## Heat Transfer Module Updates

For users of the Heat Transfer Module, COMSOL Multiphysics^{®} version 5.3a brings a new *Inflow* boundary condition that can account for upstream temperature and pressure, a complete multiphysics coupling for modeling moisture transport in air, as well as a new interface for modeling radiative beams in absorbing media. Learn about these heat transfer features and more below.

### New Boundary Condition: Inflow

The new *Inflow* boundary condition applies an inflow of heat coming from a virtual domain, which has been excluded from the model to simplify the analysis, with known upstream conditions. Applied at inlets, where you would previously apply a *Temperature* boundary condition, the *Inflow* condition accounts for temperature and pressure from upstream phenomena. Additionally, it does not constrain the temperature at the inlet's adjacent edges (or points in 2D), but instead assigns a heat flux that is consistent with the upstream conditions. Overall, this leads to more accurate and realistic physical models. All the applicable models in the Application Libraries have been updated to take advantage of this boundary condition.

*The crossflow heat exchanger model has more realistic results with the upstream properties of the inflow taken into account.*

### Moisture Flow Multiphysics Coupling

Managing moisture transport is important in a large number of applications, including electronics packaging and building physics. COMSOL Multiphysics^{®} version 5.3a brings a complete suite of multiphysics couplings for modeling heat transfer, moisture transport, and fluid flow, enabling quick and easy modeling of real-world heat and moisture transport.

Expanding upon moisture modeling functionality included in previous releases, the new *Moisture Flow* multiphysics coupling node is now available to model moisture transport in air by laminar and turbulent flows. It couples the laminar and turbulent versions of the *Single-Phase Flow* interfaces with the *Moisture Transport in Air* interface. One benefit of the *Moisture Flow* coupling, found in the *Chemical Species Transport* branch, is that it handles turbulent mixing and moisture wall functions for turbulent flows. When combined with the *Nonisothermal Flow* and the *Heat and Moisture* multiphysics couplings, you have a complete and comprehensive set of features for heat and moisture modeling in building material and moist air. To implement the full multiphysics coupling, first add the *Moist Air* version of the *Heat and Moisture Transport* coupling. Next, add a laminar or turbulent single-phase flow interface. Finally, add the *Nonisothermal Flow* and *Moisture Flow* multiphysics couplings. When adding each multiphysics coupling, the software will automatically couple the appropriate single physics interfaces together.

Representation of the *Heat Transfer*, *Single-Phase Flow*, and *Moisture Transport* interfaces with the associated multiphysics couplings.

*Heat Transfer*,

*Single-Phase Flow*, and

*Moisture Transport*interfaces with the associated multiphysics couplings.

### Irreversible Transformation in Solids

The *Irreversible Transformation* attribute feature, available for solid heat transfer under the *Solid* domain node, now has extended capabilities to model thermally induced irreversible transformations. Applications include phenomenological modeling of solid combustion and melting. The previously named *Energy absorption* transformation model has been renamed *Arrhenius kinetics* and allows you to set more configurations for the rate of reaction with an option to specify the polynomial for the Arrhenius kinetics equation of any order *n*.

Additionally, the attribute feature has a new *User defined* option for the transformation model, where you can set the *Fraction of transformation*. This new option is particularly useful when none of the predefined transformation models fit with your model, and/or when the fraction of transformation is obtained by a separate user-defined physics or mathematics interface. With the user-defined options, you also have the capabilities to specify enthalpy change, account for the generation or loss of heat in the energy balance, and define different thermal properties for the transformed state.

### Modeling of Thermal Contact by an Equivalent Thin Resistive Layer

You can now model thermal contact with a new *Equivalent thin resistive layer* option for the thermal contact model. Using this option, you can define thermal contact based on effective thermal contact conductance. This is useful when the effective thermal contact conductance is known from thermal measurements or when the surface properties needed in the other contact models are unknown. This option offers three possibilities to define the layer conductance, by specifying either the layer conductance, layer resistance, or layer thermal conductivity and thickness.

The new *Equivalent thin resistive layer* option in the *Thermal Contact* node.

*Equivalent thin resistive layer*option in the

*Thermal Contact*node.

### Heat Transfer Coefficients Library for Arbitrary Fluids

The heat transfer coefficients available in the coefficient libraries are defined for a number of configurations and are used to simulate heating or cooling due to an external fluid flow that is not part of the model. The choice of the fluid material was previously restricted to air, water, or transformer oil. With the release of COMSOL Multiphysics^{®} version 5.3a, two new options are introduced for the external fluid when the heat transfer coefficient is defined by a correlation: *Moist air* and *From material*.

When the *Fluid* option is set to *Moist air*, the external relative humidity has to be specified for an accurate definition of the correlation. When the *Fluid* option is set to *From material*, you can choose any material available in the *Materials* node. The corresponding material properties are then used to define the heat transfer coefficient for the selected configuration.

### Improved Capabilities for Heat and Moisture Transport

#### Latent Heat Sources

The *Heat and Moisture Transport* multiphysics coupling combines the *Heat Transfer* and *Moisture Transport* interfaces. When evaporation or condensation occurs, it can absorb or release large quantities of energy, which can be an important factor to include in a model. Now, you can account for evaporation and the associated latent heat source in the *Moisture flux* boundary node, by selecting the *Contributes to evaporation flux* check box available in the new *Evaporation* section.

In addition, an update to the *Heat and Moisture* multiphysics coupling interface automates the definition of latent heat sources induced by the *Moisture Transport* interface. The heat flux, induced by evaporation or condensation and defined by the *Wet Surface*, *Moist Surface*, or *Moisture Flux* nodes, is added to the heat transfer equation on the corresponding boundaries. An *Include latent heat source on surfaces* check box is available in the new *Latent Heat* section of the *Heat and Moisture* node to include this behavior.

#### Moisture Transfer Coefficients

Similarly to convective heat fluxes, the moisture flux may be defined from established Nusselt correlations for a number of configurations. With version 5.3a of COMSOL Multiphysics^{®} and the Heat Transfer Module, you can define the moisture flux by using the heat and mass boundary layer analogy. Hence, all of the correlations available for different geometry and fluid flow configurations in the *Heat Flux* node are now also available in the *Moisture Flux* node to define convective moisture flux. Additionally, when a heat transfer interface is present in a model, you can link the moisture transfer coefficient definition to the heat transfer coefficient defined in a *Heat Flux* node, instead of defining it manually.

### Radiative Beam in Absorbing Media Interface with Beer-Lambert Law

Focused electromagnetic radiation that propagates in specific directions, such as laser beams, is progressively absorbed as it penetrates into a partially transparent material, depositing power into the material itself. A classical and computationally efficient model for the absorption of the refracted radiative beams is the Beer-Lambert law. The new *Radiative Beam in Absorbing Media* physics interface provides features to define the absorbing media properties, as well as options for multiple incident beams, as seen in the associated image. This formulation is valid for incoherent as well as coherent light sources, as long as the length scales of the deposited heat are much larger than any interference patterns. Additionally, it is possible to either specify an opaque wall that absorbs all of the radiative intensity, which produces heat, or to define transparent boundaries that let the radiative intensity exit without depositing energy at said boundary.

Model containing the *Radiative Beam in Absorbing Media* interface with two incident beams with different propagating directions crossing each other in the bulk of the absorbing media.

*Radiative Beam in Absorbing Media*interface with two incident beams with different propagating directions crossing each other in the bulk of the absorbing media.

### Time-Dependent Climate Data Improvements

The latest version of the ASHRAE climate database, Weather Data Viewer version 6.0, is now available for defining ambient variables in the *Ambient Settings* section of the *Heat Transfer* interfaces. Monthly and hourly averaged measurements, listed in the *ASHRAE 2017* handbook by the American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE), are available for about 8000 weather stations worldwide. In addition, the *Ambient Settings* section has been improved upon for easier browsing and searching the list of weather stations (see associated image).

New *Climate data (ASHRAE 2017)* option for the definition of ambient variables in the *Ambient Settings* section of the *Heat Transfer* interface.

*Climate data (ASHRAE 2017)*option for the definition of ambient variables in the

*Ambient Settings*section of the

*Heat Transfer*interface.

### Heat Transfer in Shape Memory Alloys

The behavior of shape memory alloys (SMA) is tightly related to temperature, and any structural changes (Austenite ↔ Martensite) will release or absorb energy, changing the thermal properties of the alloys. The *Shape Memory Alloy* feature in the heat transfer interfaces accounts for the Martensite and Austenite volume fraction. Effective thermal properties are then defined from the thermal properties of each phase. This *Shape Memory Alloy* feature is designed to be combined with the new *Shape Memory Alloy* feature included with the Nonlinear Structural Materials Module. To include it in your model, select the *Heat transfer in alloys* check box in the main *Heat Transfer* interface node, and the *Shape Memory Alloy* feature will be available as a *Domain* boundary condition.

### Shell Version of the Geometry Parts for Heat Sinks

Modeling heat transfer in thin shells is an important and useful tool for reducing the computational cost of your models. Recognizing this, the Part Library in the Heat Transfer Module has been updated to include shell versions of the different parameterized geometry parts dedicated to heat sinks with pins, straight fins, or pins with dissimilar dimensions on the borders. These new parts are specifically tailored to geometries where meshing the thickness of thin structures can be avoided by representing them as surfaces, in order to reduce the computational cost. The *Thin Layer* feature for heat transfer and the *Interior Wall* feature for fluid flow can be used on such shell boundaries.

*Heat sink with chamfers with 3D fins (left) or shell fins (right) generated from the heat sink parts.*

### New and Improved Electromagnetic Heating Multiphysics Coupling

The new *Electromagnetic Heating* multiphysics coupling node simplifies the setup of models coupling electromagnetic and heat transfer physics interfaces. It consolidates and replaces the *Electromagnetic Heat Source*, *Boundary Electromagnetic Heat Source*, and *Temperature Coupling* nodes into a single node with the same functionalities. Within this node, you can select domains, for volumetric electromagnetic heat sources, and boundaries, for surface electromagnetic heat sources in the heat transfer equation. Additionally, it communicates the temperature computed by the heat transfer interface to the electromagnetic interface. The temperature coupling is automatic, and the *Domain Selection* and *Boundary Selection* sections (shown in the associated image) allow you to control on which entities the coupling is active. This feature is used to model electromagnetic heating like Joule heating, inductive heating, microwave heating, or laser heating. Note that additional modules are needed for inductive, microwave, or laser heating.

### Thermoelectric Effect Multiphysics Coupling

The new *Thermoelectric Effect* multiphysics coupling node accounts for both volumetric and surface thermoelectric heat sources in the heat transfer equation. In addition, it adds the thermoelectric effect's contribution to the current density due to temperature differences in domains and on boundaries. It replaces the *Thermoelectric Effect* and *Boundary Thermoelectric Effect* nodes for modeling Peltier, Seebeck, or Thomson effects. The *Thermoelectric Effect* multiphysics coupling feature is the default feature of the *Thermoelectric Effect* multiphysics interface, along with the new *Electromagnetic Heating* multiphysics coupling node.

### Buoyancy-Induced Turbulence

Buoyancy introduces a volume force in the bulk of a fluid that may naturally cause instabilities. Eventually, these instabilities in the flow become chaotic, leading to the onset of turbulence. The *Gravity* feature, used for modeling buoyancy in the CFD Module, now includes the option of accounting for buoyancy-induced turbulence by selecting the corresponding check box. This contribution to the turbulent flow can then be defined either automatically from the *Nonisothermal Flow* multiphysics coupling or from a user-defined turbulent Schmidt number.

The *Gravity* feature now includes an option to *Include buoyancy-induced turbulence*.

*Gravity*feature now includes an option to

*Include buoyancy-induced turbulence*.

### Inlet Boundary Condition for Fully Developed Turbulent Flow

The *Inlet* boundary condition for fully developed turbulent flow gives the velocity profile and the turbulence variable values at an inlet cross section, assuming that the inlet channel upstream is of a certain length and that the flow is fully developed. In previous versions of the COMSOL^{®} software, a decent estimate of the cross section velocity profile would have required modeling a very long inlet section of the channel. The new boundary condition gives a very accurate inlet profile without the need for extra geometry and therefore reduces the computational resources.

The inlet from a nozzle with star-shaped cross section is modeled using the fully developed turbulent flow inlet condition.

### New Tutorial Model: Buoyancy Flow in Air

The new Buoyancy Flow in Air tutorial model studies the stationary state of free convection in a cavity filled with air and bounded by two vertical plates. The two plates are maintained at different temperatures, inducing a buoyancy flow in the air domain. Operating conditions are defined so that the flow regime is laminar. The model contains two components: one 2D and one 3D, thus providing the fundamentals for you to include natural convection in air in your models.

Note that the model is built in a similar manner as the already existing Buoyancy Flow in Water model. The main difference between the two models is that air density, modeled using the ideal gas law, is temperature and pressure dependent.

*Temperature distribution (isothermal contour) and velocity field (arrow) induced by buoyancy forces when the temperature difference between two opposite vertical walls is 10 K.*

**Application Library path:**

*Heat_Transfer_Module/Tutorials_Forced_and_Natural_Convection/buoyancy_air*

### New Tutorial Model: Laminar Nonisothermal Flow in a Circular Tube

This new verification tutorial model computes the velocity, pressure, and temperature distribution in a circular tube using a 2D axisymmetric geometry. The operating conditions correspond to a laminar flow. This nonisothermal flow configuration has been well studied and the heat flux between the fluid and the wall has been measured experimentally. The associated figure shows the heat transfer coefficient deduced from the simulation compared with the one based on the published Nusselt number. The simulation results are in good agreement with experimental measurements.

Comparison of the heat transfer coefficients obtained from the temperature numerical solution (red) and from correlations for the Nusselt number (green and blue).

**Application Library path:**

*Heat_Transfer_Module/Verification_Examples/circular_tube_nitf_laminar*

### New Tutorial Model: Turbulent Nonisothermal Flow over a Flat Plate

This new verification tutorial model computes the velocity, pressure, and temperature distribution over a plate. When the flow is turbulent and fully developed, it reaches a hot region of the plate. The heat transfer coefficient between the air flow and the plate has been measured experimentally and different Nusselt-number-based correlations are available. The simulation results are in good agreement with the published data.

*Comparison of the heat transfer coefficients obtained from the temperature numerical solution (solid lines) and from a correlation for the Nusselt number (dashed line).*

**Application Library path:**

*Heat_Transfer_Module/Verification_Examples/flat_plate_nitf_turbulent*

### New Tutorial Model: Dynamic Wall Heat Exchanger

Inspired from a published paper, the Dynamic Wall Heat Exchanger tutorial model shows a compact heat exchanger that has enhanced performance thanks to the use of a deforming wall with an oscillating wave shape. The wall oscillations induce mixing in the fluid and reduce the formation of thermal boundary layers. Additionally, the wave-shaped deformation induces a pumping effect similar to the peristaltic pumping that mitigates the pressure losses. This model includes the *Conjugate Heat Transfer* multiphysics coupling and moving mesh features to handle the wall and channel deformation. The pressure drop across the heat exchanger and the overall heat transfer coefficient are computed for a static and a dynamic heat exchanger.

Temperature distribution in the channel of the dynamic heat exchanger.

**Application Library path:**

*Heat_Transfer_Module/Heat_Exchangers/Dynamic_wall_heat_exchanger*