Heat Transfer and Thermal Boundary Conditions

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Heat Transfer and Thermal Boundary Conditions

• Headlamp modeled with
• Discrete Ordinates
• Radiation Model

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Outline

• Introduction
• Thermal Boundary Conditions
• Fluid Properties
• Conjugate Heat Transfer
• Natural Convection
• Radiation
• Periodic Heat Transfer

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Introduction

• Heat transfer in Fluent solvers allows inclusion
  of heat transfer within fluid and solid regions
  in your model.
• Handles problems ranging from thermal mixing
  within a fluid to conduction in composite solids.
  
• Energy transport equation is solved, subject to a
  wide range of thermal boundary conditions.

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Options

• Inclusion of species diffusion term
• Energy equation includes effect of enthalpy
  transport due to species diffusion, which
  contributes to energy balance.
• This term is included in the energy equation by
  default.
• You can turn off the Diffusion Energy Source
  option in the Species Model panel.
• Term always included in the coupled solver.
• Energy equation in conducting solids
• In conducting solid regions, simple conduction
  equation solved
• Includes heat flux due to conduction and
  volumetric heat sources within solid.
• Convective term also included for moving solids.
• Energy sources due to chemical reaction are
  included for reacting flow cases.

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User Inputs for Heat Transfer (1)

• 1. Activate calculation of heat transfer.
• Select the Enable Energy option in the Energy
  panel.
• Define ? Models ? Energy...
• Enabling reacting flow or radiation will toggle
  Enable Energy on without visiting this panel.

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User Inputs for Heat Transfer (2)

• 2. To include viscous heating terms in energy
  equation, turn on Viscous Heating in Viscous
  Model panel.
• Describes thermal energy created by viscous shear
  in the flow.
• Often negligible not included in default form of
  energy equation.
• Enable when shear stress in fluid is large (e.g.,
  in lubrication problems) and/or in high-velocity,
  compressible flows.
• 3. Define thermal boundary conditions.
• Define ? Boundary Conditions...
• 4. Define material properties for heat transfer.
• Define ? Materials...
• Heat capacity and thermal conductivity must be
  defined.
• You can specify many properties as functions of
  temperature.

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Solution Process for Heat Transfer

• Many simple heat transfer problems can be
  successfully solved using default solution
  parameters.
• However, you may accelerate convergence and/or
  improve the stability of the solution process by
  changing the options below
• Underrelaxation of energy equation.
• Solve ? Controls ? Solution...
• Disabling species diffusion term.
• Define ? Models ? Species...
• Compute isothermal flow first, then add
  calculation of energy equation.
• Solve ? Controls ? Solution...

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Theoretical Basis of Wall Heat Transfer

• For laminar flows, fluid side heat transfer is
  approximated as
• n local coordinate normal to wall
• For turbulent flows, law of the wall is extended
  to treat wall heat flux.
• The wall-function approach implicitly accounts
  for viscous sublayer.
• The near-wall treatment is extended to account
  for viscous dissipation which occurs in the
  boundary layer of high-speed flows.

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Thermal Boundary Conditions at Flow Inlets and
Exits

• At flow inlets, must supply fluid temperature.
• At flow exits, fluid temperature extrapolated
  from upstream value.
• At pressure outlets, where flow reversal may
  occur, backflow temperature is required.

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Thermal Conditions for Fluids and Solids

• Can specify an energy source using Source Terms
  option.

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Thermal Boundary Conditions at Walls

• Use any of following thermal conditions at walls
  
• Specified heat flux
• Specified temperature
• Convective heat transfer
• External radiation
• Combined external radiation and external
  convective heat transfer

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Fluid Properties

• Fluid properties such as heat capacity,
  conductivity, and viscosity can be defined as
• Constant
• Temperature-dependent
• Composition-dependent
• Computed by kinetic theory
• Computed by user-defined functions
• Density can be computed by ideal gas law.
• Alternately, density can be treated as
• Constant (with optional Boussinesq modeling)
• Temperature-dependent
• Composition-dependent

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Conjugate Heat Transfer

• Ability to compute conduction of heat through
  solids, coupled with convective heat transfer in
  fluid.
• In 2D Cartesian coordinates
• Solid properties may vary with location, e.g.,
• Density, ?w
• Specific heat, cw
• Conductivity, kw
• Solid conductivity, kw, may also be function of
  temperature.
• is a uniformly distributed volumetric heat
  source.
• May be function of time and space (using profiles
  or user-defined functions).

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Conjugate Heat Transfer in Fuel-Rod Assembly

• Fluid flow equations not solved within solid
  regions.
• Energy equation solved simultaneously in full
  domain.
• Convective terms dropped in stationary solid
  regions.

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Natural Convection - Introduction

• Natural convection occurs when heat is added to
  fluid and fluid density varies with temperature.
• Flow is induced by force of gravity acting on
  density variation.

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Natural Convection - Boussinesq Model

• Makes simplifying assumption that density is
  uniform.
• Except for body force term in momentum equation,
  which is replaced by
• Valid when density variations are small.
• When to use Boussinesq model
• Essential to calculate time-dependent natural
  convection inside closed domains.
• Can also be used for steady-state problems.
• Provided changes in temperature are small
• You can get faster convergence for many
  natural-convection flows than by using fluid
  density as function of temperature.
• Cannot be used with species calculations or
  reacting flows.

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User Inputs for Natural Convection (1)

• 1. Set gravitational acceleration.
• Define ? Operating Conditions...
• 2. Fluid density
• (a) If using Boussinesq model
• Select boussinesq as the Density method and
  assign a constant value.
• Set the Thermal Expansion Coefficient.
• Define ? Materials
• Set the Operating Temperature in the Operating
  Conditions panel.
• Define ? Operating Conditions...
• (b) Otherwise, define fluid density as function
  of
  
  temperature.

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User Inputs for Natural Convection (2)

• 3. Optionally, specify Operating Density.
• Does not apply for Boussinesq model.
• 4. Set boundary conditions.
• Define ? Boundary Conditions...

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Radiation

• Radiation intensity along any
  direction
  entering medium
  is reduced by
• Local absorption
• Out-scattering (scattering away
  
  from the direction)
• Radiation intensity along any
  direction
  entering medium is
  augmented by
• Local emission
• In-scattering (scattering into the direction)
• Four radiation models are provided in FLUENT
• Discrete Ordinates Model (DOM)
• Discrete Transfer Radiation Model (DTRM)
• P-1 Radiation Model
• Rosseland Model (limited applicability)

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Discrete Ordinates Model

• The radiative transfer equation is solved for a
  discrete number of finite solid angles
• Advantages
• Conservative method leads to heat balance for
  coarse discretization.
• Accuracy can be increased by using a finer
  discretization.
• Accounts for scattering, semi-transparent media,
  specular surfaces.
• Banded-gray option for wavelength-dependent
  transmission.
• Limitations
• Solving a problem with a large number of
  ordinates is CPU-intensive.

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Discrete Transfer Radiation Model (DTRM)

• Main assumption radiation leaving surface
  element in a specific range of solid angles can
  be approximated by a single ray.
• Uses ray-tracing technique to integrate radiant
  intensity along each ray
• Advantages
• Relatively simple model.
• Can increase accuracy by increasing number of
  rays.
• Applies to wide range of optical thicknesses.
• Limitations
• Assumes all surfaces are diffuse.
• Effect of scattering not included.
• Solving a problem with a large number of rays is
  CPU-intensive.

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P-1 Model

• Main assumption radiation intensity can be
  decomposed into series of spherical harmonics.
• Only first term in this (rapidly converging)
  series used in P-1 model.
• Effects of particles, droplets, and soot can be
  included.
• Advantages
• Radiative transfer equation easy to solve with
  little CPU demand.
• Includes effect of scattering.
• Works reasonably well for combustion applications
  where optical thickness is large.
• Easily applied to complicated geometries with
  curvilinear coordinates.
• Limitations
• Assumes all surfaces are diffuse.
• May result in loss of accuracy, depending on
  complexity of geometry, if optical thickness is
  small.
• Tends to overpredict radiative fluxes from
  localized heat sources or sinks.

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Choosing a Radiation Model

• For certain problems, one radiation model may be
  more appropriate in general.
• Define ? Models ? Radiation...
• Computational effort P-1 gives reasonable
  accuracy with
  less effort.
• Accuracy DTRM and DOM more accurate.
• Optical thickness DTRM/DOM for optically thin
  media (optical
  thickness ltlt 1) P-1 better for optically thick
  media.
• Scattering P-1 and DOM account for scattering.
• Particulate effects P-1 and DOM account for
  radiation exchange between gas and particulates.
• Localized heat sources DTRM/DOM with
  sufficiently large number of rays/ ordinates is
  more appropriate.

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Periodic Heat Transfer (1)

• Also known as streamwise-periodic or
  fully-developed flow.
• Used when flow and heat transfer patterns are
  repeated, e.g.,
• Compact heat exchangers
• Flow across tube banks
• Geometry and boundary conditions repeat in
  streamwise direction.

Outflow at one periodic boundary is inflow at the
other
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Periodic Heat Transfer (2)

• Temperature (and pressure) vary in streamwise
  direction.
• Scaled temperature (and periodic pressure) is
  same at periodic boundaries.
• For fixed wall temperature problems, scaled
  temperature defined as
• Tb suitably defined bulk temperature
• Can also model flows with specified wall heat
  flux.

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Periodic Heat Transfer (3)

• Periodic heat transfer is subject to the
  following constraints
• Either constant temperature or fixed flux bounds.
• Conducting regions cannot straddle periodic
  plane.
• Properties cannot be functions of temperature.
• Radiative heat transfer cannot be modeled.
• Viscous heating only available with heat flux
  wall boundaries.
• Flow must be specified by pressure jump in
  coupled solvers.

Contours of Scaled Temperature
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Summary

• Heat transfer modeling is available in all Fluent
  solvers.
• After activating heat transfer, you must provide
• Thermal conditions at walls and flow boundaries
• Fluid properties for energy equation
• Available heat transfer modeling options include
• Species diffusion heat source
• Combustion heat source
• Conjugate heat transfer
• Natural convection
• Radiation
• Periodic heat transfer