shortens the design cycle and reduces costs, because the number of failed prototypes and rework decreases. The cost of any changes in the digital model is negligible compared with reworking a finished prototype. As a result, time to market can be reduced, and the financial savings from limiting physical testing are significant.
• Longer product durability and service life: By taking thermal effects into account during design, a device can be engineered to operate under safer thermal conditions throughout its entire service life. Avoiding overheating and excessive thermal stresses means that structural components will not fail prematurely due to damage such as deformation, cracking, or material degradation (e.g., insulation burnout, seal aging). Products designed with the support of thermal analyses therefore feature an extended service life. For the end user, this translates into a longer period of trouble-free operation, and for the manufacturer—an improved reputation and lower warranty costs. Thermal analysis also helps meet the requirements of norms and standards related to heat dissipation or resistance to temperature fluctuations, which can be critical, for example, in aviation or the energy sector.

Thermal FEA analysis is a powerful tool in a design engineer’s toolkit. It enables thermal simulation of complex structures under real operating conditions, providing insight into temperature distributions and the resulting thermal stresses even before a prototype is built. This makes it possible to prevent failures proactively and optimize the design—both for strength and for efficient cooling. A wide range of examples from electronics, power engineering, machinery, and aerospace shows that in each of these fields the benefits of thermal analyses are tangible: safer and more durable products, better-controlled operating temperatures, and savings of time and money during development. In an era of increasing device complexity and a drive for reliability, thermal analysis combined with structural analysis is becoming a standard of good engineering practice. It is worth implementing early in the project, treating it as an investment in the quality and reliability of the final product.