Heat Transfer

Tutorial: Solving a Conjugate Heat Transfer Problem using

FLUENT

Introduction

The physics of conjugate heat transfer is common in many engineering applications, includ-ing heat exchangers, HVAC, and electronic component design. The purpose of this tutorialis to provide guidelines and recommendations for setting up and solving a conjugate heattransfer problem using FLUENT.

The geometry and flow domain consists of a flat circuit board with a heat generating elec-tronic chip mounted on it. Heat is conducted through the source (chip) and the board onwhich it is mounted. A laminar stream of air flows over the board and the chip, causing si-multaneous cooling of the solid components and heating of the air stream due to convection.Thermal energy is also transported due to the complex flow field.

In this tutorial, you will:

• Set up appropriate boundary conditions for a conjugate heat transfer simulation inFLUENT.

• Enable source terms for specified zones.

• Perform flow and energy calculations using various materials (both solid and fluid).

• Manipulate mesh adaption registers and perform Boolean operations on them.

• Perform mesh adaption and verify that the solution is mesh independent.

Prerequisites

This tutorial assumes that you are familiar with the FLUENT interface and that you havea good understanding of the basic setup and solution procedures. Some steps will not beshown explicitly.

You will perform postprocessing related only to mesh adaption and verification of a meshindependent solution. For detailed postprocessing of this simulation, refer to Tutorial 22:Postprocessing in the FLUENT 6.2 Tutorial Guide.

c© Fluent Inc. August 31, 2005 1

http://www.fluentusers.com/fluent/doc/ori/html/tg/node319.htm

http://www.fluentusers.com/fluent/doc/ori/html/tg/node319.htm

Solving a Conjugate Heat Transfer Problem using FLUENT

Problem Description

The problem considered is shown schematically in Figure 1. The configuration consists ofa series of heat-generating electronic chips mounted on a circuit board. Air flow, confinedbetween the circuit board and an upper wall, cools the chips and the board. As the airflows over the chips and the board, its temperature rises. Taking the symmetry of theconfiguration into consideration, the model extends from the middle of one chip to theplane of symmetry between it and the next chip.

As shown in Figure 1, each half chip is assumed to generate 1 Watt and have a thermalconductivity of 1.0 W/m-K. The circuit board conductivity is assumed to be one order ofmagnitude lower, at 0.1 W/m-K. Air enters the system at 298 K with a velocity of 0.5 m/s.The inlet Reynolds number (based on the spacing between the upper and lower walls) isaround 870 and thus, the flow is treated as laminar.

Figure 1: Problem Schematic

Preparation

1. Copy the mesh file, chip3d.msh.gz to your working directory.

2. Start the 3D version of FLUENT.

2 c© Fluent Inc. August 31, 2005


Setup and Solution

Step 1: Grid

1. Read the mesh file (chip3d.msh.gz).

2. Set inches as the working unit for length.

Grid −→Scale...

(a) Under Unit Conversion, select in from the Grid Was Created In drop-down list.

(b) Click Change Length Units.

3. Check the grid.

Ensure that there are no negative volumes.

4. Display the grid (Figure 2).

Figure 2: Grid Display

Step 2: Models

1. Define the solver settings.

(a) Under Gradient Option, select Node-Based.

(b) Retain the default settings for the other parameters.

2. Enable the Energy Equation.

3. Define a laminar flow simulation.

Define −→ Models −→Viscous...



Step 3: Materials

The working fluid is air. You need to specify the materials for the chip and the board. Thesematerials are assumed to have the same density and heat capacity as that of aluminum, butdifferent thermal conductivities.

1. Model air as an incompressible ideal gas.

For this simulation, model air as an incompressible gas because there is a maximum airtemperature rise of about 150◦C, but very little pressure change. The incompressibleideal gas option for density treats the fluid density as a function of temperature only.

(a) Select fluid in the Material Type drop-down list.

(b) Under Properties, select incompressible-ideal-gas in the Density drop-down list.

(c) Click Change/Create.

2. Create the chip material.

(a) Select solid in the Material Type drop-down list.

(b) Under Name, enter chip and delete the entry under Chemical Formula.

(c) Specify the Thermal Conductivity as 1.0.

(d) Click Change/Create.

Do not overwrite aluminum.

3. Create the board material.

(a) Under Name, enter board and delete the entry under Chemical Formula.

(b) Specify the Thermal Conductivity as 0.1.

(c) Click Change/Create.

Do not overwrite aluminum.

(d) Close the Materials panel.

Step 4: Operating Conditions

1. Retain the default operating conditions.

Step 5: Boundary Conditions

1. Specify the boundary conditions for the continuum regions.

(a) Specify the boundary conditions for the cont-fluid-air zone.

i. Verify that the Type is fluid and click Set....

ii. Verify that air is selected in the Material Name drop-down list.

(b) Specify the boundary conditions for the cont-solid-board zone.

i. Verify that the Type is solid and click Set....

ii. Select board in the Material Name drop-down list.



(c) Specify the boundary conditions for the cont-solid-chip zone.

i. Verify that the Type is solid and click Set....

ii. Select chip in the Material Name drop-down list.

2. Define the inflow and outflow boundaries.

(a) Set the boundary conditions for the inlet zone.

i. Specify a value of 0.5 for Velocity Magnitude.

ii. Specify the Temperature as 298.

(b) Set the boundary conditions for the outlet zone.

i. Specify the Gauge Pressure as 0.

ii. Specify the Backflow Total Temperature as 298.

3. Define the thermal boundary conditions.

(a) Verify that the Coupled boundary condition is applied for the following walls:

• wall-chip and wall-chip-shadow

• wall-chip-bottom and wall-chip-bottom-shadow

• wall-duct-bottom and wall-duct-bottom-shadow

(b) Set the boundary conditions for the wall-board-bottom zone.

i. Under Thermal Conditions, select Convection.

ii. Specify the Heat Transfer Coefficient as 1.5.

iii. Specify the Free Stream Temperature as 298.

(c) Copy the boundary conditions set for the wall-board-bottom zone to the wall-duct-top zone.

i. In the Boundary Conditions panel, click Copy....

The Copy BCs panel is displayed.

ii. Under From Zone, select wall-board-bottom.

iii. Under To Zones, select wall-duct-top.

iv. Click Copy.

A Warning dialog box is displayed asking if you want to copy wall-board-bottom boundary conditions to wall-duct-top.

v. Click OK and close the Copy BCs panel.

Verify that the boundary conditions were copied correctly. Copying a bound-ary condition does not create a link from one zone to another. If you wantto change boundary conditions on these zones, you will have to change eachone separately.



(d) Set the boundary conditions for the cont-solid-chip zone.

i. Enable Source Terms.

ii. Select constant in the Energy drop-down list and enter a value of 904055.

This value, based on the half-volume of the chip, yields a total energy sourceof 2 Watts in the chip zone.

Step 6: Solution

1. Define the solution control parameters.

(a) Retain the default settings for the Under-Relaxation Factors.

(b) Under Discretization, select Second Order Upwind for Momentum and Energy.

2. Enable the plotting of residuals during the calculation.

3. Set the Convergence Criterion for continuity to 0.0001.

4. Define a point monitor for the energy equation.

You will define a point monitor in the recirculation region behind the chip. The solu-tion convergence is critical in this region.

Surface −→Point...

(a) Set the Coordinates (x0, y0, z0) to (2.85, 0.25, 0.3).

(b) Under New Surface Name, enter point-monitor.

(c) Click Create and close the panel.

5. Enable the plotting of the point monitor.

(a) Set the number of Surface Monitors to 1.

(b) Enable Plot and Print for monitor-1.

(c) In the drop-down list for Every, select Iteration.

(d) Click Define....

The Define Surface Monitor panel is displayed.

i. Select Vertex Average in the Report Type drop-down list.

ii. Set Plot Window to 1.

iii. Select Temperature... and Static Temperature in the Report of drop-downlists.

iv. Under Surfaces, select point-monitor.

v. Click OK.

6. Save the case file chip3d.cas.gz.

7. Initialize the solution.

(a) Select inlet in the Compute From drop-down list.

(b) Click Init.

8. Request 200 iterations (Figures 3 and 4).



Z

YX

Scaled ResidualsFLUENT 6.2 (3d, segregated, lam)

Iterations160140120100806040200

1e+01

1e+00

1e-01

1e-02

1e-03

1e-04

1e-05

1e-06

1e-07

1e-08

energyz-velocityy-velocityx-velocitycontinuityResiduals

Figure 3: Residual Plot

Z

Y

X

Convergence history of Static Temperature on point-monitorFLUENT 6.2 (3d, segregated, lam)

Iteration

(k)ValuesVertex

Surfaceof

Average

160140120100806040200

410.0000

400.0000

390.0000

380.0000

370.0000

360.0000

350.0000

340.0000

330.0000

320.0000

monitor-1Monitors

Figure 4: Convergence History of Static Temperature at Monitor Point



Step 7: Data Analysis

1. Verify that mass is conserved.

Report −→Fluxes...

(a) Under Options, select Mass Flow Rate.

(b) In the Boundaries list, select inlet and outlet.

(c) Click Compute.

FLUENT displays the total mass flux across each boundary selected. As seen inthe panel:

• The mass flow rate for the inlet is positive (indicating that mass is enteringthe domain), while that for the outlet is negative (indicating that mass isleaving the domain).

• The net mass flux appears in the box at the lower right corner of the FluxReports panel.

• The net mass flux (inlet plus outlet) is almost zero, indicating that mass isconserved.



2. Verify that energy is conserved.

(a) Under Options, select Total Heat Transfer Rate.

(b) Deselect the previously selected boundaries (inlet and outlet).

(c) In the Boundaries list, select wall-chip and wall-chip-bottom.

(d) Click Compute.

The net heat transfer from the chip is 1 Watt since only half the chip is modeled.

(e) Select surfaces where heat flows into and/or out of the computational domain.

i. Retain the selection of wall-chip and wall-chip-bottom.

ii. Select the convection boundaries, wall-duct-top and wall-board-bottom.



iii. Select inlet and outlet.

The selection of the inlet and outlet surfaces accounts for the heat carried bythe air as it enters and leaves the domain.

(f) Click Compute.

The net heat transfer error is very small, indicating that an overall heat balancehas been achieved.

A good rule of thumb is to have the heat transfer error less than 1% of the smallestsource.

Step 8: Postprocessing

You will perform postprocessing relating to mesh adaption and verification of a mesh inde-pendent solution.

1. Set up line surfaces for plotting.

Surface −→Line/Rake...

(a) Create line surfaces line-xwss and line-cross with end points as follows:

Line x0 y0 z0 x1 y1 z1

line-xwss 2.75 0.1001 0 4.75 0.1001 0line-cross 3.5 0.25 0 3.5 0.25 0.5



2. Generate an XY plot of the cross-stream temperature profile downstream of the chipalong the line surface, line-cross.

Plot −→XY Plot...

(a) Under Options, enable Node Values and Position on X Axis.

(b) Set the plot vector to (0, 0, 1).

(c) Select Temperature... and Static Temperature in the Y Axis Function drop-downlists.

(d) Under Surfaces, select line-cross.

(e) Click Plot (Figure 5).

ZY

X

Static TemperatureFLUENT 6.2 (3d, segregated, lam)

Position (in)

(k)Temperature

Static

0.50.40.30.20.10

3.55e+02

3.50e+02

3.45e+02

3.40e+02

3.35e+02

3.30e+02

Original Mesh

Figure 5: Cross-Stream Static Temperature Profile at x = 3.5 in, y = 0.25 in

Figure 5 shows the predicted cross stream temperature profile behind the block.The effects of the heated block are apparent. The mesh is currently too coarse toresolve the heat transfer details accurately.

(f) Write the data to an output file temp-0.xy.

i. Under Options, enable Write to File and click Write....

The Select File panel is displayed.

ii. Under XY File, enter temp-0.xy and click OK.

3. Generate an XY plot of the cross-stream velocity profile downstream of the chip alongthe line surface line-cross.





(c) Select Velocity... and Velocity Magnitude in the Y Axis Function drop-down lists.

(d) Under Surfaces, select line-cross and click Plot (Figure 6).

ZY

X

Velocity MagnitudeFLUENT 6.2 (3d, segregated, lam)

Position (in)

(m/s)Magnitude

Velocity

0.50.40.30.20.10

4.50e-01

4.00e-01

3.50e-01

3.00e-01

2.50e-01

2.00e-01

1.50e-01

1.00e-01

5.00e-02

0.00e+00

Original Mesh

Figure 6: Cross-Stream Velocity Magnitude Profile at x = 3.5 in, y = 0.25 in

Figure 6 shows the predicted cross stream velocity profile behind the block. Flowdetails are smeared due to the relatively coarse mesh used. The mesh is currentlytoo coarse to resolve the flow details accurately.

(e) Write the data to an output file velocity-0.xy.

4. Generate an XY plot of the stream-wise component of wall shear stress in the stream-wise direction along the center of the chip.

(a) Under Options, disable Node Values and enable Position on X Axis.


(c) Select Wall Fluxes... and X-Wall Shear Stress in the Y Axis Function drop-downlists.

(d) Under Surfaces, select line-xwss and click Plot (Figure 7).

(e) Write the data to an output file xwss-0.xy.

5. Save the case and data files (chip3d.cas.gz and chip3d.dat.gz).



ZY

X

X-Wall Shear StressFLUENT 6.2 (3d, segregated, lam)

Position (in)

(pascal)StressShear

X-Wall

4.84.64.44.243.83.63.43.232.82.6

2.50e-03

2.00e-03

1.50e-03

1.00e-03

5.00e-04

0.00e+00

-5.00e-04

-1.00e-03

-1.50e-03

-2.00e-03

Original Mesh

Figure 7: X-Wall Shear Stress Profile Downstream of the Chip

Step 9: Mesh Adaption

The solution can be improved by refining the grid to better resolve the flow details. It isalso important to verify if the flow solution is independent of the mesh size used. Createmesh adaption registers based on gradients of pressure, velocity, and temperature, as wellas a region adaption register. An adaption register is a logical collection of cells that havebeen marked for adaption.

Then, combine the adaption registers using Boolean addition and adapt the mesh using thecombination register. After continuing the iterations, examine the results obtained usingthe refined mesh to determine if the solution is mesh independent or if further adaption isrequired. Mesh adaption should always be performed until mesh independence is achieved.

1. Create a pressure gradient adaption register.

Adapt −→Gradient...

The Gradient Adaption panel is displayed.

(a) Under Method, retain the selection of Curvature.

(b) Select Pressure... and Static Pressure in the Gradients of drop-down lists.

(c) Click Compute.

FLUENT reports that the maximum adaption function value is around 0.000177.

(d) Enter a value of 1.77e-5 for Refine Threshold.

Coarsen Threshold specifies the threshold values for coarsening the grid. Cellswith adaption function values (in this case, pressure gradient) below the Coarsen



Threshold will be marked for coarsening. Refine Threshold specifies the thresholdvalues for refining the grid. Cells with adaption function values above the RefineThreshold will be marked for refining.

When selecting values for Refine Threshold, a good rule of thumb is to use ap-proximately 10% of the value reported in the Max field (i.e., the maximum valueof the adaption function).

For more information on adaption, refer to Section 27: Grid Adaption in theFLUENT 6.2 User’s Guide.

(e) Click Mark.

FLUENT creates a pressure gradient adaption register. The FLUENT consolewindow reports that around 150 cells were marked for refinement and no cellswere marked for coarsening.

(f) View the cells marked for pressure gradient adaption (Figure 8).

i. Click Manage....

The Manage Adaption Registers panel is displayed.

ii. Under Registers, select gradient-r0.

iii. Click Display.

You can modify the display of the adaption register by setting the respectiveoptions in the Adaption Display Options panel. You can open this panel byclicking on the Options... button in the Manage Adaption Registers panel.

Adaption Markings (gradient-r0)FLUENT 6.2 (3d, segregated, lam)

ZY

X

Figure 8: Cells Marked for Pressure Gradient Adaption (Approx. 150 Cells Marked)

Figure 8 shows the cells marked for pressure gradient adaption. These cells areconcentrated on the front face of the block, where the static pressure is changingabruptly due to stagnation and change in the direction of the air flow.


http://www.fluentusers.com/fluent/doc/ori/html/ug/node964.htm


2. Create a velocity gradient adaption register.

(a) In the Gradient Adaption panel, select Velocity... and Velocity Magnitude in theGradients of drop-down lists.

(b) Click Compute.


(c) Enter a value of 5.7e-5 for Refine Threshold (10% of the maximum value).

(d) Click Mark.

FLUENT creates a velocity gradient adaption register. The FLUENT console win-dow reports that around 1550 cells were marked for refinement.

(e) View the cells marked for velocity gradient adaption (Figure 9).

ZY

X


Figure 9: Cells Marked for Velocity Gradient Adaption (Approx. 1550 Cells Marked)

3. Create a temperature gradient adaption register.

(a) In the Gradient Adaption panel, select Temperature... and Static Temperature inthe Gradients of drop-down lists.

(b) Click Compute.


(c) Enter a value of 0.00977 for Refine Threshold (10% of the maximum value).

(d) Click Mark.

FLUENT creates a temperature gradient adaption register. The FLUENT consolewindow reports that around 380 cells were marked for refinement.

(e) View the cells marked for temperature gradient adaption (Figure 10).



ZY

X


Figure 10: Cells Marked for Temperature Gradient Adaption (Approx. 380 Cells Marked)

Figure 10 shows the cells marked for temperature gradient adaption. Thesecells are concentrated mainly near the block (where the temperature is changingrapidly).

4. Create a region adaption register.

Adapt −→Region...

The Region Adaption panel is displayed.

(a) Enter the Input Coordinates as follows to select the region for adaption.

Min (in) Max (in)

X 2.75 5.0Y 0.1 0.4Z 0 0.5

(b) Click Mark.

The FLUENT console window reports that around 1450 cells were marked forrefinement.

(c) View the cells marked for region adaption (Figure 11).



ZY

X

Adaption Markings (hexahedron-r3)FLUENT 6.2 (3d, segregated, lam)

Figure 11: Cells Marked for Region Adaption (Approx. 1450 Cells Marked)

Figure 11 shows the cells marked for region adaption. Region adaption allowsyou to specify a bounding box that is used to select cells for adaption. In thiscase, the cells behind the block are selected for refinement.

5. Perform a Boolean addition of the pressure gradient, velocity gradient, temperaturegradient, and region adaption registers.

(a) In the Manage Adaption Registers panel, select the registers gradient-r0, gradient-r1, gradient-r2, and hexahedron-r3.

(b) Click Combine.

A fifth register (combination-r4) is created. This register represents the Booleanaddition of the pressure gradient, velocity gradient, temperature gradient, andregion adaption registers. The FLUENT console window reports that a total ofaround 3100 cells are marked as a result of combining the four adaption criteria.

(c) View the cells marked for adaption (Figure 12).



ZY

X

Adaption Markings (combination-r4)FLUENT 6.2 (3d, segregated, lam)

Figure 12: Combination of Pressure Gradient, Velocity Gradient, Temperature Gradient,and Region Adaption Registers (Approx. 3100 Cells Marked)

6. Adapt the mesh using the combination register, combination-r4.

(a) In the Manage Adaption Registers panel, select combination-r4.

(b) Click Adapt.

A Question dialog box is displayed asking for confirmation of Hanging-node mode.

(c) Click Yes to confirm Hanging-node mode.

FLUENT indicates that the cell count has increased to around 39220 as a resultof mesh adaption.

Step 10: Solution

1. Request an additional 400 iterations (Figures 13 and 14).

2. Save the case and data files (chip3d-adapt1.cas.gz and chip3d-adapt1.dat.gz).



ZY

X


Iterations500450400350300250200150100500

1e+00

1e-01

1e-02

1e-03

1e-04

1e-05

1e-06

1e-07

1e-08


Figure 13: Residual Plot After First Mesh Adaption

Z

Y

X


Iteration

(k)ValuesVertex

Surfaceof

Average

500450400350300250200150100500

410.0000

400.0000

390.0000

380.0000

370.0000

360.0000

350.0000

340.0000

330.0000

320.0000

monitor-1Monitors

Figure 14: Convergence History of Static Temperature at Monitor Point After First MeshAdaption



Step 11: Postprocessing

In this step, you will determine whether the solution is independent of the mesh, or iffurther mesh adaption is required. This is determined by comparing the predicted profiles oftemperature, velocity, and wall shear stress for the refined mesh with those obtained for arelatively coarse mesh. Hence, you can evaluate how sensitive the solution is, with respectto changes in mesh size.

1. Compare the temperature profiles obtained for the original and the adapted meshes.

Plot −→XY Plot...



(c) Select Temperature... and Static Temperature in the Y Axis Function drop-downlists.


(e) Load the file, temp-0.xy.

i. Click Load File....

The Select File panel is displayed.

ii. Under Files, select temp-0.xy and click OK.

(f) Under File Data, select Static Temperature.

(g) Click Plot (Figure 15).

2. Compare the velocity profiles obtained for the original and the adapted meshes.



(c) Select Velocity... and Velocity Magnitude in the Y Axis Function drop-down lists.


(e) Load the file, velocity-0.xy.

(f) Under File Data, select Velocity Magnitude.

Remember to deselect any previous selections under File Data.




ZY

X


Position (in)

(k)Temperature

Static

0.50.40.30.20.10

3.55e+02

3.50e+02

3.45e+02

3.40e+02

3.35e+02

3.30e+02

First AdaptionOriginal Mesh

Figure 15: Comparison of Temperature Profiles After First Mesh Adaption

Figure 15 indicates that the temperature distribution has changed considerably after adapting themesh. This is because the original mesh was too coarse to resolve temperature gradients and thus,predict accurate heat transfer. Based on this comparison, you can conclude that the solution isdependent on the mesh and that a further mesh adaption should be performed.

ZY

X


Position (in)

(m/s)Magnitude

Velocity

0.50.40.30.20.10

4.50e-01

4.00e-01

3.50e-01

3.00e-01

2.50e-01

2.00e-01

1.50e-01

1.00e-01

5.00e-02

0.00e+00


Figure 16: Comparison of Velocity Magnitude Profiles After First Mesh Adaption

Figure 16 indicates that the velocity distribution appears to be approaching mesh independence. How-ever, based on the comparison of temperature profiles, you have already determined that anotheradaption should be performed.



3. Compare the wall shear stress profiles obtained for the original and the adaptedmeshes.

(a) Under Options, disable Node Values.


(c) Select Wall Fluxes... and X-Wall Shear Stress in the Y Axis Function drop-downlists.

(d) Under Surfaces, select line-xwss.

(e) Load the file, xwss-0.xy.

(f) Under File Data, select X-Wall Shear Stress.

Remember to deselect any previous selections under File Data.


ZY

X


Position (in)

(pascal)StressShear

X-Wall

4.84.64.44.243.83.63.43.232.82.6

2.50e-03

2.00e-03

1.50e-03

1.00e-03

5.00e-04

0.00e+00

-5.00e-04

-1.00e-03

-1.50e-03

-2.00e-03


Figure 17: Comparison of X-Wall Shear Stress Profiles After First Mesh Adaption

Figure 17 indicates that the wall shear stress distribution is essentially meshindependent. However, you have already determined that another adaption shouldbe performed based on the comparison of temperature profiles.



Step 12: Further Mesh Adaption and Postprocessing

For most cases, one or two mesh adaptions are sufficient to obtain a mesh independentsolution. So far, you performed one adaption in an attempt to improve the solution andmigrate toward a solution that is independent of the mesh. However, another adaptionshould be performed to investigate if considerable changes are seen in the solution (as seenin Figure 15) after mesh refinement.

When performing successive mesh adaptions, the adaption threshold values should not bechanged. If they are changed (usually the tendency is to reduce them), the solution accuracywill not meet the criteria set forth by specifying the threshold values.

The second level of mesh adaption is not shown explicitly. The results are presented andare briefly discussed.

• Figure 18 shows the cells marked for the second pressure gradient adaption.

• Figure 19 shows the cells marked for the second velocity gradient adaption.

• Figure 20 shows the cells marked for the second temperature gradient adaption.

• Figure 21 shows the cells marked for the second region adaption.

• Figure 22 shows the cells marked for the second mesh adaption (combination of pres-sure gradient, velocity gradient, temperature gradient, and region adaption registers).

• Figures 23 and 24 show the residual plot and convergence history of temperature atthe monitor point respectively.

• Figure 25 shows the predicted cross-stream temperature profiles for the three meshrefinement levels. As the mesh is made successively finer, the predicted profile ap-proaches a shape that is independent of the mesh.

• Figure 26 shows the predicted velocity profiles for the three mesh refinement levels.The velocity profile approaches a shape that is independent of the mesh.

• Figure 27 shows the predicted wall shear stress profiles for the three mesh refine-ment levels. The wall shear stress exhibits mesh independence upon successive meshrefinement.



ZY

X


Figure 18: Cells Marked for Second Pressure Gradient Adaption (Approx. 210 Cells)

ZY

X


Figure 19: Cells Marked for Second Velocity Gradient Adaption (Approx. 690 Cells)



ZY

X


Figure 20: Cells Marked for Second Temperature Gradient Adaption (Approx. 250 Cells)

ZY

X

Adaption Markings (hexahedron-r3)FLUENT 6.2 (3d, segregated, lam)

Figure 21: Cells Marked for Second Region Adaption (Approx. 11300 Cells)



ZY

X


Figure 22: Cells Marked for Second Mesh Adaption (Combination of Pressure Gradient,Velocity Gradient, Temperature Gradient, and Region Adaption Registers, Approx. 12220Cells)

ZY

X


Iterations8007006005004003002001000

1e+00

1e-01

1e-02

1e-03

1e-04

1e-05

1e-06

1e-07

1e-08


Figure 23: Residual Plot After Second Mesh Adaption



Z

Y

X


Iteration

(k)ValuesVertex

Surfaceof

Average

8007006005004003002001000

410.0000

400.0000

390.0000

380.0000

370.0000

360.0000

350.0000

340.0000

330.0000

320.0000

monitor-1Monitors

Figure 24: Convergence History of Static Temperature at Monitor Point After Second MeshAdaption

ZY

X


Position (in)

(k)Temperature

Static

0.50.40.30.20.10

3.55e+02

3.50e+02

3.45e+02

3.40e+02

3.35e+02

3.30e+02

Second AdaptionFirst AdaptionOriginal Mesh

Figure 25: Comparison of Temperature Profiles After Two Mesh Adaptions



ZY

X


Position (in)

(m/s)Magnitude

Velocity

0.50.40.30.20.10

4.50e-01

4.00e-01

3.50e-01

3.00e-01

2.50e-01

2.00e-01

1.50e-01

1.00e-01

5.00e-02

0.00e+00


Figure 26: Comparison of Velocity Profiles After Two Mesh Adaptions

ZY

X


Position (in)

(pascal)StressShear

X-Wall

54.754.54.2543.753.53.2532.752.5

3.00e-03

2.50e-03

2.00e-03

1.50e-03

1.00e-03

5.00e-04

0.00e+00

-5.00e-04

-1.00e-03

-1.50e-03

-2.00e-03


Figure 27: Comparison of X-Wall Shear Stress Profiles After Two Mesh Adaptions



Step 13: Final Mesh Adaption and Postprocessing

You have performed two mesh adaptions in an attempt to improve the solution and obtaina mesh independent solution. However, the results (see Figure 25) still indicate meshdependence and hence, a third mesh adaption is required.

When performing successive mesh adaptions, the adaption threshold values should not bechanged. If they are changed (usually the tendency is to reduce them), the solution accuracywill not meet the criteria set forth by specifying the threshold values.

The third level of mesh adaption is not shown explicitly. The results are presented and arebriefly discussed.

Although this step is necessary to obtain a fully mesh independent solution, performing this!step severely increases the cell count. Hence, the calculations take a significant amount oftime. If you wish to examine the results more thoroughly, the files chip3d-adapt3.cas.gzand chip3d-adapt3.dat.gz are provided.

• Figure 28 shows the cells marked for the third mesh adaption.

• Figures 29 and 30 show the residual plot and convergence history of temperature atthe monitor point after the mesh adaption.

• Figure 31 shows the predicted cross-stream temperature profiles for the four meshesconsidered. From this plot, you can see that as the mesh is refined, the temperatureprofile converges on a single profile. Thus, the temperature field is judged to beindependent of the mesh.

• Figure 32 shows the predicted cross-stream velocity profiles for the four meshes con-sidered. The velocity demonstrates similar behavior as the temperature profile uponsuccessive mesh refinements. Based on this plot, the velocity is judged to be indepen-dent of the mesh.

• Figure 33 shows that the wall shear stress profiles do not change much upon successivemesh refinements.

If this were the only variable checked, you might have incorrectly concluded that thesolution is mesh independent.

• When the solution does not change significantly between successive mesh adaptions,the solution is judged to be independent of the mesh and further adaption is notnecessary.



ZY

X


Figure 28: Cells Marked for Third Mesh Adaption (Combination of Pressure Gradient,Velocity Gradient, Temperature Gradient, and Region Adaption Registers, Approx. 90500Cells)

ZY

X


Iterations1400120010008006004002000

1e+00

1e-01

1e-02

1e-03

1e-04

1e-05

1e-06

1e-07

1e-08


Figure 29: Residual Plot After Third Mesh Adaption



Z

Y

X


Iteration

(k)ValuesVertex

Surfaceof

Average

1400120010008006004002000

410.0000

400.0000

390.0000

380.0000

370.0000

360.0000

350.0000

340.0000

330.0000

320.0000

monitor-1Monitors

Figure 30: Convergence History of Static Temperature at Monitor Point After Third MeshAdaption

ZY

X


Position (in)

(k)Temperature

Static

0.50.40.30.20.10

3.55e+02

3.50e+02

3.45e+02

3.40e+02

3.35e+02

3.30e+02

Third AdaptionSecond AdaptionFirst AdaptionOriginal Mesh

Figure 31: Comparison of Temperature Profiles After Three Mesh Adaptions



ZY

X


Position (in)

(m/s)Magnitude

Velocity

0.50.40.30.20.10

4.50e-01

4.00e-01

3.50e-01

3.00e-01

2.50e-01

2.00e-01

1.50e-01

1.00e-01

5.00e-02

0.00e+00


Figure 32: Comparison of Velocity Profiles After Three Mesh Adaptions

ZY

X


Position (in)

(pascal)StressShear

X-Wall

54.754.54.2543.753.53.2532.752.5

3.00e-03

2.50e-03

2.00e-03

1.50e-03

1.00e-03

5.00e-04

0.00e+00

-5.00e-04

-1.00e-03

-1.50e-03

-2.00e-03


Figure 33: Comparison of X-Wall Shear Stress Profiles After Three Mesh Adaptions



Summary

Laminar air flow around an electronic component (chip) was simulated using FLUENT. Asource term was enabled in order to simulate the heat generated by the chip. Conjugateheat transfer was investigated in the form of the heating of air as it flows around the chip,conduction in the chip itself, and conduction/convection in the board. Three levels ofsolution-based mesh adaption (based on gradients of pressure, velocity, and temperature)were performed. After the third adaption, it was determined that the solution is independentof the mesh.


Heat Transfer

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