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© Fluent Inc. 04/21/23F1
Fluent Software TrainingTRN-98-006
Heat Transfer and Thermal Boundary Conditions
Headlamp modeled with
Discrete Ordinates
Radiation Model
© Fluent Inc. 04/21/23F2
Fluent Software TrainingTRN-98-006
Outline Introduction Thermal Boundary Conditions Fluid Properties Conjugate Heat Transfer Natural Convection Radiation Periodic Heat Transfer
© Fluent Inc. 04/21/23F3
Fluent Software TrainingTRN-98-006
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.
© Fluent Inc. 04/21/23F4
Fluent Software TrainingTRN-98-006
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.
© Fluent Inc. 04/21/23F5
Fluent Software TrainingTRN-98-006
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.
© Fluent Inc. 04/21/23F6
Fluent Software TrainingTRN-98-006
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.
© Fluent Inc. 04/21/23F7
Fluent Software TrainingTRN-98-006
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...
© Fluent Inc. 04/21/23F8
Fluent Software TrainingTRN-98-006
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.
q kT
nk
T
nwall
© Fluent Inc. 04/21/23F9
Fluent Software TrainingTRN-98-006
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.
© Fluent Inc. 04/21/23F10
Fluent Software TrainingTRN-98-006
Thermal Conditions for Fluids and Solids
Can specify an energy source using Source Terms option.
© Fluent Inc. 04/21/23F11
Fluent Software TrainingTRN-98-006
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
© Fluent Inc. 04/21/23F12
Fluent Software TrainingTRN-98-006
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
Fluid Properties
© Fluent Inc. 04/21/23F13
Fluent Software TrainingTRN-98-006
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).
qy
Tk
yx
Tk
xTc
t wwww
q
© Fluent Inc. 04/21/23F14
Fluent Software TrainingTRN-98-006
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.
Temperature contours
Grid
Velocity vectors
© Fluent Inc. 04/21/23F15
Fluent Software TrainingTRN-98-006
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.
© Fluent Inc. 04/21/23F16
Fluent Software TrainingTRN-98-006
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.
( ) ( ) 0 0 0g T T g
© Fluent Inc. 04/21/23F17
Fluent Software TrainingTRN-98-006
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.
© Fluent Inc. 04/21/23F18
Fluent Software TrainingTRN-98-006
User Inputs for Natural Convection (2)
3. Optionally, specify Operating Density. Does not apply for Boussinesq model.
4. Set boundary conditions.Define Boundary Conditions...
© Fluent Inc. 04/21/23F19
Fluent Software TrainingTRN-98-006
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)
© Fluent Inc. 04/21/23F20
Fluent Software TrainingTRN-98-006
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.
ii
i scatteringemmisionabsorptionx
I
© Fluent Inc. 04/21/23F21
Fluent Software TrainingTRN-98-006
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.
4TI
ds
dI
© Fluent Inc. 04/21/23F22
Fluent Software TrainingTRN-98-006
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.
© Fluent Inc. 04/21/23F23
Fluent Software TrainingTRN-98-006
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 << 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.
© Fluent Inc. 04/21/23F24
Fluent Software TrainingTRN-98-006
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
inflow outflow
© Fluent Inc. 04/21/23F25
Fluent Software TrainingTRN-98-006
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.
T T
T Twall
b wall
© Fluent Inc. 04/21/23F26
Fluent Software TrainingTRN-98-006
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
© Fluent Inc. 04/21/23F27
Fluent Software TrainingTRN-98-006
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