© Fluent Inc. 2/20/01F1Fluent Software TrainingTRN-99-003Heat Transfer and Thermal BoundaryConditionsHeadlamp modeled withDiscrete OrdinatesRadiation Model© Fluent Inc. 2/20/01F2Fluent Software TrainingTRN-99-003Outlineu Introductionu Thermal Boundary Conditionsu Fluid Propertiesu Conjugate Heat Transferu Natural Convectionu Radiationu Periodic Heat Transfer© Fluent Inc. 2/20/01F3Fluent Software TrainingTRN-99-003Introductionu Energy transport equation is solved, subject to a wide range of thermalboundary conditions.l Energy source due to chemical reaction is included for reacting flows.l Energy source due to species diffusion included for multiple species flows.n Always included in coupled solver.n Can be disabled in segregated solver.l Energy source due to viscous heating:n Describes thermal energy created by viscous shear in the flow.s Important when shear stress in fluid is large (e.g., lubrication) and/or inhigh-velocity, compressible flows.n Often negligibles not included by default for segregated solvers always included for coupled solver.l In solid regions, simple conduction equation solved.n Convective term can also be included for moving solids.© Fluent Inc. 2/20/01F4Fluent Software TrainingTRN-99-003User Inputs for Heat Transfer1. Activate calculation of heat transfer.l Select the Enable Energy option in the Energy panel.Define Õ Models Õ Energy...l Enabling a temperature dependent density model, reacting flow model, or aradiation model will toggle Enable Energy on without visiting this panel.2. Enable appropriate options:l Viscous Heating in Viscous Model panell Diffusion Energy Source option in the Species Model panel3. Define thermal boundary conditions.Define Õ Boundary Conditions...4. Define material properties for heat transfer.Define Õ Materials...l Heat capacity and thermal conductivity must be defined.© Fluent Inc. 2/20/01F5Fluent Software TrainingTRN-99-003Solution Process for Heat Transferu Many simple heat transfer problems can be successfully solved usingdefault solution parameters.u However, you may accelerate convergence and/or improve the stabilityof the solution process by changing the options below:l Under-relaxation of energy equation.Solve Õ Controls Õ Solution...l Disabling species diffusion term.Define Õ Models Õ Species...l Compute isothermal flow first, then add calculation of energy equation.Solve Õ Controls Õ Solution...© Fluent Inc. 2/20/01F6Fluent Software TrainingTRN-99-003Theoretical Basis of Wall Heat Transferu For laminar flows, fluid side heat transfer is approximated as:n = local coordinate normal to wallu For turbulent flows:l Law of the wall is extended to treat wall heat flux.n The wall-function approach implicitly accounts for viscous sublayer.l The near-wall treatment is extended to account for viscous dissipationwhich occurs in the boundary layer of high-speed flows.′′= ≈q kTnkTnwall∂∂∆∆© Fluent Inc. 2/20/01F7Fluent Software TrainingTRN-99-003Thermal Boundary Conditions at Flow Inletsand Exitsu At flow inlets, must supplyfluid temperature.u At flow exits, fluidtemperature extrapolatedfrom upstream value.u At pressure outlets, whereflow reversal may occur,“backflow” temperature isrequired.© Fluent Inc. 2/20/01F8Fluent Software TrainingTRN-99-003Thermal Conditions for Fluids and Solidsu Can specify an energy sourceusing Source Terms option.© Fluent Inc. 2/20/01F9Fluent Software TrainingTRN-99-003Thermal Boundary Conditions at Wallsu Use any of following thermalconditions at walls:l Specified heat fluxl Specified temperaturel Convective heat transferl External radiationl Combined external radiationand external convective heattransfer© Fluent Inc. 2/20/01F10Fluent Software TrainingTRN-99-003u Fluid properties such as heat capacity, conductivity, and viscosity canbe defined as:l Constantl Temperature-dependentl Composition-dependentl Computed by kinetic theoryl Computed by user-defined functionsu Density can be computed by ideal gas law.u Alternately, density can be treated as:l Constant (with optional Boussinesq modeling)l Temperature-dependentl Composition-dependentl User Defined FunctionFluid Properties© Fluent Inc. 2/20/01F11Fluent Software TrainingTRN-99-003Conjugate Heat Transferu Ability to compute conduction of heat through solids, coupled withconvective heat transfer in fluid.u Coupled Boundary Condition:l available to wall zone thatseparates two cell zones.GridTemperature contoursVelocity vectorsExample: Cooling flow over fuel rods© Fluent Inc. 2/20/01F12Fluent Software TrainingTRN-99-003Natural Convection - Introductionu Natural convection occurswhen heat is added to fluidand fluid density varieswith temperature.u Flow is induced by force ofgravity acting on densityvariation.u When gravity term isincluded, pressure gradientand body force term is writtenas:gxpgxpo)('ρρρ −+∂∂−⇒+∂∂−wheregxppoρ−='• This format avoids potential roundoff errorwhen gravitational body force term is included.© Fluent Inc. 2/20/01F13Fluent Software TrainingTRN-99-003Natural Convection - Boussinesq Modelu Makes simplifying assumption that density is uniform.l Except for body force term in momentum equation, which is replaced by:l Valid when density variations are small (i.e., small variations in T).u Provides faster convergence for many natural-convection flows thanby using fluid density as function of temperature.l Constant density assumptions reduces non-linearity.l Use when density variations are small.l Cannot be used with species calculations or reacting flows.u Natural convection problems inside closed domains:l For steady-state solver, Boussinesq model must be used.n Constant density, ρo, allows mass in volume to be defined.l For unsteady solver, Boussinesq model or Ideal gas law can be used.n Initial conditions define mass in volume.( ) ( )ρρρβ−=−−000g T T g© Fluent Inc. 2/20/01F14Fluent Software TrainingTRN-99-003User Inputs for Natural Convection1. Set gravitational acceleration.Define Õ Operating Conditions...2. Define density model.l If using Boussinesq model:n Select boussinesq as the Density methodand assign constant value, ρo.Define Õ Materials...n Set Thermal Expansion Coefficient, β.n Set Operating Temperature, To.l If using temperature dependent model,(e.g., ideal gas or polynomial):n Specify Operating Density or,n Allow Fluent to calculate ρo from a cellaverage (default, every iteration).3. Set boundary conditions.© Fluent Inc.