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Heat Transfer Module User’s Guide Heat Transfer Module User’s Guide © 1998–2018 COMSOL Protected 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. Patents pending. This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the terms of the license agreement. COMSOL, the COMSOL logo, COMSOL Multiphysics, COMSOL Desktop, COMSOL Server, and LiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/trademarks. Version: COMSOL 5.4 Contact Information Visit the Contact COMSOL page at www.comsol.com/contact to submit general inquiries, contact Technical Support, or search for an address and phone number. You can also visit the Worldwide Sales Offices page at www.comsol.com/contact/offices for address and contact information. If you need to contact Support, an online request form is located at the COMSOL Access page 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/knowledgebase Part number: CM020801 Contents Chapter 1: Introduction About the Heat Transfer Module 20 Why Heat Transfer is Important to Modeling . 20 How the Heat Transfer Module Improves Your Modeling . 21 The Heat Transfer Module Physics Interface Guide . 21 Common Physics Interface and Feature Settings and Nodes . 29 The Heat Transfer Module Study Capabilities . 29 Additional Materials Database . 33 Where Do I Access the Documentation and Application Libraries? . 34 Overview of the User’s Guide 38 Chapter 2: Notations Chapter 3: Modeling with the Heat Transfer Module Heat Transfer Variables 60 Predefined Variables . 60 Global Variables . 63 Domain Fluxes. 66 Out-of-Plane Domain Fluxes . 68 Boundary Fluxes (Heat Transfer interface) . 68 Internal Boundary Heat Fluxes. 70 Domain Heat Sources . 71 Boundary Heat Sources . 72 Line and Point Heat Sources . 72 Ambient Variables . 72 Moist Air Variables . 73 CONTENTS | 3 Moisture Transport Variables 76 Predefined Variables . 76 Moist air properties. 77 Domain Moisture Fluxes . 79 Boundary Moisture Fluxes . 79 Domain Moisture Source. 81 Using the Boundary Conditions for the Heat Transfer Interfaces 82 Temperature and Heat Flux Boundary Conditions . 82 Overriding Mechanism for Heat Transfer Boundary Conditions . 83 Handling Frames in Heat Transfer 86 Heat Transfer Analysis with Moving Frames. 86 Material Density in Features Defined in the Material Frame . 91 Heat Transfer Consistent and Inconsistent Stabilization Methods 92 Consistent Stabilization . 92 Inconsistent Stabilization . 93 Heat Transfer and Fluid Flow Coupling 94 Coupling Based on Model Inputs . 94 Temperature Coupling and Flow Coupling Multiphysics Features. 95 Adding Nonisothermal Flow Coupling in an Existing Model . 95 Nonisothermal Flow and Conjugate Heat Transfer Multiphysics Interfaces . 96 Boundary Wall Temperature 97 Solver Settings 102 Linearity property of the temperature equation . 102 Linear Solver . 103 Nonlinear Solver . 105 Time-Dependent Study Step . 107 Guidelines for Solving Surface-to-Surface Radiation Problems . 109 Guidelines for Solving Multiphysics problems . 109 4 | CONTENTS Plotting Results in Thin Layers Extra Dimensions 112 Along the Layer . 112 Through the Thin Layer . 113 Ambient Thermal Properties 115 Settings for the Ambient Thermal Properties . 115 Processing of ASHRAE Data . 119 Ambient Data Interpolation . 120 Ambient Variables and Conditions . 120 Use of Ambient Data From the Features . 128 Modeling Heat Transfer by Radiation 130 Interfaces and Features for Radiation in Transparent Media . 132 Interfaces and Features for Radiation in Participating Media . 134 Specifying the temperature at a flow inlet 136 Using the Temperature condition . 136 Using the Inflow condition . 136 Temperature contribution to the Inflow boundary condition . 138 Pressure contribution to the Inflow boundary condition . 139 Choosing between the Temperature and the Inflow conditions . 139 Heat Part Library 140 Heat Part Library Contents . 140 Heat Sink - Parameterized Fin Types Part . 143 Heat Sink - Dissimilar Border Pins Part . 146 Heat Sink - Pin Fins Part . 146 Heat Sink - Straight Fins Part . 146 References 147 Chapter 4: Theory for the Heat Transfer Module Foundations of the General Heat Transfer Equation 151 Thermodynamic Description of Heat Transfer. 151 The Physical Mechanisms under Heat Transfer . 155 CONTENTS | 5 The Heat Balance Equation . 156 Consistency with Mass and Momentum Conservation Laws. 159 Theory for Heat Transfer in Solids 161 Theory for Heat Transfer in Fluids 162 Theory for Bioheat Transfer 164 The Bioheat Equation . 164 Damaged Tissue . 164 Theory for Heat Transfer in Porous Media 168 When Should Local Thermal Equilibrium and Non-Equilibrium be Considered? . 168 Local Thermal Equilibrium . 169 Local Thermal Non-Equilibrium . 171 Theory for Heat Transfer with Phase Change 174 Phase change in solid materials . 176 Theory for Heat Transfer in Building Materials 178 Theory for Harmonic Heat Transfer 180 Theory for Lumped Isothermal Domain 182 Theory for Heat Transfer in Thin Structures 185 Modeling Layered Materials . 185 Theoretical Background of the Different Formulations . 189 Thin Layer . 194 Thin Film . 197 Fracture . 199 Thin Rod . 200 Theory for Surface-to-Surface Radiation 201 Deriving the Radiative Heat Flux for Opaque Surfaces . 201 Deriving the Radiative Heat Flux for Semi-Transparent Surfaces . 202 Wavelength Dependence of Surface Emissivity and Absorptivity . 204 6 | CONTENTS The Radiosity Method for Diffuse-Gray Surfaces . 210 The Radiosity Method for Diffuse-Spectral Surfaces. 213 View Factor Evaluation . 216 Theory for Radiation in Participating Media 220 Radiation and Participating Media Interactions . 220 Radiative Transfer Equation . 221 Boundary Condition for the Radiative Transfer Equation . 223 Heat Transfer Equation in Participating Media . 224 Discrete Ordinates Method (DOM) . 224 Discrete Ordinates Method Implementation in 2D . 225 Rosseland Approximation Theory . 227 P1 Approximation Theory . 228 Radiation in Absorbing-Scattering Media Theory . 231 Radiative Beam in Absorbing Media Theory . 233 Theory for Moisture Transport 234 Theory for moisture transport in building materials. 234 Theory for moisture transport in air . 234 Theory for the Heat Transfer Multiphysics Couplings 236 Theory for the Nonisothermal Flow and Conjugate Heat Transfer Interfaces . 236 Theory for the Moisture Flow Interface . 244 Theory for the Thermoelectric Effect Interface . 248 Theory for the Local Thermal Non-Equilibrium Interface. 251 Theory for the Building Materials version of the Heat and Moisture Transport Interface . 252 Theory for the Moist Air version of the Heat and Moisture Transport Interface . 253 Theory for the Heat and Moisture Flow Interfaces . 254 Theory for the Electromagnetic Heating Interfaces . 254 Theory for the Thermal Stress Interface . 254 Theory for Thermal Contact 255 Theory for the Thermal Contact Feature . 255 CONTENTS | 7 Moist Air Fluid Type 260 Humidity . 260 Saturation State . 262 Moist Air Properties . 262 Out-of-Plane Heat Transfer 267 Equation Formulation . 267 The Heat Transfer Coefficients 270 Defining the Heat Transfer Coefficients . 271 Nature of the Flow — The Grashof Number . 272 Heat Transfer Coefficients — External Natural Convection . 274 Heat Transfer Coefficients — Internal Natural Convection . 281 Heat Transfer Coefficients — External Forced Convection . 282 Heat Transfer Coefficients — Internal Forced Convection . 285 Using the Heat and Mass Transfer Analogy for the Evaluation of Moisture Transfer Coefficients . 285 Equivalent Thermal Conductivity Correlations 287 Horizontal Cavity With Bottom Heating . 288 Vertical Cavity With Sidewall Heating . 288 Temperature Dependence of Surface Tension 290 Heat Flux and Heat Balance 291 Total Heat Flux and Energy Flux . 291 Heat and Energy Balance . 292 Frames for the Heat Transfer Equations 295 Material and Spatial Frames . 295 Conversion Between Material and Spatial Frames . 296 8 | CONTENTS References 300 Chapter 5: The Heat Transfer Module Interfaces About the Heat Transfer Interfaces 307 Space Dimensions . 307 Study Types . 307 Versions of the Heat Transfer Physics Interface . 308 Benefits of the Different Heat Transfer Interfaces . 308 Versions of the Heat Transfer in Shells Physics Interface . 309 Benefits of the Different Heat Transfer in Shells Interfaces . 310 The Layer Selection and Interface Selection Sections . 310 Using the Extra Dimension Coordinates . 314 Versions of the Moisture Transport Physics Interface . 314 Benefits of the Different Moisture Transport Interfaces . 315 Additional physics options . 315 Settings for the Heat Transfer Interface . 316 Settings for the Heat Transfer in Shells Interface . 319 The Heat Transfer in Solids Interface 322 Feature
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