Slide 1

Chapter 7

Heat Transfer ModelingIntroductory FLUENT Training7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualOutlineEnergy Equation

Wall Boundary Conditions

Conjugate Heat Transfer

Thin and two-sided walls

Natural Convection

Radiation Models

Reporting - Export

Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualEnergy Equation IntroductionEnergy transport equation:

Energy E per unit mass is defined as:

Pressure work and kinetic energy are always accounted for with compressible flows or when using the density-based solvers. For the pressure-based solver, they are omitted and can be added through the text command:

The TUI command define/models/energy? Will give more options when enabling the energy equation.ConductionSpeciesDiffusionViscousDissipationConductionUnsteadyEnthalpy Source/Sink

Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualThe definition of E is E= h pv + V^2/2But pressure work and kinetic energy are not included by default for incompressible flows using segregated solver. Energy Equation for Solid RegionsAbility to compute conduction of heat through solids

Energy equation:

h is the sensible enthalpy:

Anisotropic conductivity in solids (pressure-based solver only)

Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualWall Boundary ConditionsFive thermal conditionsHeat FluxTemperatureConvection simulates an external convection environment which is not modeled (user-prescribed heat transfer coefficient).Radiation simulates an external radiation environment which is not modeled (user-prescribed external emissivity and radiation temperature).Mixed Combination of Convection and Radiation boundary conditions.

Wall material and thickness can be defined for 1D or shell conduction calculations. heat transfer calculations.

Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualConjugate Heat TransferIn CHT, heat conduction in solid regions is coupled to convective heat transfer in fluid regions.Makes use of the Coupled boundary condition on wall zones which define fluid/solid interfaces.Coolant Flow Past Heated Rods

Grid

Velocity Vectors

Temperature Contours

Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training Manual

Conjugate Heat Transfer ExampleCircuit board (externally cooled)k = 0.1 W/mKh = 1.5 W/m2KT = 298 K

Air inletV = 0.5 m/sT = 298 KElectronic Component(one half is modeled)k = 1.0 W/mKHeat generation rate of 2 watts (each component)Top wall(externally cooled)h = 1.5 W/m2KT = 298 K

SymmetryPlanesAir outletHeat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualAs an example illustrating FLUENTs capability to handle conjugate heat transfer problems, flow over an electronic chip mounted on a circuit board is presented. Here, the small box represents the chip, which contains a total energy source of 2 watts. The air heats as it flows over the chip, causing the chip to cool simulatneously. Heat transfer mechanisms considered in this simulation are:

Heat conduction inside the chip Conduction from the chip to the wall Conduction along the length of the board Convection from the chip and board to the flowing air.

The upper wall as well as the bottom surface of the circuit board are assumed to be externally cooled due to convection. The model is intended to be applicable to flow over an array of chips, so symmetry planes are employed on the sides of the computational domain. Taking further advantage of symmetry, only half of the chip is modeled.

Problem Setup Heat SourceAn energy (heat) source is added to the solid zone to simulate the heat generation by the heat-generating electronic components.

Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualIt is necessary to specify the energy source that will be applied to the chip. Opening the Solid panel from the Boundary Conditions specification panel and checking the source terms box enables specification of this term. Based on the half-volume of the chip, it has been determined that the total source term requirement is 904,050 watts per cubic meter. This is to say that if the chip had a volume of one cubic meter, it would dissipate a total of around 904,000 watts of thermal energy. For this model, we will assume this value to be constant.

INCREASE VOLUME LEVEL!!

Temperature Distribution (Front and Top View)FlowdirectionConvection Boundary1.5 W/m2 K298 K free stream temp.Convection boundary1.5 W/m2 K298 K free stream tempFront ViewTop View(image mirrored about symmetry plane)Elect. Component(solid zone)2 Watts sourceBoard(solid zone)Air (fluid zone)

298426410394378362346330314Temp.(F)FlowdirectionHeat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualLets take a look at the predicted temperature distribution inside the domain for our example problem. On the left side near the inlet, the temperatures are nearly that of the inlet conditions of 298 K. also, the board temperature is nearly that of the incoming air. As we move downstream, we see the effects of the energy source that exists in the chip. As expected, the front edge of the chip is cooled, while the trailing face of the chip is significantly hotter. Some of the thermal energy emitted by the chip is convected to the surrounding air, which can be seen here. Also, some of the energy produced by the chip is conducted into the board and along the length of the board. Looking carefully at the interface between the air and the board downstream of the chip, we see that the board temperature is everywhere slightly larger than that of the adjacent air flow, as expected.Alternate Modeling StrategiesAn alternate treatment of the board surface would be to model it as a wall with specified thickness (Thin Wall model).In this case, there is no need to mesh the lower solid zone (representing the board).

Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualIn the example we just discussed, the entire board thickness was meshed. If we had chosen not to mesh the board, we could have still obtained similar results. An alternate treatment of the board would be to model it as an infinintely thin surface using the so-called Thin Wall approach. This approach can be enabled by setting a convection boundary condition on the wall of interest. In addition, a wall thickness can be artificially introduced into the calculations by specification in the panel shown. Also, if the wall is to represent some energy generating surface (as in the case of a radiator), the amount of energy production can be specifed here as well. Meshed Wall vs. Thin Wall ApproachMeshed wall approachEnergy equation is solved in a solid zone representing the wall.Wall thickness must be meshed.This is the most accurate approach but requires more meshing effort.Always uses the coupled thermal boundary condition since there are cells on both sides of the wall.Fluid zoneSolid zoneWall zone(with shadow)Wall thermal resistance directly accounted for in the Energy equation; Through-thickness temperature distribution is calculated.Bidirectional heat conduction is calculated.Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualMeshed Wall vs. Thin Wall ApproachThin wall approachArtificially models models the thermal resistance of the wall.Necessary data is supplied through wall boundary conditions (material conductivity and thickness).Uses the coupled thermal boundary condition only for internal walls.Fluid zoneWall zone(no shadow)Wall thermal resistance is calculated using artificial wall thickness and material type. Through-thickness temperature distribution is assumed to be linear.Conduction is only calculated in the wall-normal direction unless Shell Conduction is enabled.Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualShell Conduction OptionThe shell conduction option is used to enable in-plane conduction calculations.

Additional conduction cells are created but cannot be displayed and cannot be accessed by UDFs.

Solid properties of the conduction zones must be constant and cannot be temperature-dependent.

Static Temperature(cell value)Virtual conduction cellsHeat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualNatural ConvectionNatural 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.

When gravity term is included, pressure gradient and body force term in the momentum equation are rewritten as:

where

This pressure transformation avoids round off error when gravity is enabled.

Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualNatural Convection the Boussinesq ModelBoussinesq model assumes the fluid density is uniform except for the body force term in the momentum equation along the direction of gravity, we have:

Valid when density variations are small (i.e., small variations in temperature).

The Boussinesq approximation provides improved convergence for many natural convection flows than by using fluid density as function of temperature.Constant density assumptions reduces nonlinearity.Suitable when density variations are small.Cannot be used together with species transport or reacting flows.

Natural convection problems inside closed domains:For steady-state solver, Boussinesq model must be used.For unsteady solver, Boussinesq model or ideal gas law can be used.

Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training Manual

User Inputs for Natural ConvectionDefine the gravitational acceleration done in Operating Conditions panel.

Define density model (several options are available).Boussinesq modelEnable gravity.Set Operating Temperature, T0.Select Boussinesq as the Density Method and assign constant value, 0.Set Thermal Expansion Coefficient, .If using a temperature dependentmodel (ideal gas, Aungier-Redlich-Kwong, polynomial):Specify Operating Density or,Allow FLUENT to calculate 0 from a cell average (default, every iteration).Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training Manual

RadiationRadiation effects should be accounted for when is of comparable magnitude as the convection and conduction heat transfer rates. is the Stefan-Boltzmann constant, 5.6710-8 W/(m2K4)

To account for radiation, radiative intensity transport equations (RTEs) are solved.Local absorption by fluid and at boundaries couples these RTEs with the energy equation.These equations are often solved separate from the fluid flow solution; however, they can be coupled to the flow.

Radiation intensity, I(r,s), is directionally and spatially dependent.

Five radiation models are available in FLUENT(see the Appendix for details on each model).Discrete Ordinates Model (DOM)Discrete Transfer Radiation Model (DTRM)P1 Radiation ModelRosseland ModelSurface-to-Surface (S2S)

Heat Transfer Modeling7-#ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.April 28, 2009Inventory #002600Training ManualSelecting a Radiation ModelSome general guidelines for radiation model selection:Computational effortP1 gives reasonable accuracy with the least amount of effort.AccuracyDTRM and DOM are the most accurate. Optical thicknessUse DTRM/DOM for optically thinmedia (L