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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.

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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)

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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. Grid Velocity vectors Temperature contours

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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 << 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. inflow outflow 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

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