pat328, section 3, march 2001mar120, lecture 4, march 2001s16-1mar120, section 16, december 2001...

PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001 S16-1MAR120, Section 16, December 2001

SECTION 16

HEAT TRANSFER ANALYSIS


TABLE OF CONTENTS (cont.)

Section Page

16.0 Heat Transfer AnalysisOverview …………………………………………………………………...………………………………………..

16-3Heat Transfer Modes …………………………..…………………………………………………………………..

16-4Heat Transfer Example ………………...…………………………...……………………………………………..

16-5Heat Transfer Mathematics ……………………...………………………………………………………………..

16-6Heat Transfer Loads & Boundary Conditions ………………………………………………………………….. 16-7Heat Transfer Initial Conditions ………………………………………………………………………………….. 16-10Heat Transfer In Msc.Patran Marc Preference ………………………………………………………..………..

16-11Thermal Nonlinear Analyses …………………………………………………………………………….………..

16-12Minimum Allowable Time Increment ……………………………………………………………………………..

16-13Minimum Time Increment:physical Interpretation ..……………………………………………………………..

16-14Difficulties With Time Incrementation ……………………………………..……………………………………..16-15Limitations and Capabilities……………………… ..…………………………………………………………….. 16-16Sequentially Coupled Problems …………………………………………………………………………………..

16-17Fully Coupled Problems ……………………………………….…………………………………………………..

16-18


OVERVIEW

Why a Structural Analyst may have to perform Thermal Analysis

Modes of Heat Transfer Available in MSC.Marcand 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


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 +

**(T24-T14) +

(hct – (hct-hbl)*gap/dqnear)*(T2-T1)


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)


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


HEAT TRANSFER LOADS & BOUNDARY CONDITIONS


contact

HEAT TRANSFER LOADS & BOUNDARY CONDITIONS (CONT.)


contact6) Contact conduction:

h : Transfer coeff.

= Temp.Body 2 = Temp.Body 1

HEAT TRANSFER LOADS & BOUNDARY CONDITIONS (CONT.)


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


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).


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


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


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

2

6l

k

pct


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.

2

6l

k

pct


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


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.


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


FULLY COUPLED PROBLEMS (CONT.)

Example: Disk Brake


FULLY COUPLED PROBLEMS (CONT.)

Example:Thread Forming

pat328, section 3, march 2001mar120, lecture 4, march 2001s16-1mar120, section 16, december 2001...

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