Heat Transfer Module
Heat Transfer Module
Software for General-Purpose Modeling of Heat Transfer in Solids and Fluids
The Creation, Consumption, and Transfer of Heat
The Heat Transfer Module helps investigate the effects of heating and cooling in devices, components, or processes. The module 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.
Material and Thermodynamic Data
The Heat Transfer Module comes stocked with an internal material database containing the material properties of a number of common fluids and gases that includes many of the thermodynamic data required for accurate analysis. This includes thermal conductivity, heat capacities, and densities. The Material Library is also a source for material properties, with either the data or algebraic relations of over 2,500 solid materials, where many of their properties, such as Young’s Modulus and electrical conductivity, are temperature-dependent. The Heat Transfer Module also supports the import of thermodynamic and other material data from Excel® and MATLAB®, and for connecting with external thermodynamic databases through the CAPE-OPEN interfacing standard.
- 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 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.
Numerical Simulation-Based Topology Optimization Leads to Better Cooling of Electronic Components in Toyota Hybrid Vehicles
Toyota Research Institute of North America, MI, USA
The Toyota Research Institute in Ann Arbor drives cutting-edge research in energy efficiency, mobility infrastructure, and safety. Here, Ercan Dede and his team are designing heat sinks (or cold plates), which are affixed to fragile electrical systems and other applications in Toyota’s hybrid vehicles. Their simulations simulate the cold plate ...
Switching Made Easy
Matthias Richwin, Leopold Kostal GmbH, Dortmund, Germany
Modern cars offer a wide range of complex functionality that comes with several design challenges. This story discusses some of the necessary updates to a roof module in a premium car and the charging system of an electric car. The roof module of a particular model houses several components. 90% of the generated heat goes into its printed ...
Cluster Simulation of Refrigeration Systems
Stephen Codyer & Mehdi Raessi Department of Mechanical Engineering UMass Dartmouth Dartmouth, MA Jessica Currie & Vladimir GoldsteinSunwell Technologies, Inc., Woodbridge ON, Canada
Sunwell Technologies Inc. produces and distributes the slurry ice (Deepchill™) that is an environmentally-friendly way to refrigerate foods and other items in trucks and the like. They commissioned the Computational Multiphase Flows group at the University of Massachusetts, Dartmouth (UMass Dartmouth) to provide simulation support to the ...
Multiphysics Simulation Helps Miele to Optimize Induction Stove Designs
Christian Schröder mieletec FH Bielefeld Germany Holger Ernst Miele Germany
The induction stove was designed to meet a consumer need for better precision and speed than traditional stoves. Designers were tasked with improving the energy efficiency of the induction coils-stovepot interaction considering both the thermal and electromagnetics of the system. Miele, a world leader in domestic appliances and commercial ...
Keeping LEDs Cool Gets More Manageable Through Simulation
Aulis Tuominen and Mika Maaspuro University of Turku Turku, Finland Toni Lopez Philips Research Eindhoven, The Netherlands Sami Yllikäinen Hella Lighting Finland Oy Salo, Finland Raimo Laitinen ...
Light-emitting diodes (LEDs) offer many benefits over incandescent lighting, such as long life spans and high luminous efficiency, and they are environmentally friendly. One of the drawbacks, however, is that LEDs need to operate at the lowest possible temperatures and this must be carefully regulated. Researchers at Business and Innovation ...
Simulation-Based Engineering Fosters Innovation and Invention
Ozgur Yildirim and Zihong Guo Intellectual Ventures Bellevue, WA
Simulation-based engineering is the key to shortening time to market for innovations. Intellectual Ventures, in Bellevue, WA, is reaping the benefits of using COMSOL Multiphysics to accelerate their workflow from design study to prototype, and then on to their customers as inventions through various partnerships and licensing programs. Projects ...
Battery Simulation Propels Electric Cars in China
Dr. Songrui Wang Tianjin Institute of Power Sources, Tianjin, China
Dr. Songrui Wang is a researcher at The Tianjin Institute of Power Sources, involved in battery testing and evaluation for design recommendations on safety. She analyzes the risk of potential fire hazards associated with lithium ion batteries, which are fast becoming the most popular sort of battery for vehicles, mobile devices, and many other ...
Around the Clock Solar Power
ENEL, Rome, Italy
Italian utility ENEL and the Italian National Agency for New Technologies joined together to develop a new kind of Concentrating Solar Power (CSP), using Parabolic Trough CSP to generate electricity during sunny hours as well as under overcast conditions or at night. This new type of CSP plant depends on molten salt as a medium for storing heat ...
Doubling Beam Intensity Unlocks Rare Opportunities for Discovery at Fermi National Accelerator Laboratory
M. A. Hassan, T. Khabiboulline, J. Reid Fermilab, IL, USA
Behind the discovery of the most fundamental and rare physical processes within our universe is powerful technology, such as the particle accelerators in use today at Fermilab. For over 40 years, one particle accelerator in particular, the Booster synchrotron, has been instrumental in providing high-intensity proton beams for particle physics ...
Simulation Turns Up the Heat and Energy Efficiency at Whirlpool Corporation
N. Garcia-Polanco Whirlpool Corporation, Italy
Engineers working on a joint research project between Whirlpool Corporation and the European initiative GREENKITCHEN project are using simulation to improve the energy efficiency of domestic ovens. Since only ten to twelve percent of the total energy expended by an oven is actually used to heat the food, the researchers had plenty to investigate. ...
Simulation Software Brings Big Changes to Cable Industry
M. Bechis Prysmian, Italy
The design and testing of high-voltage cables for terrestrial and submarine applications is paramount to Prysmian's business model. A fundamental challenge in designing power transmission systems is optimizing the cables so that they can reliably deliver the required steady-state current while remaining at, or preferably below, the maximum ...
Using Multiphysics Simulation to Prevent Building Damage
P. Sekki Vahanen Group, Finland
In addition to surviving normal winters, a strong building must be able to survive the worst winters expected in a 50-year period. When moisture and contaminants enter concrete foundations, they create the risk of cracking or other structural damage once the soil or foundation freezes. Vahanen Group specializes in building services and performs ...
Battling Corrosion in Nuclear Waste Storage Facilities
G. Barbella, P. Geraldini Sogin, Italy
Nuclear sites in Italy are being decommissioned, leaving questions about how to safely manage and store radioactive waste. Nuclear waste can be stored temporarily in steel drums encased in concrete, but environmental factors must be carefully controlled to prevent corrosion of the steel. It is difficult to constantly monitor the corrosion ...
Conjugate Heat Transfer
Luke T. Gritter, Jeffrey S. Crompton, Sergei Yushanov, and Kyle C. Koppenhoefer AltaSim Technologies Columbus, OH USA
This is an application brief describing the concept of Conjugate Heat Transfer, which is important in many industrial processes, such as quenching. In this brief, they simulate the heat transfer with and without phase transformation to analyze the rate of heat dissipation with respect to the flow conditions of the coolant media. The fluid flow ...
Multiphysics Analysis of a Burning Candle
Luke T. Gritter, Sergei Yushanov, Jeffrey S. Crompton, and Kyle C. Koppenhoefer AltaSim Technologies, Columbus, Ohio
Using COMSOL Multiphysics, AltaSim Technologies were able to predict the temperature distribution and flow pattern of a burning flame during steady state candle burning. In a burning candle, local temperatures in the flame exceed 1400 °C. The heat transfer would include radiation, conduction, and convection components while the low melting ...
Optimization Slashes Energy Consumption in Silicon-Based MEMS CO2 Detectors
Serge Gidon CEA, Leti, Minatec, Grenoble, France
CEA-MINATEC is an international center for micro and nano-technologies which is funded by CEA, a French government-funded technological research organization. One of their current projects is developing silicon-based MEMS CO2 sensors that employ optical detection for monitoring adequate building ventilation. For the sensor to function, a ...
COMSOL Assists Master Chef in Winning International Competition
Dagbjorn Skipnes Nofima Norconserv AS, Stavanger, Norway
Nofima is a research group majority owned by the Ministry of Fisheries that performs research and development in aquaculture, fisheries, and the food industry. Nofima collaborated with the Norwegian Centres of Expertise – Culinology and Chef Gunnar Hvarnes to promote halibut through a cooking competition and provided research to ensure a new ...
Understanding the Origin of Uncertainty in Thermometer Calibration
Jonathan Pearce National Physical Laboratory UK
Thermometers have widespread application and like any measurement device, they must be calibrated. Many do this with the International Temperature Scale of 1990 (ITS-90), which is a platinum resistance thermometer that calibrates using a fixed point cell, which is a container with a well running through its center for insertion of the ...
When it’s Impossible to Take Actual Measurements, Multiphysics Provides the Answers
Simon Chiartano, Terres Réfractaires du Boulonnais (TRB), France
To contain splashes and provide protection at plants where metal is fabricated, blast furnace runners need a roof made of cast iron and concrete. Terres Réfractaires Du Boulonnais, a manufacturing company in France, has hundreds of blast furnaces with a short functional lifespan, so engineers need to design roof runners as economically as ...
Multiphysics Software, a Versatile, Cost-Effective R&D Tool at Sharp
Chris Brown Sharp Laboratories of Europe, UK
There are several kinds of technology that designers at Sharp Laboratories of Europe work to create. From LED lighting, displays, and microfluidic lab-on-a-chip technology, to complex energy systems used in various devices, Sharp needed a new approach to finding the best designs. COMSOL Multiphysics and its add-on products provided the ...
Innovative Thermal Insulation Techniques Bring Vaccines to the Developing World
D. Gasperino, O. Yildirim Intellectual Ventures, WA, USA
When medical professionals transport vaccines, their cargo needs to be kept at a cool temperature. This limits their ability to travel to regions where there is not enough electricity. Intellectual Ventures’ Global Good program designed a thermos-like container that is powered by ice and keeps vaccines cool for long periods of time. They used ...
Modeling of Complex Physics Speeds Chip Development
P. Woytowitz Lam Research Corporation, CA, USA
With technological advancements accelerating so rapidly, more powerful computer chips are needed to meet the high demands of fast-growing industries. Lam Research Corporation manufactures semiconductor devices and equipment used to deposit, etch, and clean material layers laid onto wafers during semiconductor processing. With processes as precise ...
Continuous Casting: Optimizing Both Machine and Process with Simulation
N. Grundy SMS Concast, Switzerland
The process of continuous casting has transformed steel production, saving valuable resources while improving steel quality and process efficiency. Continuous casting involves carrying molten refined steel to a caster. There, water-cooled copper molds are used to form steel strands that are cut and then cooled. High-quality steel production ...
Simulation Helps Improve Atmosphere Revitalization Systems for Manned Spacecraft
J. Knox, R. Coker NASA Marshall Space Flight Center, AL, USA
To ensure astronaut safety on space missions, it is necessary to routinely revitalize the atmosphere in manned spacecraft. Jim Knox, Rob Coker, and a team of engineers at the NASA Marshall Space Flight Center have developed a water-saving system called an Isothermal Bulk Dessicant (IBD). The IBD is used to collect water from the atmosphere for re ...
Actuation Technique for Miniature Robots Developed using Multiphysics Simulation
P. Lazarou, C. Rotinat CEA LIST, France
Robotic devices for minimally invasive surgery procedures require flexible tools and careful actuation. But most robotic surgery devices are bulky, expensive, and physically draining for surgeons to operate for long periods of time. At the French Atomic and Alternative Energies Commission (CEA LIST), researchers are investigating miniature phase ...
Developing a New Microreactor for Organic Synthesis Using Microwave Heating
W. Lee, K. Jensen MIT, MA, USA
The chemical reactions used to generate solvents and certain pharmaceuticals rely on organic synthesis, a process of combining individual chemicals that can be accelerated through microwave heating. A microreactor system facilitates the direct, localized, and efficient temperature change necessary for successful synthesis. However, a uniform ...
Keeping Cool: SRON Develops Thermal Calibration System for Deep-Space Telescope
C. de Jonge SRON, Netherlands
Deep-space telescopes require ultrasensitive detectors and calibration to pick up weak far-infrared signals. The SpicA Far-InfraRed Instrument (SAFARI), an infrared camera that will fly aboard the Space Infrared Telescope for Cosmology and Astrophysics (SPICA), has sensors that measure the far-infrared spectrum. The SAFARI system includes a ...
This model is intended as a first introduction to simulations of fluid flow and conjugate heat transfer. It shows you how to: Draw an air box around a device in order to model convective cooling in this box, set a total heat flux on a boundary using automatic area computation, and display results in an efficient way using selections in data sets.
Shell-and-Tube Heat Exchanger
Shell-and-tube heat exchangers are commonly used in oil refineries and other large chemical processes. In this model, two separated fluids at different temperatures flow through the heat exchanger, one through the tubes (tube side) and the other through the shell around the tubes (shell side). Several design parameters and operating conditions ...
Parameterized Electronic Enclosure Geometry
This study simulates the thermal behavior of a computer Power Supply Unit (PSU). Most of such electronic enclosures include cooling devices to avoid electronic components to be damaged by excessively high temperatures. In this model, an extracting fan and a perforated grille cause an air flow in the enclosure to cool internal heating.
This example demonstrates how to model a phase change and predict its impact on a heat transfer analysis. When a material changes phase, for instance from solid to liquid, energy is added to the solid. Instead of creating a temperature rise, the energy alters the material’s molecular structure. Equations for the latent heat of phase changes ...
Tin Melting Front
This example demonstrates how to model phase transition by a moving boundary interface according to the Stefan problem. A square cavity containing both solid and liquid tin is submitted to a temperature difference between left and right boundaries. Fluid and solid parts are solved in separate domains sharing a moving melting front. The position ...
Small heating circuits find use in many applications. For example, in manufacturing processes they heat up reactive fluids. The device used consists of an electrically resistive layer deposited on a glass plate. The layer causes Joule heating when a voltage is applied to the circuit. The layer’s properties determine the amount of heat produced. ...
Fluid-Structure Interaction in Aluminum Extrusion
In massive forming processes like rolling or extrusion, metal alloys are deformed in a hot solid state with material flowing under ideally plastic conditions. Such processes can be simulated effectively using computational fluid dynamics, where the material is considered as a fluid with a very high viscosity that depends on velocity and ...
Thermoelectric coolers are widely used for electronics cooling in various application areas, ranging from consumer products to spacecraft design. Exploiting the Peltier effect, they consist of several thermoelectric legs sandwiched between two thermally conductive plates, one cold and one hot. Due the variety of applications, there can be many ...
Evaporation in Porous Media with Large Evaporation Rate
Evaporation in porous media is an important process in the food and paper industries, among others. Many physical effects must be considered: fluid flow, heat transfer, and transport of participating fluids and gases. All of these effects are strongly coupled and predefined interfaces can be used to model these effects with the Heat Transfer ...
Convection Cooling of Circuit Boards - 3D Natural Convection
The suite of models examine the air cooling of circuit boards populated with multiple integrated circuits (ICs), which act as heat sources. Two possible cooling scenarios are depicted: vertically aligned boards using natural convection, and horizontal boards with forced convection (fan cooling). In this case, contributions caused by the induced ...