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  • Description

The Creation, Consumption, and Transfer of Heat


Material and Thermodynamic Data


Additional Images:

  • Conjugate Heat Transfer: A fan and a perforated grille induce an air flow in the enclosure of a computer power supply unit to abate internal heating.
  • Thermal Contact: Electric current produces joule heating in a contacting switch. The thermal and electrical resistances at the point of the contacts are coupled to the mechanical contact pressure at the interface.
  • Induction Heating: Creation of high temperatures in a semiconductor manufacturing hot-wall furnace is achieved through induction heating. Surface-to surface radiation between the wafer slab and the furnace walls as well as conduction and convection are considered.
  • Radiation: Free convection of argon gas occurs through density variations caused by temperature differentials. These are caused by the coupling of thermal radiation to heat transfer through conduction and convection.
  • Phase Change: A rod of ice is held at freezing at one end, and 80 oC at the other. The graph indicates it temperature profile over a period time taking into consideration the latent heat and the difference between solid and material properties, such as conductivity and heat capacity.
  • Thin Layers: Simulation of a heating circuit including DC induced Joule heating, heat transfer and a structural mechanics analysis of the thin resistive layer on a solid glass plate.

A Unified Workflow

The Heat Transfer Module is unique to the world of modeling as it is a dedicated tool for simulating thermal effects in your manufacturing processes and product designs. COMSOL takes a unified approach to both the model set-up and operation of your simulations for heat transfer and all other physical phenomena involved in your applications. You are thereby empowered with a standard tool for communicating with other engineers and engineering departments looking at alternate phenomena to yours. Irrespective of which physics you or your colleagues are working on within a particular application, your workflow is uniform and straightforward, and occurs as follows:

  • Import or draw the device or system geometry in question
  • Select material data or relations from the same files using constant or temperature-dependent properties
  • Decide the best description of the heat transfer of your system from a range of tailor-made interfaces that may or may not depend on other physics coupled to your system
  • Include any other physical effects that are coupled with the effects of heat transfer
  • Define conditions and constraints on your system’s boundaries
  • Mesh your system, then use the same or derived meshes between different simulations
  • Run the solving process, with an appropriate solver and settings for the analysis being performed
  • Process and visualize your results, and present these on the same graphs and figures even if from different simulations

Unified Platform for Simulating Thermal Effects on Manufacturing Processes and Product Designs

Together with COMSOL Multiphysics and the wealth of add-on modules, COMSOL provides you with a unified tool for all facets of your processes and designs, regardless of the physical phenomena you are studying. You can be modeling the joule heating of your system’s devices one day, the cooling of them by passing air through your system the next, and the thermal stresses your devices incur because of it the day after that. Or model all effects at once.

Heat transfer is an important physical effect that is mostly taken into consideration with other physical effects. Temperature fields lead to thermal stresses, while electromagnetic fields create resistive, induction, microwave, and RF heating. Fluid flow over different components and parts is essential for cooling them, while temperature variations have a very large impact on the material properties and their physical behavior when being thermally processed, such as casting or welding. The Heat Transfer Module includes a number of user interfaces for easy modeling of heat transfer coupled with other phenomena, and can be integrated into any of the other modules in the COMSOL® Product Suite.

The Mechanisms of Heat Transfer

Fundamental to the Heat Transfer Module is the ability to perform computations relating to the conservation of heat, or energy balances, where a variety of phenomena such as mechanical losses, latent heats, joule heating, or heat of reaction are available. The Heat Transfer Module provides ready-made interfaces, known as physics interfaces, that are configured to receive model inputs via the graphical user interface (GUI), and to use these inputs to formulate your energy balances. As with all physics interfaces within the software from the COMSOL Product Suite, you can manipulate the underlying equations to provide flexibility for modifying the transfer mechanisms, defining specific heat sources, or coupling to other physics.


The Heat Transfer Module helps you investigate the effects of heating and cooling in devices, components, or processes. The software furnishes you with simulation tools to study the mechanisms of heat transfer – conduction, convection, and radiation – often in collaboration with other physics, such as structural mechanics, fluid dynamics, electromagnetics, and chemical reactions. In this context, the Heat Transfer Module acts as a platform for all possible industries and applications where the creation, consumption, or transfer of heat or energy is the focus of or contributes significantly to the studied process.


Support for modeling radiation is provided for a number of scenarios in the Heat Transfer Module, which includes specialized solvers to model the phenomenon and couple it with convection and conduction. The Heat Transfer Module provides tools for modeling surface-to-ambient radiation, ambient-to-surface radiation, and surface-to-surface radiation in transparent, opaque, and participating media.

The module uses the radiosity method to model surface-to-surface radiation, and accounts for surface-properties dependent on the wavelength where you can simultaneously consider up to five spectral bands in the same model. This is appropriate for modeling sun radiation, where the surface absorptivity for short wavelengths (solar spectral band) may differ from the surface emissivity for the longer wavelengths (ambient spectral band). In addition, transparency properties can be defined for each spectral band. The Heat Transfer Module also models radiative heat transfer in participating media, which accounts for the absorption, emission, and scattering of heat radiation in such media.


The presence of fluids in your systems invariably introduces convection to your heat transfer applications and energy contributions, through pressure work and viscous effects. The Heat Transfer Module easily supports these processes and accounts for both forced and free or natural convection. It includes a specific physics interface for conjugate heat transfer, where solid and fluid materials are modeled in one and the same system. To account for fluid flow, the Heat Transfer Module contains physics interfaces to model laminar flow and turbulent flow through using high-Reynolds and low-Reynolds k-ε turbulent models. In all flow cases, natural buoyancy effects occurring due to differences in temperature are respected by assuming nonisothermal flow. Integrating your heat transfer models with the CFD Module allows for further simulations of the fluid flow, including alternate turbulence models, porous media flow, and two-phase flow.

Additionally, the Heat Transfer Module provides features for simplifying modeling of convection, where fully modeling the fluid dynamics does not provide extra accuracy or is computationally prohibitive. The features are available through a built-in library of heat transfer coefficients, and can be used to simulate the transfer of heat between the surroundings of your systems and your boundaries through either forced or natural convection. The module also contains relations for different types of geometric configurations, like chimneys or plates (vertical, inclined, or horizontal), and different external fluids (air, water, and oil).

Heat Transfer in Porous Media

While the concepts of heat transfer in fluid flow for both laminar and turbulent flow in free media are quite well-known, the Heat Transfer Module also has robust interfaces for the modeling of heat transfer in porous media, accounting for both conduction and convection, in solid and open pore phases of the porous matrix. You can select different averaging models to define effective heat transfer properties that are automatically calculated from the respective properties of the solid and fluid materials. You can also access a predefined feature for heat dispersion in porous media, caused by the tortuous path taken by fluids through the pores.


A physics interface for the bioheat equation is provided in the Heat Transfer Module. The Bioheat Equation interface is the perfect tool for simulating thermal effects in human tissue and other biological systems, whether through microwave heating, resistive heating, heating through chemical reaction, or radiative heating. As always in the COMSOL simulation environment, temperature changes can easily be funneled back to the material properties of other physics, such as electrical material properties for a strongly coupled multiphysics simulation. Bioheating can be combined with a variety of phase change phenomena, including tissue necrosis.

Phase Change

Phase change is a disruptive property in heat transfer analysis. It can introduce hard-to-predict transformations of either the transient geometric interfaces between the phases, or sudden changes in material properties like conductivity, heat capacity, or flow behavior that can differ by orders of magnitude between the solid, liquid, and gas phases of the material. Phase change also introduces latent heats, which dominates in many heat balances. Through a number of different features and user interfaces, COMSOL Multiphysics and the Heat Transfer Module have the ability to account for these disruptions, including the ability to model volume changes using moving meshes. Also supported is the automatic definition of thermodynamic properties to account for sudden changes in material properties and still allow continuity through control of the interval between phase changes.

Thermal Contact Resistance

When two solid objects are in connection with each other, the resistance to heat transfer is often a function of how well they are pressed together and their respective surface roughness. The roughness creates small gaps between surfaces, which inhibits heat transfer, while pressing them together reduces these gap sizes. Physics interfaces are provided in the Heat Transfer Module to simulate the contact thermal conductance coefficient being dependent on the applied stress, on the specific conductivity in the gap, and also by accounting for the surface-to-surface radiation contribution between surfaces separated by small gaps. Integrating your heat transfer models with the Structural Mechanics Module provides direct coupling capability between the thermal and mechanical aspects of the contact, including thermal expansion.

Thin Layers and Shells

Your devices or processes will often consist of materials or domains that are geometrically much smaller than the rest of your system. Such examples include thin copper layers on PCBs, the wall of a pressure vessel, or thin insulating layers. Specialized modeling tools available in the Heat Transfer Module simulate these features and conserve computational resources. Highly-conductive shells are used in situations where the gradient of heat transfer is significant in the tangential directions of a layer or shell, and not across its thickness, avoiding the necessity to mesh over the width of this layer or shell. Yet, they couple the results from their solutions to the 3D entities, with which the layer or shell is in connection. This could be either a thin wall between two larger domains, a domain and its surroundings, or a layer embedded into the surface of another solid. In a similar way, physics interfaces for thin, thermally-resistive layers provide an easy way of representing poorly conducting materials.

The Thermoelectric Effect Multiphysics Node

Materials that display the thermoelectric effect are able to convert temperature differences to electric voltages as the heat flux contains charge carriers. Alternatively, applying a voltage to these materials results in a temperature gradient across the material. Devices made from thermoelectric materials are often used for electronic cooling or portable refrigerators, while thermoelectric energy harvesting devices are also popular.

The Thermoelectric Effect multiphysics interface is a combination of the Electric Currents and Heat Transfer in Solids interfaces. You get access to the full range of heat transfer capabilities of the Heat Transfer Module such as advanced boundary conditions and heat radiation. As with all other physics interfaces within the COMSOL Multiphysics software, the Thermoelectric Effect interface can be coupled to any other physics interface, such as the Solid Mechanics interfaced. Material properties for two common thermoelectric materials are available: Bismuth Telluride and Lead Telluride, and you can easily add user-defined thermoelectric materials.