Heat Transfer Module - COMSOL Multiphysics
Heat Transfer ModuleUser’s Guide
Heat Transfer Module User’s Guide 1998–2018 COMSOLProtected by patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474;7,623,991; 8,457,932; 8,954,302; 9,098,106; 9,146,652; 9,323,503; 9,372,673; and 9,454,625. Patentspending.This Documentation and the Programs described herein are furnished under the COMSOL Software LicenseAgreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the termsof the license agreement.COMSOL, the COMSOL logo, COMSOL Multiphysics, COMSOL Desktop, COMSOL Server, andLiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are theproperty of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliatedwith, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademarkowners, see www.comsol.com/trademarks.Version: COMSOL 5.4Contact InformationVisit the Contact COMSOL page at www.comsol.com/contact to submit generalinquiries, contact Technical Support, or search for an address and phone number. You canalso visit the Worldwide Sales Offices page at www.comsol.com/contact/offices foraddress and contact information.If you need to contact Support, an online request form is located at the COMSOL Accesspage at www.comsol.com/support/case. Other useful links include: Support Center: www.comsol.com/support Product Download: www.comsol.com/product-download Product Updates: www.comsol.com/support/updates COMSOL Blog: www.comsol.com/blogs Discussion Forum: www.comsol.com/community Events: www.comsol.com/events COMSOL Video Gallery: www.comsol.com/video Support Knowledge Base: www.comsol.com/support/knowledgebasePart number: CM020801
C o n t e n t sChapter 1: IntroductionAbout the Heat Transfer Module20Why Heat Transfer is Important to Modeling . . . . . . . . . . . . 20How the Heat Transfer Module Improves Your Modeling . . . . . . . 21The Heat Transfer Module Physics Interface Guide . . . . . . . . . . 21Common Physics Interface and Feature Settings and Nodes. . . . . . 29The Heat Transfer Module Study Capabilities . . . . . . . . . . . . 29Additional Materials Database . . . . . . . . . . . . . . . . . . 33Where Do I Access the Documentation and Application Libraries? . . . . 34Overview of the User’s Guide38Chapter 2: NotationsChapter 3: Modeling with the Heat Transfer ModuleHeat Transfer Variables60Predefined Variables . . . . . . . . . . . . . . . . . . . . . 60Global Variables . . . . . . . . . . . . . . . . . . . . . . . 63Domain Fluxes. . . . . . . . . . . . . . . . . . . . . . . . 66Out-of-Plane Domain Fluxes . . . . . . . . . . . . . . . . . . 68Boundary Fluxes (Heat Transfer interface) . . . . . . . . . . . . . 68Internal Boundary Heat Fluxes. . . . . . . . . . . . . . . . . . 70Domain Heat Sources . . . . . . . . . . . . . . . . . . . . . 71Boundary Heat Sources . . . . . . . . . . . . . . . . . . . . 72Line and Point Heat Sources . . . . . . . . . . . . . . . . . . 72Ambient Variables . . . . . . . . . . . . . . . . . . . . . . 72Moist Air Variables . . . . . . . . . . . . . . . . . . . . . . 73CONTENTS 3
Moisture Transport Variables76Predefined Variables . . . . . . . . . . . . . . . . . . . . . 76Moist air properties . . . . . . . . . . . . . . . . . . . . . . 77Domain Moisture Fluxes . . . . . . . . . . . . . . . . . . . . 79Boundary Moisture Fluxes . . . . . . . . . . . . . . . . . . . 79Domain Moisture Source. . . . . . . . . . . . . . . . . . . . 81Using the Boundary Conditions for the Heat TransferInterfaces82Temperature and Heat Flux Boundary Conditions . . . . . . . . . . 82Overriding Mechanism for Heat Transfer Boundary Conditions . . . . . 83Handling Frames in Heat Transfer86Heat Transfer Analysis with Moving Frames. . . . . . . . . . . . . 86Material Density in Features Defined in the Material Frame . . . . . . . 91Heat Transfer Consistent and Inconsistent StabilizationMethods92Consistent Stabilization . . . . . . . . . . . . . . . . . . . . 92Inconsistent Stabilization . . . . . . . . . . . . . . . . . . . . 93Heat Transfer and Fluid Flow Coupling94Coupling Based on Model Inputs . . . . . . . . . . . . . . . . . 94Temperature Coupling and Flow Coupling Multiphysics Features. . . . . 95Adding Nonisothermal Flow Coupling in an Existing Model . . . . . . . 95Nonisothermal Flow and Conjugate Heat Transfer MultiphysicsInterfaces . . . . . . . . . . . . . . . . . . . . . . . . 96Boundary Wall TemperatureSolver Settings4 CONTENTS97102Linearity property of the temperature equation . . . . . . . . . .102Linear Solver . . . . . . . . . . . . . . . . . . . . . . .103Nonlinear Solver . . . . . . . . . . . . . . . . . . . . . .105Time-Dependent Study Step . . . . . . . . . . . . . . . . .107Guidelines for Solving Surface-to-Surface Radiation Problems . . . . .109Guidelines for Solving Multiphysics problems . . . . . . . . . . .109
Plotting Results in Thin Layers Extra Dimensions112Along the Layer . . . . . . . . . . . . . . . . . . . . . .112Through the Thin Layer . . . . . . . . . . . . . . . . . . .113Ambient Thermal Properties115Settings for the Ambient Thermal Properties . . . . . . . . . . .115Processing of ASHRAE Data . . . . . . . . . . . . . . . . .119Ambient Data Interpolation . . . . . . . . . . . . . . . . . .120Ambient Variables and Conditions . . . . . . . . . . . . . . .120Use of Ambient Data From the Features . . . . . . . . . . . . .128Modeling Heat Transfer by Radiation130Interfaces and Features for Radiation in Transparent Media . . . . . .132Interfaces and Features for Radiation in Participating Media . . . . . .134Specifying the temperature at a flow inlet136Using the Temperature condition . . . . . . . . . . . . . . .136Using the Inflow condition . . . . . . . . . . . . . . . . . .136Temperature contribution to the Inflow boundary condition . . . . .138Pressure contribution to the Inflow boundary condition . . . . . . .139Choosing between the Temperature and the Inflow conditions . . . .139Heat Part Library140Heat Part Library Contents . . . . . . . . . . . . . . . . . .140Heat Sink - Parameterized Fin Types Part . . . . . . . . . . . .143Heat Sink - Dissimilar Border Pins Part . . . . . . . . . . . . .146Heat Sink - Pin Fins Part . . . . . . . . . . . . . . . . . . .146Heat Sink - Straight Fins Part . . . . . . . . . . . . . . . . .146References147Chapter 4: Theory for the Heat Transfer ModuleFoundations of the General Heat Transfer Equation151Thermodynamic Description of Heat Transfer. . . . . . . . . . .151The Physical Mechanisms under Heat Transfer155. . . . . . . . . .CONTENTS 5
The Heat Balance Equation . . . . . . . . . . . . . . . . . .156Consistency with Mass and Momentum Conservation Laws. . . . . .159Theory for Heat Transfer in Solids161Theory for Heat Transfer in Fluids162Theory for Bioheat Transfer164The Bioheat Equation . . . . . . . . . . . . . . . . . . . .164Damaged Tissue . . . . . . . . . . . . . . . . . . . . . .164Theory for Heat Transfer in Porous Media168When Should Local Thermal Equilibrium and Non-Equilibrium be6 CONTENTSConsidered? . . . . . . . . . . . . . . . . . . . . . .168Local Thermal Equilibrium . . . . . . . . . . . . . . . . . .169Local Thermal Non-Equilibrium . . . . . . . . . . . . . . . .171Theory for Heat Transfer with Phase Change174Phase change in solid materials176. . . . . . . . . . . . . . . .Theory for Heat Transfer in Building Materials178Theory for Harmonic Heat Transfer180Theory for Lumped Isothermal Domain182Theory for Heat Transfer in Thin Structures185Modeling Layered Materials . . . . . . . . . . . . . . . . . .185Theoretical Background of the Different Formulations189. . . . . . .Thin Layer . . . . . . . . . . . . . . . . . . . . . . . .194Thin Film . . . . . . . . . . . . . . . . . . . . . . . . .197Fracture . . . . . . . . . . . . . . . . . . . . . . . . .199Thin Rod . . . . . . . . . . . . . . . . . . . . . . . . .200Theory for Surface-to-Surface Radiation201Deriving the Radiative Heat Flux for Opaque Surfaces . . . . . . . .201Deriving the Radiative Heat Flux for Semi-Transparent Surfaces . . . .202Wavelength Dependence of Surface Emissivity and Absorptivity . . . .204
The Radiosity Method for Diffuse-Gray Surfaces . . . . . . . . . .210The Radiosity Method for Diffuse-Spectral Surfaces. . . . . . . . .213View Factor Evaluation216. . . . . . . . . . . . . . . . . . .Theory for Radiation in Participating Media220Radiation and Participating Media Interactions . . . . . . . . . . .220Radiative Transfer Equation . . . . . . . . . . . . . . . . . .221Boundary Condition for the Radiative Transfer Equation . . . . . . .223Heat Transfer Equation in Participating Media . . . . . . . . . . .224Discrete Ordinates Method (DOM). . . . . . . . . . . . . .224Discrete Ordinates Method Implementation in 2D . . . . . . . . .225Rosseland Approximation Theory . . . . . . . . . . . . . . .227P1 Approximation Theory . . . . . . . . . . . . . . . . . .228Radiation in Absorbing-Scattering Media Theory . . . . . . . . . .231Radiative Beam in Absorbing Media Theory . . . . . . . . . . . .233Theory for Moisture Transport234Theory for moisture transport in building materials. . . . . . . . .234Theory for moisture transport in air . . . . . . . . . . . . . .234Theory for the Heat Transfer Multiphysics Couplings236Theory for the Nonisothermal Flow and Conjugate Heat TransferInterfaces . . . . . . . . . . . . . . . . . . . . . . .236Theory for the Moisture Flow Interface . . . . . . . . . . . . .244Theory for the Thermoelectric Effect Interface . . . . . . . . . .248Theory for the Local Thermal Non-Equilibrium Interface. . . . . . .251Theory for the Building Materials version of the Heat and MoistureTransport Interface. . . . . . . . . . . . . . . . . . .252Theory for the Moist Air version of the Heat and Moisture. . . . . . . . . . . . . . . . . . .253Theory for the Heat and Moisture Flow Interfaces . . . . . . . . .Transport Interface254Theory for the Electromagnetic Heating Interfaces . . . . . . . . .254Theory for the Thermal Stress Interface . . . . . . . . . . . . .254Theory for Thermal Contact255Theory for the Thermal Contact Feature. . . . . . . . . . . .255CONTENTS 7
Moist Air Fluid Type260Humidity . . . . . . . . . . . . . . . . . . . . . . . . .260Saturation State . . . . . . . . . . . . . . . . . . . . . .262Moist Air Properties . . . . . . . . . . . . . . . . . . . .262Out-of-Plane Heat Transfer267Equation Formulation . . . . . . . . . . . . . . . . . . . .267The Heat Transfer Coefficients270Defining the Heat Transfer Coefficients . . . . . . . . . . . . .271Nature of the Flow — The Grashof Number . . . . . . . . . . .272Heat Transfer Coefficients — External Natural Convection. . . . .274Heat Transfer Coefficients — Internal Natural Convection . . . . . .281Heat Transfer Coefficients — External Forced Convection . . . . . .282Heat Transfer Coefficients — Internal Forced Convection . . . . . .285Using the Heat and Mass Transfer Analogy for the Evaluation ofMoisture Transfer Coefficients . . . . . . . . . . . . . . .8 CONTENTS285Equivalent Thermal Conductivity Correlations287Horizontal Cavity With Bottom Heating . . . . . . . . . . . . .288Vertical Cavity With Sidewall Heating . . . . . . . . . . . . . .288Temperature Dependence of Surface Tension290Heat Flux and Heat Balance291Total Heat Flux and Energy Flux . . . . . . . . . . . . . . . .291Heat and Energy Balance . . . . . . . . . . . . . . . . . . .292Frames for the Heat Transfer Equations295Material and Spatial Frames . . . . . . . . . . . . . . . . . .295Conversion Between Material and Spatial Frames . . . . . . . . .296
References300Chapter 5: The Heat Transfer Module InterfacesAbout the Heat Transfer Interfaces307Space Dimensions . . . . . . . . . . . . . . . . . . . . .307Study Types . . . . . . . . . . . . . . . . . . . . . . . .307Versions of the Heat Transfer Physics Interface . . . . . . . . . .308Benefits of the Different Heat Transfer Interfaces . . . . . . . . .308Versions of the Heat Transfer in Shells Physics Interface . . . . . . .309Benefits of the Different Heat Transfer in Shells Interfaces . . . . . .310The Layer Selection and Interface Selection Sections . . . . . . . .310Using the Extra Dimension Coordinates . . . . . . . . . . . . .314Versions of the Moisture Transport Physics Interface . . . . . . . .314Benefits of the Different Moisture Transport Interfaces . . . . . . .315Additional physics options . . . . . . . . . . . . . . . . . .315Settings for the Heat Transfer Interface . . . . . . . . . . . . .316Settings for the Heat Transfer in Shells Interface . . . . . . . . . .319The Heat Transfer in Solids Interface322Feature Nodes for the Heat Transfer in Solids Interface . . . . . . .323The Heat Transfer in Fluids Interface327Feature Nodes for the Heat Transfer in Fluids Interface . . . . . . .328The Heat Transfer in Solids and Fluids Interface331Feature Nodes for the Heat Transfer in Solids and Fluids Interface . . .331The Heat Transfer in Porous Media Interface332Feature Nodes for the Heat Transfer in Porous Media Interface . . . .334The Heat Transfer in Building Materials Interface338Settings for the Heat Transfer in Building Materials Interface . . . . .338Feature Nodes for the Heat Transfer in Building Materials Interface . .338CONTENTS 9
The Heat Transfer in Moist Air Interface340Settings for the Heat Transfer in Moist Air Interface . . . . . . . .340Feature Nodes for the Heat Transfer in Moist Air Interface340. . . . .The Bioheat Transfer Interface341Feature Nodes for the Bioheat Transfer Interface . . . . . . . . .342The Heat Transfer in Shells Interface346Feature Nodes for the Heat Transfer in Shells Interface . . . . . . .348The Heat Transfer in Films Interface350Feature Nodes for the Heat Transfer in Films Interface . . . . . . .352The Heat Transfer in Fractures Interface354Feature Nodes for the Heat Transfer in Fractures Interface. . . . .The Surface-to-Surface Radiation Interface356358Settings for the Surface-to-Surface Radiation Interface. . . . . . . .359Feature Nodes for the Surface-to-Surface Radiation Interface . . . . .362The Radiation in Participating Media Interface364Settings for the Radiation in Participating Media Interface . . . . . .364Feature Nodes for the Radiation in Participating Media Interface . . . .367The Radiation in Absorbing-Scattering Media Interface369Settings for the Radiation in Absorbing-Scattering Media Interface . . .369Feature Nodes for the Radiation in Absorbing-Scattering MediaInterface. . . . . . . . . . . . . . . . . . . . . . . .372The Radiative Beam in Absorbing Media Interface374Settings for the Radiative Beam in Absorbing Media Interface . . . . .374Feature Nodes for the Radiative Beam in Absorbing Media Interface . .375The Moisture Transport in Building Materials Interface377Settings for the Moisture Transport in Building Materials Interface . . .377Feature Nodes for the Moisture Transport in Building MaterialsInterface. . . . . . . . . . . . . . . . . . . . . . . .10 C O N T E N T S379
The Moisture Transport in Air InterfaceSettings for the Moisture Transport in Air Interface380. . . . . . . .380Feature Nodes for the Moisture Transport in Air Interface . . . . . .382Chapter 6: The Heat Transfer FeaturesDomain Features384Absorbing Medium (Radiative Beam in Absorbing Medium Interface) . .385Absorbing-Scattering Medium (Radiation in Absorbing-Scattering MediumInterface) . . . . . . . . . . . . . . . . . . . . . . .386Bioheat . . . . . . . . . . . . . . . . . . . . . . . . .390Biological Tissue . . . . . . . . . . . . . . . . . . . . . .392Building Material . . . . . . . . . . . . . . . . . . . . . .394Convectively Enhanced Conductivity . . . . . . . . . . . . . .399Cross Section . . . . . . . . . . . . . . . . . . . . . . .401Fluid. . . . . . . . . . . . . . . . . . . . . . . . . .402Geothermal Heating . . . . . . . . . . . . . . . . . . . .406Heat Source. . . . . . . . . . . . . . . . . . . . . . .408Immobile Fluids . . . . . . . . . . . . . . . . . . . . . .411Initial Values. . . . . . . . . . . . . . . . . . . . . . .414Initial Values (Radiative Beam in Absorbing Medium interface) . . . . .414Irreversible Transformation . . . . . . . . . . . . . . . . . .415Isothermal Domain . . . . . . . . . . . . . . . . . . . . .418Moist Air (HT Interface) . . . . . . . . . . . . . . . . . . .420Opacity (Surface-to-Surface Radiation interface) . . . . . . . . . .423Optically Thick Participating Medium . . . . . . . . . . . . . .424Out-of-Plane Heat Flux . . . . . . . . . . . . . . . . . . .426Out-of-Plane Radiation. . . . . . . . . . . . . . . . . . .428Participating Medium (Radiation in Participating Medium Interface) . . .430Phase Change Material. . . . . . . . . . . . . . . . . . . .434Porous Medium . . . . . . . . . . . . . . . . . . . . . .438Pressure Work . . . . . . . . . . . . . . . . . . . . . .446Shape Memory Alloy . . . . . . . . . . . . . . . . . . . .447Solid . . . . . . . . . . . . . . . . . . . . . . . . . .450Thermal Damage . . . . . . . . . . . . . . . . . . . . . .454Thermal Dispersion . . . . . . . . . . . . . . . . . . . . .457CONTENTS 11
Thermoelastic Damping . . . . . . . . . . . . . . . . . . .459Thickness. . . . . . . . . . . . . . . . . . . . . . . . .460Translational Motion . . . . . . . . . . . . . . . . . . . .461Viscous Dissipation . . . . . . . . . . . . . . . . . . . . .462Boundary Features464Boundary Heat Source. . . . . . . . . . . . . . . . . . . .466Continuity . . . . . . . . . . . . . . . . . . . . . . . .469Continuity (Radiation in Participating Medium and Radiation inAbsorbing-Scattering Medium interfaces) . . . . . . . . . . .470Continuity on Interior Boundary (Radiation in Participating Mediumand Radiation in Absorbing-Scattering Medium Interfaces) . . . . .470Deposited Beam Power . . . . . . . . . . . . . . . . . . .471Diffuse Mirror (Surface-to-Surface Radiation interface) . . . . . . .473Diffuse Surface (Surface-to-Surface Radiation interface) . . . . . . .474External Temperature (Thin Layer, Thin Film, Fracture) . . . . . . .479Fracture (Heat Transfer interface) and Porous Medium (Heat Transferin Shells interface) . . . . . . . . . . . . . . . . . . . .480Harmonic Perturbation . . . . . . . . . . . . . . . . . . .484Heat Flux. . . . . . . . . . . . . . . . . . . . . . . . .485Heat Source (Heat Transfer in Shells Interface) . . . . . . . . . .489Heat Source (Thin Layer, Thin Film, Fracture) . . . . . . . . . . .491Incident Intensity (Radiation in Participating Medium and Radiation inAbsorbing-Scattering Medium Interfaces) . . . . . . . . . . .494Incident Intensity (Radiative Beam in Absorbing Medium Interface) . . .495Inflow . . . . . . . . . . . . . . . . . . . . . . . . . .497Initial Values (Heat Transfer in Shells interface) . . . . . . . . . .498Initial Values (Surface-to-Surface Radiation Interface) . . . . . . . .500Isothermal Domain Interface . . . . . . . . . . . . . . . . .501Layer Opacity (Surface-to-Surface Radiation interface)505. . . . . . .Line Heat Source on Axis . . . . . . . . . . . . . . . . . .506Opaque Surface (Surface-to-Surface Radiation interface) . . . . . . .506Opaque Surface (Radiation in Participating Medium and Radiation in12 C O N T E N T SAbsorbing-Scattering Medium Interfaces) . . . . . . . . . . .509Opaque Surface (Radiative Beam in Absorbing Medium Interface) . . .512Open Boundary . . . . . . . . . . . . . . . . . . . . . .512Outflow . . . . . . . . . . . . . . . . . . . . . . . . .513Periodic Condition (Heat Transfer interface) . . . . . . . . . . .514
Periodic Condition (Radiation in Participating Medium and Radiationin Absorbing-Scattering Medium interfaces) . . . . . . . . . .515Prescribed Radiosity (Surface-to-Surface Radiation interface) . . . . .515Radiation Group (Surface-to-Surface Radiation Interface). . . . . .519Semi-Transparent Surface (Surface-to-Surface Radiation interface) . . .522Surface-to-Ambient Radiation (Heat Transfer interface) . . . . . . .525Symmetry (Heat Transfer interface). . . . . . . . . . . . . . .527Symmetry (Radiation in Participating Medium and Radiation inAbsorbing-Scattering Medium Interfaces) . . . . . . . . . . .528Temperature . . . . . . . . . . . . . . . . . . . . . . .528Thermal Contact . . . . . . . . . . . . . . . . . . . . . .530Thermal Insulation . . . . . . . . . . . . . . . . . . . . .535Thickness (Heat Transfer in Shells interface) . . . . . . . . . . .535Thin Film (Heat Transfer interface) and Fluid (Heat Transfer inShells interface) . . . . . . . . . . . . . . . . . . . . .536Thin Layer (Heat Transfer interface) and Solid (Heat Transfer inShells interface) . . . . . . . . . . . . . . . . . . . . .539Transparent Surface (Radiative Beam in Absorbing Medium Interface) . .543Boundary Interface Features545Deposited Beam Power, Interface (Heat Transfer in Shells Interface) . .545Heat Flux, interface (Heat Transfer in Shells Interface). . . . . . .547Heat Source, Interface (Heat Transfer in Shells Interface) . . . . . .550Surface-to-Ambient Radiation, Interface (Heat Transfer in ShellsInterface) . . . . . . . . . . . . . . . . . . . . . . .552Temperature, interface (Heat Transfer in Shells Interface) . . . . . .555Edge Features557Heat Flux (Heat Transfer in Shells Interface) . . . . . . . . . . .557Heat Flux (Thin Layer, Thin Film, Fracture) . . . . . . . . . . . .560Heat Source (Heat Transfer in Shells Interface) . . . . . . . . . .562Line Heat Source . . . . . . . . . . . . . . . . . . . . . .565Shell Continuity (Heat Transfer interface) and Continuity (HeatTransfer in Shells Interface) . . . . . . . . . . . . . . . .567Surface-to-Ambient Radiation (Thin Layer, Thin Film, Fracture, andHeat Transfer in Shells interface) . . . . . . . . . . . . . .568Thermal Insulation (Heat Transfer in Shells Interface) . . . . . . . .571Temperature (Thin Layer, Thin Film, Fracture, and Heat Transfer inCONTENTS 13
Shells). . . . . . . . . . . . . . . . . . . . . . . . .573Thin Rod . . . . . . . . . . . . . . . . . . . . . . . . .575Point Features577Point Heat Flux (Thin Rod) . . . . . . . . . . . . . . . . . .577Point Heat Source . . . . . . . . . . . . . . . . . . . . .578Point Heat Source on Axis . . . . . . . . . . . . . . . . . .579Surface-to-Ambient Radiation (Thin Rod) . . . . . . . . . . . .580Temperature (Thin Rod) . . . . . . . . . . . . . . . . . . .581Global Features583External Radiation Source . . . . . . . . . . . . . . . . . .583Symmetry for Surface-to-Surface Radiation . . . . . . . . . . . .588Chapter 7: The Moisture Transport FeaturesDomain Features594Building Material . . . . . . . . . . . . . . . . . . . . . .594Initial Values14 C O N T E N T S. . . . . . . . . . . . . . . . . . . . . . .596Moist Air (MT Interface) . . . . . . . . . . . . . . . . . . .597Moisture Source . . . . . . . . . . . . . . . . . . . . . .599Turbulent Mixing . . . . . . . . . . . . . . . . . . . . . .599Boundary Features601Continuity . . . . . . . . . . . . . . . . . . . . . . . .601Insulation . . . . . . . . . . . . . . . . . . . . . . . . .602Moist Surface . . . . . . . . . . . . . . . . . . . . . . .602Moisture Content . . . . . . . . . . . . . . . . . . . . .604Moisture Flux . . . . . . . . . . . . . . . . . . . . . . .605Outflow . . . . . . . . . . . . . . . . . . . . . . . . .607Symmetry . . . . . . . . . . . . . . . . . . . . . . . .607Thin Moisture Barrier . . . . . . . . . . . . . . . . . . . .608Wet Surface609. . . . . . . . . . . . . . . . . . . . . . .
Chapter 8: Multiphysics InterfacesThe Nonisothermal Flow and Conjugate Heat TransferInterfacesAdvantages of Using the Multiphysics Interfaces . . . . . . . . . .614614The Nonisothermal Flow, Laminar Flow and Turbulent FlowInterfaces . . . . . . . . . . . . . . . . . . . . . . .615The Conjugate Heat Transfer, Laminar Flow and Turbulent FlowInterfaces . . . . . . . . . . . . . . . . . . . . . . .616Settings for Physics Interfaces and Coupling Features . . . . . . . .617Coupling Features . . . . . . . . . . . . . . . . . . . . .618Physics Interface Features . . . . . . . . . . . . . . . . . .618Preset Studies . . . . . . . . . . . . . . . . . . . . . . .619The Heat Transfer with Surface-to-Surface Radiation Interface620The Heat Transfer with Surface-to-Surface Radiation MultiphysicsInterface. . . . . . . . . . . . . . . . . . . . . . . .620Physics Interface Features . . . . . . . . . . . . . . . . . .621Coupling Feature . . . . . . . . . . . . . . . . . . . . . .622The Heat Transfer with Radiation in Participating MediaInterface623The Heat Transfer with Radiation in Participating Media MultiphysicsInterface. . . . . . . . . . . . . . . . . . . . . . . .623Physics Interface Features . . . . . . . . . . . . . . . . . .624Coupling Feature . . . . . . . . . . . . . . . . . . . . . .625The Heat Transfer with Radiation in Absorbing-ScatteringMedia Interface626The Heat Transfer with Radiation in Absorbing-Scattering MediaMultiphysics Interface . . . . . . . . . . . . . . . . . . .626Physics Interface Features . . . . . . . . . . . . . . . . . .627Coupling Feature . . . . . . . . . . . . . . . . . . . . . .628The Heat Transfer with Radiative Beam in Absorbing MediaCONTENTS 15
Interface629The Heat Transfer with Radiative Beam in Absorbing MediaMultiphysics Interface . . . . . . . . . . . . . . . . . . .629Physics Interface Features . . . . . . . . . . . . . . . . . .630Coupling Feature . . . . . . . . . . . . . . . . . . . . . .630The Thermoelectric Effect Interface631About The Thermoelectric Effect Interface . . . . . . . . . . . .631Settings for Physics Interfaces and Coupling Features . . . . . . . .632Coupling Features . . . . . . . . . . . . . . . . . . . . .633Physics Interface Features . . . . . . . . . . . . . . . . . .634The Local Thermal Non-Equilibrium Interface635About the Local Thermal Non-Equilibrium Interface . . . . . . . .635Coupling Feature . . . . . . . . . . . . . . . . . . . . . .636Physics Interface Features . . . . . . . . . . . . . . . . . .636The Heat and Moisture Transport Interfaces637The Heat and Moisture Transport Multiphysics Interfaces . . . . . .637The Building Materials version of the Heat and Moisture TransportMultiphysics Interface . . . . . . . . . . . . . . . . . . .637Physics Interface Features in the Building Materials Version . . . . . .639The Moist Air version of the Heat and Moisture TransportMultiphysics Interface . . . . . . . . . . . . . . . . . . .639Physics Interface Features in the Moist Air Version . . . . . . . . .641Coupling Feature . . . . . . . . . . . . . . . . . . . . . .642The Moisture Flow Interfaces643The Moisture Flow, Laminar Flow and Turbulent Flow MultiphysicsInterfaces . . . . . . . . . . . . . . . . . . . . . . .643Coupling Feature . . . . . . . . . . . . . . . . . . . . . .645Physics Interface Features . . . . . . . . . . . . . . . . . .646The Heat and Moisture Flow Interfaces648The Heat and Moisture Flow, Laminar Flow and Turbulent Flow16 C O N T E N T SMultiphysics Interfaces . . . . . . . . . . . . . . . . . .648Coupling Features . . . . . . . . . . . . . . . . . . . . .652Physics Interface Features . . . . . . . . . . . . . . . . . .652
The Joule Heating Interface654The Joule Heating Interface . . . . . . . . . . . . . . . . . .654Coupling Feature . . . . . . . . . . . . . . . . . . . . . .654The Laser Heating Interface655The Laser Heating Interface . . . . . . . . . . . . . . . . . .655Coupling Feature . . . . . . . . . . . . . . . . . . . . . .655The Induction Heating Interface656The Induction Heating Interface . . . . . . . . . . . . . . . .656Coupling Feature . . . . . . . . . . . . . . . . . . . . . .656The Microwave Heating Interface657The Microwave Heating Interface. . . . . . . . . . . . . . .657Coupling Feature . . . . . . . . . . . . . . . . . . . . . .657Chapter 9: Multiphysics CouplingsDomain Multiphysics Couplings661Electromagnetic Heating . . . . . . . . . . . . . . . . . . .661Flow Coupling . . . . . . . . . . . . . . . . . . . . . . .662Heat and Moisture . . . . . . . . . . . . . . . . . . . . .664Heat Transfer with Radiation in Participating Media . . . . . . . . .666Heat Transfer with Radiation in Absorbing-Scattering Media . . . . .667Heat Transfer with Radiative Beam in Absorbing Media . . . . . . .669Local Thermal Non-Equilibrium . . . . . . . . . . . . . . . .670Moisture Flow . . . . . . . . . . . . . . . . . . . . . . .672Nonisothermal Flow . . . . . . . . . . . . . . . . . . . .675Temperature Coupling. . . . . . . . . . . . . . . . . . .679Thermal Expansion . . . . . . . . . . . . . . . . . . . . .679Thermoelectric Effect . . . . . . . . . . . . . . . . . . . .680Boundary Multiphysics Couplings683Electromagnetic Heating, Layered Shell . . . . . . . . . . . . .683Heat Transfer with Surface-to-Surface Radiation . . . . . . . . . .685Marangoni Effect . . . . . . . . . . . . . . . . . . . . . .687CONTENTS 17
18 C O N T E N T SThermal Expansion, Layered Shell . . . . . . . . . . . . . . .689Thermoelectric Effect, Layered Shell . . . . . . . . . . . . . .689Index693
1IntroductionThis guide describes the Heat Transfer Module, an optional package that extendsthe COMSOL Multiphysics modeling environment with customized physicsinterfaces for the analysis of heat transfer.This chapter introduces you to the capabilities of this module. A summary of thephysics interfaces and where you can find documentation and model examples isalso included. The last section is a brief overview with links to each chapter in thisguide. About the Heat Transfer Module Overview of the User’s Guide19
About the Heat Transfer ModuleIn this section: Why Heat Transfer is Important to Modeling How the Heat Transfer Module Improves Your Modeling The Heat Transfer Module Physics Interface Guide Common Physics Interface and Feature Settings and Nodes The Heat Transfer Module Study Capabilities Additional Materials
Feature Nodes for the Heat Transfer in Solids and Fluids Interface . . . 331 The Heat Transfer in Porous Media Interface 332 Feature Nodes for the Heat Transfer in Porous Media Interface . . . . 334 The Heat Transfer in Building Materials Interface 338 Settings for the Heat Transfer in Building Materials Interface . . . . . 338
The COMSOL Multiphysics User’s Guide and COMSOL Multiphysics Reference Guide describe all interfaces and functionality included with the basic COMSOL Multiphysics license. These guides also have instructions about how to use COMSOL Multiphysics and how to access the documentation electronically through the COMSOL Multiphysics help desk.
import and export functionality available in COMSOL Multiphysics and a detailed description of the import, export, and native COMSOL formats. For more detailed information on how to use COMSOL Multiphysics for import and export of data, see the COMSOL Multiphysics Reference Manual in the installed documentation set. Overview of Data Formats
COMSOL 5.3 Growing at a double-digit rate '14 COMSOL 5.0 '15 '16 5.1 '01 Started sales in Japan '17 COMSOL 5.2 COMSOL, Inc. General agency in Japan: Keisoku Engineering System Co., Ltd. (KESCO) 3 Multiphysics and Single-Physics Simulation Platform Mechanical, Fluid, Electrical, and Chemical Simulations Multiphysics -Coupled Phenomena
The Physics Interfaces and Building a COMSOL Multiphysics Model in the COMSOL Multiphysics Reference Manual. ABOUT THE ELECTROCHEMISTRY MODULE 15 The physics interfaces include chemical species transport, charge balances, heat transfer, and fluid flow. You can use the module to model electrochemical and
The numerical model was developed using COMSOL Multiphysics Software. COMSOL Multiphysics is a finite element modeling package capable of solving fully coupled multiphysics problems. The equations used to solve for heat transfer and variable-density groundwater flow are standard, and the reader is referred to the COMSOL Reference Manual.
The Physics Interfaces and Building a COMSOL Multiphysics Model in the COMSOL Multiphysics Reference Manual. ABOUT THE SUBSURFACE FLOW MODULE 15 Brinkman Equations interface where shear is non-negligible. The Laminar Flow interface uses the Navier-Stokes equations to cover free flows and the Fracture Flow
Magnetics Modeling in COMSOL Multiphysics Andrew Foote ECE682 Power Electronics Technologies 2-13-20. Outline Introduction COMSOL Overview . Wireless Power Transfer (WPT) for EVs Overview o WPT Magnetics Simulation in COMSOL. Introduction Finite-Element Method/Analysis o Solving partial differential equations (PDEs) by breaking .
Use of COMSOL Multiphysics to Simulate RF Heating of Passive Conductive Implants in MRI Scanners Alan Leewood, PhD MED Institute, Inc. West Lafayette, IN . COMSOL Users’ Conference . Boston, MA . October 3, 2012 . Excerpt from the Proceedings of the 2012 COMSOL Conference in Milan
