Introduction
The Heat Transfer Module is used by product designers, developers, and scientists who use detailed geometric models to study the influence of heating and cooling in devices and processes. It contains modeling tools for the simulation of all mechanisms of heat transfer including conduction, convection, and radiation. Simulations can be run for transient and steady conditions in 1D, 1D axisymmetric, 2D, 2D axisymmetric, and 3D coordinate systems.
The high level of detail provided by these simulations allows for the optimization of design and operational conditions in devices and processes influenced by heat transfer.
Figure 1: The temperature and flow field in an aluminum heat sink and in cooling air that is pumped over the heat sink. The temperature and flow field are solved using detailed geometry and a description of the physics.
The Application Libraries window contains tutorials as well as industrial equipment and device benchmark applications for verification and validation.
This introduction fine-tunes your COMSOL Multiphysics® modeling skills for heat transfer simulations. The model tutorial solves a conjugate heat transfer problem from the field of electronic cooling, but the principles are applicable to any field involving heat transfer in solids and fluids.
Basic Concepts Described in the Heat Transfer Module
Heat is one form of energy that, like work, is in transit inside a system or from one system to another. This energy may be stored as kinetic or potential energy in the atoms and molecules of a system.
Conduction is a form of heat transfer that can be described as proportional to the temperature gradients in a system. This is formulated mathematically by Fourier’s law. The Heat Transfer Module describes conduction in systems where thermal conductivity is constant or is a function of temperature or any other model variable, for example, chemical composition.
Figure 2: Heat transfer in a system containing a solid surrounded by a fluid (conjugate heat transfer). In the fluid, heat transfer can take place through conduction and advection, while in a solid, conduction is the main heat transfer mechanism. Heat transfer by radiation can occur between surfaces or between surfaces and their surroundings.
In the case of a moving fluid, the energy transported by the fluid has to be modeled in combination with fluid flow. This is referred to as convection of heat and must be accounted for in forced and free convection (conduction and advection). This module includes descriptions for heat transfer in fluids and conjugate heat transfer (heat transfer in solids and fluids in the same system), for both laminar and turbulent flows. In the case of turbulent flow, the module offers two algebraic turbulence models, the Algebraic yPlus and L-VEL models, as well as the standard k-ε model for high-Reynolds numbers, the low Reynolds number k-ε model, and the SST (shear stress transport) model to accurately describe conjugate heat transfer. The Gravity feature defines buoyancy forces induced by density differences, in particular due to temperature dependency of the density.
Radiation is the third mechanism for heat transfer that is included in the module. The associated features handle surface-to-ambient radiation, surface-to-surface radiation, and external radiation sources (for example, the sun). The surface-to-surface radiation capabilities support mixed diffuse-specular reflection as well as transmission through semitransparent layers. Surface properties may be a function of several parameters, in particular of the position, the temperature, the wavelength or the incident angle. The Heat Transfer Module also contains functionality for radiation in participating and absorbing media. This radiation model accounts for the absorption, emission, and scattering of radiation by the material present between radiating surfaces. The module offers three models for participating and absorbing media simulations: the discrete ordinates method (DOM), the P1 method, and the Rosseland approximation. Finally the Radiative Beam in Absorbing Media interface provides features to define the absorbing media properties, as well as options for multiple incident beams.
The basis of the Heat Transfer Module is the study of the balance of energy in a system. The contributions to this energy balance originate from conduction, convection, and radiation, as well as from latent heat, Joule heating, heat sources, and heat sinks. In the case of moving solids, translational terms may also be included in the heat transfer models, such as for solids in rotating machinery. The effects of solid deformations on thermal properties can also be modeled. Physical properties and heat sources (or sinks) can be described as arbitrary expressions containing the dependent variables in a model (for example, temperature and electric field). The heat transfer equations are defined automatically by the dedicated physics interfaces for heat transfer and fluid flow. The formulations of these equations can be visualized in detail for validation and verification purposes.
Physical properties such as thermal conductivity, heat capacity, density, and emissivity can be obtained from the built-in material library for solids and fluids and from the Material Library add-on in COMSOL Multiphysics. In addition, the Heat Transfer Module contains relations for the calculation of heat transfer coefficients for different types of convective heat transfer from a surface. For turbulent heat transfer, it also features relations used to calculate the thermal conductivity in turbulent flow, using the eddy diffusivity from turbulence models (sometimes referred to as turbulent conductivity).
The modeling workflow is straightforward and is defined by the following steps: define the geometry, select the material to be modeled, select the type of heat transfer, define the boundary and initial conditions, define the finite element mesh, select a solver, and visualize the results. All of these steps are accessed from the COMSOL Desktop. The mesh and solver steps are often automatically included with the default settings, which are tailored to each type of heat transfer interface.
The Applications
Heat generation and transfer are present in most physical processes and phenomena, either as side effects or as desired effects. The Heat Transfer Module can be effectively used to study a variety of processes (for example, building ventilation effects), to account for turbulent free convection and heat transfer; to analyze the impact of heat generation and cooling in electronic microdevices; and to study phase change effects.
The Application Library in the Heat Transfer Module contains tutorial and benchmark models from different engineering applications.
The Applications section in the Application Library contains ready-made applications than can be run using a dedicated interface. These applications are designed to solve a particular class of problems in a simplified user interface that makes it easy to use, even for non-COMSOL Multiphysics users.
Figure 3: Snapshot of an application dedicated to finned pipe characterization. The applications computes finned pipe properties such as the pressure drop and the temperature drop in the pipe. The finned pipe design and the operating conditions are customizable via a dedicated user interface.
The Building and Constructions section in the Application Library includes files that are related to energy efficiency and dissipation in buildings. Most of these use convective heat flux to account for heat exchange between a structure and its surroundings. Simulation provides accurate depictions of the heat and energy fluxes that inform energy management in buildings and construction.
Figure 4: Temperature field in a building wall exposed to a cold environment. This plot is from the model Thermal Bridge 3D — Two Floors.
The Heat Exchangers section in the Application Library presents several heat exchangers of different sizes, flow arrangements, and flow regimes. They benefit from the predefined Conjugate Heat Transfer interface that provides ready-to-use features for couplings between solids, shells, and laminar or turbulent flows. The simulation results show properties of the heat exchangers, such as their efficiency, pressure loss, or compactness.
Figure 5: Wall temperature in a shell-and-tube heat exchanger resulting from heat exchange between a cold and a hot fluids separated by a thin wall. This plot is from the Shell-and-Tube Heat Exchanger model.
The Medical Technology section in the Application Library introduces the concept of bioheating. Here, the influences of various processes in living tissue are accounted for as contributions to heat flux and as sources and sinks in the heat balance relations. Bioheating applications that can be modeled include the microwave heating of tumors (such as hyperthermia cancer therapy) and the interaction between microwave antennas and living tissue (such as the influence of a diagnostic probe or cellphone use on the temperature of tissue close to the ear). The benefit of using the bioheat equation is that it has been validated for different types of living tissue, using empirical data for the different properties, sources, and sinks. In addition, damage-integral features are provided to model tissue necrosis due to hyperthermia or hypothermia. The models and simulations available in this physics interface provide excellent complements to experimental and clinical trials; the results may be used for many purposes, for example, to develop new methods for dose planning.
The Orbital Thermal Loads section in the Application Library presents applications related to spacecraft thermal analysis. All the applications include the definition of the planet, orbit, and spacecraft properties. From this information the position and orientation of the spacecraft, but also the direct solar radiation, albedo, and planet radiative flux as well as the radiative heat transfer between the different spacecraft parts are computed. It is possible to analyze further the heat transfer in the spacecraft by including a heat transfer physics interface in the model to account for the energy balance including the heat conduction in solid parts.
Figure 6: Orbit of a satellite around the Earth. The track color indicates whether the satellite is in eclipse or not. The spacecraft surface color represents the magnitude of the incident solar irradiation.
The Phase Change section in the Application Library presents applications such as metal melting, evaporation, and food cooking. A common characteristic of these models is that the temperature field defines the material phase, which has a significant impact on the material properties. Equations representing the highly nonlinear behavior of the material properties as a function of temperature are automatically generated by the Phase Change Material subfeature or the Phase Change Interface boundary condition. The phase change model provides information to control material transformation.
The Power Electronics and Electronic Cooling section in the Application Library includes examples that often involve heat generation, heat transfer in solids, and conjugate heat transfer (where cooling is described in greater detail). The examples in these applications are often used to design cooling systems and to control the operating conditions of electronic devices and power systems. The module provides the tools needed to understand and optimize flow and heat transfer mechanisms in these systems when the model results are interpreted.
Figure 7: Temperature field and flow streamlines as a result of conjugate heat transfer in computer power supply unit (PSU). This plot is from the Electronic Enclosure Cooling tutorial model.
The Thermal Contact and Friction section in the Application Library contains examples where thermal cooling is dependent on a thermal contact or where the heat source is due to friction. The thermal contact properties can be coupled with structural mechanics that provide the contact pressure at the interface. It is also possible to combine thermal contact and electrical contact in the same model.
The Thermal Processing section in the Application Library contains examples that include thermal processes, such as continuous casting. A common characteristic of most of these examples is that the temperature field and the temperature variations have a significant impact on the material properties or the physical behavior (thermal expansion, thermophoresis, and so forth) of the modeled process or device. Since these couplings make the processes very complicated, modeling and simulation often provide a useful shortcut to a complex understanding.
Figure 8: Temperature field plot from the Continuous Casting — Arbitrary Lagrangian-Eulerian Method model. A sharp temperature gradient is found across the mushy layer, where the liquid metal solidifies.
The Thermal Radiation section in the Application Library contains applications where heat transfer by radiation must be considered in order to describe the heat flux accurately. A common feature of these examples is that they contain devices where high radiative heat transfer is observed due to high temperature, high surface emissivity, or external radiation like solar radiation. These applications account for the nonlinearity that results from the radiative heat transfer and geometric effects such as shielding between two radiating objects. The geometry or the radiation source may be moving or deformed during the simulation.
The Thermal Stress section in the Application Library presents examples where the temperature field causes thermal expansion. Thermal stress can result from heat exchanges between cold and hot devices or from processes like Joule heating. These require the Structural Mechanics Module or the MEMS Module for the portions where structural mechanics are simulated.
The Tutorials section in the Application Library contains examples that demonstrate the implementation of a particular phenomenon or the use of some features. Reproducing these applications is an effective method to discover the capabilities of the Heat Transfer Module and to get more experience using it.
The Verification Examples section in the Application Library provides examples that reproduce a case with a known solution and compare it with COMSOL Multiphysics results.
Figure 9: Comparison of the temperature obtained by COMSOL Multiphysics and an analytical solution (green line).
The next section describes the available physics interfaces in this module.