Radiation Heat Transfer

Radiation Heat Transfer
Chapter 8 Radiation Heat Transfer

Chapter Overview General Characteristics of Radiation Radiation Theory
ANSYS Solution Methodology Methods of Modeling Radiation in ANSYS Surface Effect Elements Link Elements Radiation Matrix Utility Radiosity Solver Method Example Using the Radiation Matrix Utility - Thermal Analysis of a Heat Sink Hidden Method Solution Non-Hidden Method Solution Inventory #001445 March 15, 2001 8-2

General Characteristics
Radiation Heat Transfer is a mode of energy transfer where the energy is transported via electromagnetic waves. Thermal radiation covers the portion of the electromagnetic spectrum from 0.1 to 100 mm. This includes a portion of the ultraviolet spectrum, all visible and all infrared wavelengths. Unlike other modes of heat transfer which require a conducting medium, radiation is most efficient in a vacuum (e.g., outer space). For semitransparent bodies (e.g., glass), radiation is a volumetric phenomenon since emissions can escape from within bodies. For opaque bodies, radiation is essentially a surface phenomena since nearly all internal emissions are absorbed within the body. Inventory #001445 March 15, 2001 8-3

General Characteristics (continued)
ANSYS is capable of simulating radiation between opaque bodies, so we will limit our discussion to radiation as a surface phenomenon. Radiation heat transfer between two surfaces is proportional to the difference of their surface absolute temperatures raised to the fourth power: Consequently, radiation analysis is nonlinear and requires an iterative solution. Inventory #001445 March 15, 2001 8-4

Surface Emission and Irradiation
Real surfaces emit radiation to other surfaces (emission) and receive emissions from other surfaces (irradiation). When we perform an analysis involving radiation, we are concerned with the net effect of emission and irradiation. Real surfaces emit and receive radiation at various wavelengths (spectral distribution) and preferentially with respect to direction (directional distribution). These characteristics also change with temperature. Wavelength Emissive Power Direction Distribution Inventory #001445 March 15, 2001 8-5

Diffuse or Spectral Surfaces can be idealized as either diffuse or spectral reflectors. A diffuse reflector will reflect radiation uniformly with regard to direction, regardless of the orientation of the incident radiation: Diffuse Surface A spectral surface will reflect incident radiation in a specific direction much like a mirror would reflect a beam of light: Spectral Surface q Inventory #001445 March 15, 2001 8-6

Diffuse or Spectral (continued)
Likewise, surfaces can be idealized as either diffuse or spectral emitters. No real surface is truly diffuse or spectral. Surfaces with dull finishes tend towards diffuse and highly polished surfaces tend toward spectral. To simplify calculations, properties describing the radiative behavior of surfaces can be averaged across all wavelengths and directions. Only averaged properties (designated total, hemispherical) will be referred to in the following discussion. Consequently, there will effectively be no differentiation between diffuse and spectral surfaces. Inventory #001445 March 15, 2001 8-7

Absorption and Reflection
For an opaque medium subject to irradiation of a given intensity, G , some of the incident radiation energy will be reflected away from the surface and some will be absorbed by the medium: G Incident radiation Gref Energy reflected Gabs Energy absorbed The total, hemispherical absorptivity, a, of a surface relates its tendency to absorb incident radiation. The total, hemispherical reflectivity, r, of a surface relates its tendency to reflect incident radiation. Inventory #001445 March 15, 2001 8-8

Emissivity and Emissive Power
Likewise, the total, hemispherical emissivity, e, of a surface relates its ability to emit thermal radiation energy in all directions at all wavelengths. This is a dimensionless quantity. The total power (in flux units) emitted by a surface across all wavelengths and directions is given by the Stefan-Boltzmann Law: NOTE: Absolute temperature in English is expressed in degrees Rankine (°R) which is offset from degrees Fahrenheit (°F) by 460°. In SI units, the absolute temperature is expressed in degrees Kelvin (°K) , which is offset from degrees Celsius (°C) by 273°. The offset temperature may be defined with the TOFFST command. Inventory #001445 March 15, 2001 8-9

Radiosity The Total Radiosity, J, is expressed in flux units and simply represents a combination of the energy emitted and energy reflected from a surface (i.e., total energy leaving surface): G Incident radiation Gref Energy reflected Ge Emissive Power J Radiosity Since ANSYS does not directly account for surface reflectivity, the radiosity and emissivity are assumed to be equivalent (E=J). Inventory #001445 March 15, 2001 8-10

Blackbodies A blackbody is an idealized surface that is used to characterize real surfaces by comparison. Here are a list of characteristics of blackbodies: blackbodies absorb all incident radiation (i.e., no reflection), regardless of wavelength and direction. blackbodies are perfect emitters. For a given wavelength and temperature, no surface can emit more energy than a black body. A blackbody is a perfectly diffuse emitter; emissions are uniform in all directions. Consequently, for a blackbody: aB = eB = 1. Inventory #001445 March 15, 2001 8-11

Gray Surfaces Consequently, for a gray body (e < 1) always.
Real surfaces are called gray surfaces because they do not behave as blackbodies. The total, hemispherical emissivity of a gray surface at temperature T is defined as follows: Consequently, for a gray body (e < 1) always. Inventory #001445 March 15, 2001 8-12

ANSYS and Radiation Summary of important assumptions regarding ANSYS implementation of radiation: ANSYS considers radiation to be a surface phenomenon and is therefore suitable for modeling opaque surfaces. ANSYS does not directly account for reflectivity of surfaces. It effectively assumes that the absorptivity and emissivity of a surface are equal (a = e) . Consequently, only the emissivity property needs to be defined in an ANSYS radiation analysis. ANSYS does not automatically account for the directional dependence of emissivity, nor does it allow emissivity to be defined with wavelength dependence. Emissivity can be defined as a function of temperature for some elements. Any medium which separates radiating surfaces is considered to be non-participating (i.e., it does not absorb or emit energy) with regard to computation of the radiation energy exchange. Inventory #001445 March 15, 2001 8-13

Multiple Surfaces Up to this point we have spoken of only individual radiating surfaces. However, when studying real problems, we will need to consider the interaction of multiple radiating surfaces. The more surfaces we consider, the messier our problem gets: Inventory #001445 March 15, 2001 8-14

Form Factor Before we can compute the radiant heat energy exchange between surfaces, we need to introduce the concept of Form Factor (a.k.a. view factor, shape factor, configuration factor). A form factor is defined with reference to two surfaces (i and j) which radiate to each other. It is the fraction of the emitted radiation from one surface (i) which is incident upon another surface (j): Inventory #001445 March 15, 2001 8-15

Form Factor (continued)
The form factor for two surfaces is a function of area, orientation, and distance. Inventory #001445 March 15, 2001 8-16

Form Factor (continued)
For a system of n surfaces, a form factor matrix can be assembled containing n2 terms: All of the energy emitted from any one surface must be conserved: Also, reciprocity requires: Inventory #001445 March 15, 2001 8-17

Radiation Heat Transfer Between Two Surfaces
To compute the heat transfer from one surface (i) to another (j), we use the reciprocity relationship and the Stefan-Boltzmann Law to write: The equation can be rewritten and terms factored as follows: Since K’ is a function of T3, the equation cannot be solved directly but instead requires an iterative solution. Inventory #001445 March 15, 2001 8-18

ANSYS Solution Method ANSYS employs a similar process to solve multiple surface radiation problems in matrix form: Developing the system of matrix equations for multiple surface problems requires a more involved procedure than the simplistic factoring approach presented on the previous slide. Radiation is a highly nonlinear phenomenon requiring use of the Newton-Raphson iterative solution procedure. See Chapter 4 for more information about nonlinear analysis techniques. Inventory #001445 March 15, 2001 8-19

Modeling Radiation in ANSYS
There are four methods available in ANSYS to model radiation effects: Surface Effect Elements SURF151/SURF152 elements; used for radiation between a surface and a point or between a surface and the atmosphere. Radiation Link Element LINK31; used for radiation between pairs of nodes. Radiation Matrix (superelement) used for generalized radiation problems involving two or more surfaces. Radiosity Solver Method used for 2-d and large 3d radiation problems (available for all thermal element types) Inventory #001445 March 15, 2001 8-20

Modeling Radiation Using Surface Effect Elements
Used to model radiation between a surface and a point or between a surface and the atmosphere. The form factors must be known, but usually are not known. SURF151 is used for 2D surfaces and SURF152 for 3D surfaces. Inventory #001445 March 15, 2001 8-21

Boundary Condition, SURF151 Overlay SURF151 elements on the model where radiating surfaces exist. Specify an extra node away from the base SURF151 elements. (Note: The extra node may belong to an element on another radiation surface in the model or may be isolated, with an imposed temperature constraint.) Material property: Real constants: Inventory #001445 March 15, 2001 8-22

SURF151 element options 1. Set Extra node for radiation to Include (K5). 2. Set Radiation form fact calculation (K9). Inventory #001445 March 15, 2001 8-23

3D Boundary Condition, SURF152 Overlay SURF152 elements on the model where radiating surfaces exist. Specify an extra node away from the base SURF152 elements. (Note: The extra node may belong to an element on another radiation surface in the model or may be isolated, with an imposed temperature constraint.) Material property: Real constants: Inventory #001445 March 15, 2001 8-24

SURF152 element options 1. Include extra node for radiation (K5). 2. Request form fact calculation if extra node is point source. If form factor is known, input via real constant (K9). If requested, ANSYS calculates form factor for each integration point to be cos(a). Inventory #001445 March 15, 2001 8-25

Modeling Radiation Using Link Elements
Radiation Between Two Nodes The LINK31 element may be used for simple problems involving radiation between two points or several pairs of points. Use LINK31 if the form factors are known. Inventory #001445 March 15, 2001 8-26

Modeling Radiation Using Link Elements
Radiation Link Element, LINK31 Location of remote node can be arbitrary or connected to another element. Material Property: Real Constant: A temperature-dependent emissivity may be specified for this element. Inventory #001445 March 15, 2001 8-27

Modeling Radiation Using the Radiation Matrix Utility
Use when the form factors are not known. Generates the form factors, Fij, for arbitrarily oriented surfaces. Used for radiation interchanged between surfaces. May be used for a closed or open system. This method can be very computationally intensive and may require a relatively large amount of CPU time and disk space (particularly when using the HIDDEN method). Does not allow temperature-dependent emissivities. Inventory #001445 March 15, 2001 8-28

Implements the radiant energy interchange equation: Inventory #001445 March 15, 2001 8-29

The Radiation Matrix Utility calculates a matrix, [Kts], which represents radiation effects between two or more surfaces. It includes calculated form factors for the various surfaces involved: The matrix is then used as a superelement (MATRIX50) in a thermal analysis to calculate the temperature solution. Inventory #001445 March 15, 2001 8-30

During solution, the equations are linearized (see Slides 8-17,18) for iterative solution with a linear equation solver: While [K’] is a function of {T}, [Kts] is not. Therefore, the radiation matrix does not need to be recomputed each iteration. Unfortunately, this means that temperature-dependent emissivity is not permitted. Inventory #001445 March 15, 2001 8-31

There are three main steps involved in using the radiation matrix utility to model radiation. They are: 1. Define the radiating surface(s). 2. Generate the radiation matrix. 3. Use the radiation matrix in the thermal analysis. Inventory #001445 March 15, 2001 8-32

Step 1: Defining the Radiating Surfaces 1. Build the model to be used for the thermal analysis. 2. On all radiating surfaces, overlay a mesh of: LINK32 elements on 2D radiating surfaces SHELL57 elements on 3D radiating surfaces. Important Notes: The overlaying LINK32 or SHELL57 mesh should match the underlying solid element in geometry (2D/3D) and order (linear-mesh of the model). If different emissivities exist on the radiation surfaces, be sure to assign different material properties to the appropriate surfaces. Inventory #001445 March 15, 2001 8-33

Important Notes (continued): The overlaying mesh must have the proper orientation. For LINK32 elements, the positive Y-direction of the element coordinate system must point in the viewing direction (direction of radiation). For SHELL57 elements, the positive Z-direction of the element coordinate system must be facing the viewing direction (direction of radiation). Element orientation depends upon the method of creation. For example, if lines are meshed with LINK32 the orientation comes from the direction of the line being meshed. Turn on plotting on element coordinate system symbols to check orientation graphically. Inventory #001445 March 15, 2001 8-34

Step 1: Defining the Radiating Surfaces (continued) 3. Define a node (space node) which will absorb any radiant energy not received by the other surfaces. The location of the space node is arbitrary. A space node is required for an open system. For a closed system a space node is not recommended The space node may belong to an element or may be isolated with an imposed temperature constraint. Inventory #001445 March 15, 2001 8-35

Step 2: Generating the Radiation Matrix Enter the radiation matrix utility by selecting: Main Menu>>Radiation Opt Select all the nodes and elements making up the radiating surfaces(s) including the space node (if defined). Inventory #001445 March 15, 2001 8-36

Step 2: Generating the Radiation Matrix (continued) 1. Define the emissivity of the radiating surface(s). The emissivity value defaults to 1. Inventory #001445 March 15, 2001 8-37

2. Define the Stefan-Boltzmann constant value for the proper units being used in the thermal analysis (default is 0.119e-10 BTU/hr • in² • °R4). 3. Specify whether the analysis is 2D, 3D axisymmetric or 3D (default is 3D). 4. Specify the space node for radiant energy not absorbed by other surfaces. Inventory #001445 March 15, 2001 8-38

5. Specify whether the viewing procedure uses the HIDDEN or NON- HIDDEN method (defaults to HIDDEN). The HIDDEN method should be used if any of the radiating surfaces are blocked in the direct line of vision of other surfaces. The NON-HIDDEN method makes all surfaces visible to each other. 6. Set the number of rays on the HIDDEN method. Increasing the number of rays increases accuracy of the form factor calculations (default is 20). Inventory #001445 March 15, 2001 8-39

7. Turn on the print key (if desired) to see form factors printed for verification purposes. 8. Write out the radiation matrix to filename.sub to be used as a MATRIX50 superelement in the thermal analysis phase. Inventory #001445 March 15, 2001 8-40

9. Re-select all of the other nodes and elements in the thermal model. 10. The radiation matrix is now available to be used as a superelement in the thermal analysis. Inventory #001445 March 15, 2001 8-41

Step 3: Using the Radiation Matrix 1. Re-enter the preprocessor. 2. Define a new element type as MATRIX50. Change keyoption K1 for a radiation substructure. Inventory #001445 March 15, 2001 8-42

Step 3: Using the Radiation Matrix (continued) 3. Select the superelement as the active element type for meshing. (Define attributes). 4. Define the superelement by specifying the filename written out in the radiation matrix utility. 5. Delete or un-select the elements making up the overlaid mesh on the radiating surface(s). 6. Define the temperature offset for the absolute scale. 7. Enter Solution and define the thermal boundary conditions on the space node and run the solution. Inventory #001445 March 15, 2001 8-43

Modeling Radiation Using the Radiosity Solver Method
Radiation applied as surface effect using SFx family of commands Generates form factors, Fij, for arbitrarily oriented surfaces. May be used for a closed or open system (space node or space temperature options). Always uses the HIDDEN method. Allows temperature-dependent emissivities. Inventory #001445 March 15, 2001 8-44

Procedure: Define radiating surfaces Specify radiosity options (if applicable) Specify open enclosure options (if applicable) Specify offset temperature and Stefan-Boltzmann constant Specify view factor options (if applicable) Define load options Inventory #001445 March 15, 2001 8-45

Defining Radiating Surfaces SFx commands from: Main_Menu>Solution>Apply>-Thermal-Radiation> Pick desired areas, nodes or elements Inventory #001445 March 15, 2001 8-46

Specify emissivity and enclosure number. Inventory #001445 March 15, 2001 8-47

Radiosity Solver Options RADOPT, FLUXRELX, FLUXTOL, SOLVER, MAXITER, TOLER, OVERRLEX There are 2 solvers available when using the radiosity method, Iterative (default) and Direct solvers. These solvers are independent of any of ANSYS solvers of the same name (i.e. sparse direct, PCG, etc.). Iterative solver is preferred. Direct solver is robust but costly for large problems (0=iterative, 1=direct). If iterative solver is converging but runs out of iterations, direct solver is automatically activated (default is 1000 iterations). Flux relaxation (FLUXRELX), can be increased if the problem is NOT radiation dominant, to speed up the solution (default = 0.1) Flux tolerance (FLUXTOL) affects radiation solution tolerance. Decreasing this value increases accuracy (default = 0.1). May require more iterations (MAXITER) if greater accuracy is desired. Inventory #001445 March 15, 2001 8-48

Radiosity Solver Options (continued) TOLER value relates to the iterative solver tolerance. Default is 0.1 which is fine for most problems. Decreasing this value increases the solver accuracy. OVERRLEX controls over relaxation in the iterative solver. Increasing this value can speed up solution on very large problems by reducing the number of iterations required to converge. Try increasing values from 0.1 (default) up to 1 for very large problems. Inventory #001445 March 15, 2001 8-49

Emissivity: Can be constant or temperature dependent. To specify temperature dependent emissivity, reference a material table number using a negative number. For example using the SF command where a material table N is defined (i.e. MP, N, EMIS, values), use: SF, surface_nodes, RDSF, -N Inventory #001445 March 15, 2001 8-50

Enclosure Numbers Sets of surfaces identified by common enclosure numbers are assumed to “see” one another (i.e. view factors are calculated among the members of that set). Multiple enclosure numbers may be defined within the same model. Note: The term “enclosure” is used for surface identification only. It has no reference to open or closed radiating systems. Thus, open radiating systems are identified using enclosure numbers in the same way as closed systems. Inventory #001445 March 15, 2001 8-51

Open vs. Closed Enclosure systems Closed systems do not use or require space nodes or temperatures. The presence of an open system is determined by the view factor calculation and requires the definition of a space temperature. This can be done using a space node or by defining a space temperature. Space temperature defined without using space node: SPCTEMP, enclosure number, temperature Space temperature defined using space node: SPCNOD, enclosure number, node number Note: Each open enclosure is associated with one space node or temperature. Multiple enclosure, open systems may employ multiple space node or temperature definitions, however each enclosure must be associated with only one. Inventory #001445 March 15, 2001 8-52

View factor considerations: VFOPT, opt controls when and if view factors are written (the default is jobname.vf in the working directory). VFOPT, off (default), computes and writes view factors only upon the first SOLVE. Subsequent solutions re-use the original view factors VFOPT, new computes new view factors for each load step. This option is useful for situations involving changing geometry (NLGEOM, ON) or radiating surfaces or sources that move. HEMIOPT command (radiation options) controls the resolution of the view factor calculation. The default value is 10 which is good for most problems. May be advantageous to increase HEMIOPT to when the underlying elements are very coarse. Inventory #001445 March 15, 2001 8-53

Running a “quasi-static” radiation problem (QSOPT, ON) Solution method is used for problems where radiation is the dominant form of heat transfer and/or the model is unconstrained (no temp DOF fixed). Basically, this is a transient solution (ANTYPE, TRANS) which is run to steady state. No need to issue the TIME command. QSOPT, ON procedure: Make sure density and specific heat are specified (these values need not be exact but should be representative) ANTYPE, TRANS QSOPT, ON If TIME is not specified (it need not be) it defaults to 1 If steady state is not reached, time is doubled and solution continues Inventory #001445 March 15, 2001 8-54

QSOPT, ON (additional notes): Time step sizes controlled by AUTOTS If user specifies time, solution proceeds until this time is reached. If the solution has not reached steady state, the user’s time is doubled and the solution continues. Can be activated in the final load step of multiple load step problems to run solution to steady state (note: set KBC, 1 to step final loads). OPNCONTROL is used to test for steady state. The default behavior compares the last 3 solutions and considers temperature changes of 0.1 or less as converged. Increasing the number of equilibrium iterations can help avoid unnecessary bisection during solution (NEQIT). Inventory #001445 March 15, 2001 8-55

QSOPT, ON (about time): As mentioned, density () and specific heat (c) should be specified when performing a quasi-static analysis. If conditions at steady state are the only results of interest, these material property values are arbitrary. A higher “diffusivity” (diffusivity = k/( * c)) will generally decrease solution times. Thus, adjusting density and specific heat to increase this value can be helpful. NOTE: when using arbitrary material properties to optimize quasi-static solutions, time is not representative of reality. The steady state solution is, however, valid. If realistic material properties for density and specific heat are used, the time when steady state is reached (as well as intermediate times) are valid. Inventory #001445 March 15, 2001 8-56

ANSYS input files for Case 2 and Case 3 are provided in Appendix B
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Problem Description: Case 1 - The base of an aluminum heat sink (1/2 symmetry used) is subjected to a heat flux load. Fins are cooled via convection to air. Case 2 - Radiation effects are added to Case 1 by using a Radiation Matrix created using the hidden method. Case 3 - Radiation effects are added to Case 1 by using a Radiation Matrix created using the non-hidden method. ANSYS input files for Case 2 and Case 3 are provided in Appendix B Inventory #001445 March 15, 2001 8-57

Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility
Model Dimensions: Inventory #001445 March 15, 2001 8-58

Heat Flux on Base Surface
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Guidelines: The heat sink material is aluminum, with a constant KXX = 8.5 BTU/hr-in-°F. Use BIN units to complete the analysis. Use a constant value of h for all fin convection surfaces. Apply convection using SURF151 elements with the extra node option. End surfaces of sink are adiabatic. Adiabatic Heat Flux on Base Surface Note: Not all menus and steps are detailed in the following pages. Inventory #001445 March 15, 2001 8-59

Heat flux into the base = 17 BTU/hr-in2.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Thermal Loads: Heat flux into the base = 17 BTU/hr-in2. Air temperature above the heat sink is 90 °F. Film coefficient on fin surfaces is 0.01 BTU/hr-in2-°F. Surfaces with no loads are adiabatic. Additional Assumptions: This is an open system, so radiation not absorbed by fin surfaces will go to the space node. Radiation occurs only along the fin surfaces (not adiabatic surfaces). Inventory #001445 March 15, 2001 8-60

base = .150, hgt = 1.0, ttop = 0.05, tbot = .150, fspc = .4
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Basic Procedure CASE 1- Thermal Analysis of Heat Sink (no radiation). Define scalar parameters as follows: base = .150, hgt = 1.0, ttop = 0.05, tbot = .150, fspc = .4 Manually define eight keypoints and three areas. Reflect the geometry as required to generate the model. Mesh the model using quad PLANE55 elements. Mesh the exterior fin surfaces using SURF151 elements with the extra node option. Apply heat flux, convection and temperature loads. Run an initial solution without radiation effects. Note: Use of scalar parameters is not required. It is demonstrated only as one of many possible methods of generating geometry Inventory #001445 March 15, 2001 8-61

Define element types PLANE55 and SURF151, set keyoptions.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Define element types PLANE55 and SURF151, set keyoptions. Inventory #001445 March 15, 2001 8-62

Define material properties; only KXX is required.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Define material properties; only KXX is required. Inventory #001445 March 15, 2001 8-63

Define parameters and use to create keypoint geometry.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Define parameters and use to create keypoint geometry. Inventory #001445 March 15, 2001 8-64

Plot of keypoints. The eight keypoints created can be used for generation of three areas, and then area pattern. Inventory #001445 March 15, 2001 8-65

Areas generated using initial set of keypoints.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Areas generated using initial set of keypoints. Inventory #001445 March 15, 2001 8-66

Areas after first reflection operation.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Areas after first reflection operation. Inventory #001445 March 15, 2001 8-67

Areas after final reflection operation, plotted with colors and numbers turned on. Inventory #001445 March 15, 2001 8-68

Element plot: PLANE55 quad shaped elements.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Element plot: PLANE55 quad shaped elements. Note: A global element size of inches was used. Inventory #001445 March 15, 2001 8-69

Lines for surface element meshing and convection loading.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Lines for surface element meshing and convection loading. Inventory #001445 March 15, 2001 8-70

Isolate nodes attached to lines for surface effect element generation.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Isolate nodes attached to lines for surface effect element generation. Use *get command to get maximum node number in model, assign name “nn” to this value. Create the “extra node”; assign node number “nn+1”. Inventory #001445 March 15, 2001 8-71

Set default attributes to type 2, SURF151 and generate elements with extra node specified. Inventory #001445 March 15, 2001 8-72

Plot of SURF151 elements with extra node.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Plot of SURF151 elements with extra node. Inventory #001445 March 15, 2001 8-73

Plot of applied loads and boundary conditions: convection and temperature on extra node. Inventory #001445 March 15, 2001 8-74

Plot of applied loads and boundary conditions: heat flux.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Plot of applied loads and boundary conditions: heat flux. Inventory #001445 March 15, 2001 8-75

Solve current load step. This solution includes only heat flux and convection loads, radiation will be applied next. Inventory #001445 March 15, 2001 8-76

Check results. List the reaction solution. Compare with input heat value. Inventory #001445 March 15, 2001 8-77

Compare with input heat ……
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Compare with input heat …… 17 BTU/hr-in2 * 2.2 in2 = BTU/hr Inventory #001445 March 15, 2001 8-78

Plot temperature distribution in heat sink.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Plot temperature distribution in heat sink. Inventory #001445 March 15, 2001 8-79

CASE 2- Include radiation effects; Radiation Matrix-Hidden Method.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility CASE 2- Include radiation effects; Radiation Matrix-Hidden Method. Enter the preprocessor. Define new element type, LINK32. Isolate nodes on radiating surfaces. Create LINK32 elements, check orientation. Define the space node. Use the Radiation Matrix Utility to generate the radiation matrix, radheat.sub. Note: Not all menus and steps are detailed in the following pages. Inventory #001445 March 15, 2001 8-80

CASE 2 (cont.) Radiation Matrix-Hidden Method.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility CASE 2 (cont.) Radiation Matrix-Hidden Method. Re-enter the preprocessor. Define new element type, MATRIX50. Create radiation elements by reading in matrix file radheat.sub. Apply temperature to space node. Re-run the solution. Note: Not all menus and steps are detailed in the following pages. Inventory #001445 March 15, 2001 8-81

Re-enter the preprocessor. Define element type 3, LINK32.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Re-enter the preprocessor. Define element type 3, LINK32. Before meshing, set meshing attributes to TYPE=3. Inventory #001445 March 15, 2001 8-82

Create LINK32 elements using ESURF command.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Isolate nodes on radiating surfaces for creation of superimposed LINK32 elements. Create LINK32 elements using ESURF command. Create space node, assign node number “nn+2”. Note: We could have used the existing extra-node for surface effect elements as the space node. By using two nodes we can separate effects and evaluate relative contributions of convection and radiation more easily. Inventory #001445 March 15, 2001 8-83

Check orientation of overlaying mesh…
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Check orientation of overlaying mesh… Turn on element coordinate system plotting to check orientation of element normals. Element normal direction is important since it defines the direction of incident/emitted radiation (viewing direction). Inventory #001445 March 15, 2001 8-84

Plot of LINK32 elements with element coordinate system plotting turned on. Inventory #001445 March 15, 2001 8-85

Begin Radiation Matrix definition.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Begin Radiation Matrix definition. First, define emissivities.. Inventory #001445 March 15, 2001 8-86

Define “Other Settings”
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Define “Other Settings” Stefan-Boltzmann constant; match units to analysis. Type of geometry; 2D for this problem. Specify node number of space node. Inventory #001445 March 15, 2001 8-87

Write radiation matrix.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Write radiation matrix. Select Hidden method for this problem. Specify number of sampling zones (default is 20). Specify name of matrix file to be created. Inventory #001445 March 15, 2001 8-88

Re-enter the Preprocessor.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Re-enter the Preprocessor. Define superelement, MATRIX50 and set keyoptions. Inventory #001445 March 15, 2001 8-89

Set element attributes to TYPE= 4
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Set element attributes to TYPE= 4 Create radiation elements by reading in superelement from matrix file. Specify the filename used. Inventory #001445 March 15, 2001 8-90

Delete or un-select LINK32 elements before running solution.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Delete or un-select LINK32 elements before running solution. Enter the Solution processor. Specify analysis option settings. Specify appropriate value of TOFFST, 460 for this example. Apply temperature constraint to the space node, 90 ° F. Inventory #001445 March 15, 2001 8-91

Now radiation effects will be included, making the problem non-linear.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Re-run the solution. Now radiation effects will be included, making the problem non-linear. Inventory #001445 March 15, 2001 8-92

Enter the Postprocessor and review results.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Enter the Postprocessor and review results. Note the contribution of radiation vs. that of convection: Node 813 (nn+1) “extra node” for SURF151 elements with convection loads. Node 814 (nn+2) space node for radiation solution. Inventory #001445 March 15, 2001 8-93

Temperature distribution in heat sink with radiation effects included.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Temperature distribution in heat sink with radiation effects included. Inventory #001445 March 15, 2001 8-94

CASE 3- Includes radiation effects - Non-Hidden Method.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Basic Procedure CASE 3- Includes radiation effects - Non-Hidden Method. Resume the database heatsink.db. (Note: The same underlying mesh used for generation of the radiation matrix for the Hidden method may be used for the Non-Hidden method.) Select the lines making up “bay 1” and the nodes and elements attached to these lines. Also select the space node. Enter the Radiation Matrix Utility and specify the emissivity, Stefan- Boltzmann constant, type of geometry and space node as was done for the Hidden method. Note: Not all menus and steps are detailed in the following pages. Inventory #001445 March 15, 2001 8-95

CASE 3- Includes radiation effects - Non-Hidden Method.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility CASE 3- Includes radiation effects - Non-Hidden Method. Select the NON-HIDDEN method for this analysis. Write out the radiation matrix to a file called bay1. Repeat for all six bays and the group of fin tip surfaces, generating seven total radiation matrix files. Re-solve the analysis. Note: Not all menus and steps are detailed in the following pages. Inventory #001445 March 15, 2001 8-96

This figure identifies radiating surfaces to be included in radiation matrices created using the NON-HIDDEN method. Bay 1 Bay 2 Bay 3 Bay 4 Bay 5 Bay 6 Fin tip surfaces (circled in figure) should be treated as a single radiation matrix. Inventory #001445 March 15, 2001 8-97

Showing graphical picking of lines in bay 1.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Showing graphical picking of lines in bay 1. Inventory #001445 March 15, 2001 8-98

After selecting lines in bay 1, select attached nodes and elements, as well as the space node. Note: This selection process must be completed for each of the seven bays when using the NON-HIDDEN method. The non-hidden method can be considered valid for this example since the surfaces in each bay are only visible to each other. Inventory #001445 March 15, 2001 8-99

Checking settings for radiation matrix, and specifying number of space node. Inventory #001445 March 15, 2001 8-100

Specifying name of matrix file and NON-HIDDEN method..
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility Specifying name of matrix file and NON-HIDDEN method.. Repeat these steps until all seven files have been written, one for each bay and one for all tip surfaces together. Inventory #001445 March 15, 2001 8-101

Re-run the solution, and compare results.
Example Radiation Problem Heat Sink Analysis using Radiation Matrix Utility After defining new element type, MATRIX50, create radiation elements using each of the seven files created in the previous steps. Re-run the solution, and compare results. Inventory #001445 March 15, 2001 8-102

Temperature distribution in heat sink, NON-HIDDEN Method. Compare with HIDDEN solution temperatures; they should be identical: Inventory #001445 March 15, 2001 8-103

Reaction solution listing for NON-HIDDEN solution. Compare this with previous HIDDEN solution to verify that there is no disagreement: Inventory #001445 March 15, 2001 8-104

Radiation Heat Transfer

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Radiation Heat Transfer

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