1. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-1MAR120, Section 16, December 2001 SECTION 16 HEAT TRANSFER ANALYSIS

2. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-2MAR120, Section 16, December 2001 TABLE OF CONTENTS (cont.) SectionPage 16.0 Heat Transfer Analysis Overview …………………………………………………………………...………………………………………..16-3 Heat Transfer Modes …………………………..…………………………………………………………………..16-4 Heat Transfer Example ………………...…………………………...……………………………………………..16-5 Heat Transfer Mathematics ……………………...………………………………………………………………..16-6 Heat Transfer Loads & Boundary Conditions …………………………………………………………………..16-7 Heat Transfer Initial Conditions …………………………………………………………………………………..16-10 Heat Transfer In Msc.Patran Marc Preference ………………………………………………………..………..16-11 Thermal Nonlinear Analyses …………………………………………………………………………….………..16-12 Minimum Allowable Time Increment ……………………………………………………………………………..16-13 Minimum Time Increment:physical Interpretation..……………………………………………………………..16-14 Difficulties With Time Incrementation ……………………………………..……………………………………..16-15 Limitations and Capabilities………………………..……………………………………………………………..16-16 Sequentially Coupled Problems …………………………………………………………………………………..16-17 Fully Coupled Problems ……………………………………….…………………………………………………..16-18

3. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-3MAR120, Section 16, December 2001 OVERVIEW Why a Structural Analyst may have to perform Thermal Analysis Modes of Heat Transfer Available in MSC.Marc and MSC.Patran support  Conduction  Convection  Radiation  Transient Analysis versus  Steady State Analysis Linear versus Nonlinear Minimum Allowable Time Increment Thermal Analysis  How to calculate it  Physical Interpretation  What happens if you violate the formula  Sequentially Coupled Problems versus  Fully Coupled Problems

4. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-4MAR120, Section 16, December 2001 Motivation When the solution for the temperature field in a solid (or fluid) is desired,and is not influenced by the other unknown fields, heat transfer analysis is appropriate. HEAT TRANSFER MODES Boundary Conditions :  Thermal Convection  Natural convection  Radiation Near a Contact add:  Distance dependent convection Q = hcv*(T2-T1)+hnt*(T2-T1) ent +  *  *(T2 4 -T1 4 ) + (hct – (hct-hbl)*gap/dqnear)*(T2-T1)

5. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-5MAR120, Section 16, December 2001 HEAT TRANSFER EXAMPLE Computed Temperatures Temperature given at bottom left and right end surfaces Convection given about connector Example: Steady State Analysis of Radiator (Workshop 5)

6. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-6MAR120, Section 16, December 2001 Thermal equilibrium between heat sources, energy flow density and temperature rate is expressed by the Energy Conservation Law, which may be written: Energy flow density is given by a diffusion and convection part: where is L is the conductivity matrix. Assume that the continuum is incompressible and that there is no spatial variation of r and Cp; then the conservation law becomes: HEAT TRANSFER MATHEMATICS

7. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-7MAR120, Section 16, December 2001 HEAT TRANSFER LOADS & BOUNDARY CONDITIONS

8. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-8MAR120, Section 16, December 2001 contact HEAT TRANSFER LOADS & BOUNDARY CONDITIONS (CONT.)

9. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-9MAR120, Section 16, December 2001 contact 6) Contact conduction: h : Transfer coeff. = Temp.Body 2 = Temp.Body 1 HEAT TRANSFER LOADS & BOUNDARY CONDITIONS (CONT.)

10. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-10MAR120, Section 16, December 2001 Only in transient analysis: MSC.Marc uses a backward difference scheme to approximate the time derivative as : resulting in the finite difference scheme: where C : heat capacity matrix K : conductivity and convection matrix F : contribution from convective boundary condition : vector of nodal fluxes HEAT TRANSFER INITIAL CONDITIONS

11. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-11MAR120, Section 16, December 2001 HEAT TRANSFER IN MSC.PATRAN MARC PREFERENCE All three modes of heat transfer may be present in an MSC.Marc analysis. There are two basic types of analyses:  Transient analysis: to obtain the history of the response over time with heat capacity and latent heat effects taken into account  Steady state analysis: when only the long term solution under a given set of loads and boundary conditions is sought (No heat accumulation).

12. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-12MAR120, Section 16, December 2001 Time Temperature THERMAL NONLINEAR ANALYSES Either type of thermal analysis can be nonlinear. Sources of nonlinearity include:  Temperature dependence of material properties.  Nonlinear surface conditions: e.g. radiation, temperature dependent film (surface convection) coefficients.  Loads which vary nonlinearly with temperature. These loads are described using Fields in MSC.Patran.  Latent heat (phase change) effects

13. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-13MAR120, Section 16, December 2001 In transient heat transfer there is a minimum allowable increment— the mesh refinement determines how small a time increment can be analyzed. A simple formula provides the minimum allowable increment This minimum is only a requirement for second order elements but it is good to use it as a guideline for all meshes. MINIMUM ALLOWABLE TIME INCREMENT

14. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-14MAR120, Section 16, December 2001 This expression describes the physical limitation on the amount of heat that can be moved a distance  l in an amount of time  t Think of the temperature at each node representing the amount of heat in the physical region of that node Then think of the amount of heat associated with each individual node MINIMUM TIME INCREMENT: PHYSICAL INTERPRETATION If you specify a higher temperature at node A than as at node E (as the only boundary conditions) heat must be removed from nodes B and C to comply with the specified boundary condition at node A. If  t is too small, or  l too large, to allow enough heat to move to node C, the extra heat required to comply with the specified temperature boundary condition must come from the region of node B. If too much heat is removed from node B, the temperature drops below the physically realistic value and you see a seesaw pattern of temperature distribution rather than the correct monotonically decreasing one. A B C D E

15. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-15MAR120, Section 16, December 2001 DIFFICULTIES WITH TIME INCREMENTATION Symptoms of time increments being too small  Temperature increases when it should decrease  Temperature decreases when it should increase Resolution  Use larger time increments (do not accept early transient solution) or  Refine mesh near surface Choice of Elements  Use first-order elements for highly nonlinear, discontinuous conduction such as phase changes (latent heat effects).  Use second-order elements for smooth diffusion and conduction.

16. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-16MAR120, Section 16, December 2001 LIMITATIONS AND CAPABILITIES Limitation: As discussed, oscillatory behavior will likely result if time step is too small.  Better approximation can be obtained if: time step is INCREASED mesh is refined heat capacity matrix is lumped (linear elements)  Further MARC capabilities: User subroutines for non-linear boundary conditions tying and heat transfer shell element with parabolic distribution in thickness direction phase transitions

17. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-17MAR120, Section 16, December 2001 SEQUENTIALLY COUPLED PROBLEMS Thermal field affects the mechanical field  Mechanical properties change with temperature  Thermal expansion Sequentially coupled problems are supported in MSC.Marc 2001and by MSC.Patran 2001 Mechanical field does not affect the thermal field. Temperatures may be applied directly as a Load/Boundary Condition, or be read from a file using PCL.

18. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-18MAR120, Section 16, December 2001 FULLY COUPLED PROBLEMS Thermal field affects the mechanical field as above  Thermal loads induce deformation. Mechanical field affects thermal field  Mechanically generate heat-due to plastic work or friction  Deformation changes modes of conduction, radiation, etc. Fully coupled problems are supported in MSC.Marc 2001 but not by MSC.Patran 2001 Fully coupled problems are supported in MSC.Patran 2002 Example: Turbine Blade

19. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-19MAR120, Section 16, December 2001 FULLY COUPLED PROBLEMS (CONT.) Example: Disk Brake

20. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S16-20MAR120, Section 16, December 2001 FULLY COUPLED PROBLEMS (CONT.) Example: Thread Forming