Chapter 57: Heating and Convection on a Plate for Heat Exchanger

57 Heating and Convection on a Plate

Summary 1132

Introduction 1133

Modeling Details 1133

Solution Highlights 1134

Results 1141

Modeling Tips 1142

Input File(s) 1142

Video 1142

MD Demonstration Problems

CHAPTER 571132

SummaryTitle Chapter 57: Heating and convection on a plate

Features MD Nastran SOL 400: RCNS, RCNT, HSTAT, HTRAN

Geometry and Boundary Conditions

Material propertiesAluminum: Thermal conductivity (K)= 167 W/m/°C, Specific heat (Cp) = 880 W/Kg/°C, Density(ρ) = 2700 Kg/m³

Analysis characteristics MD Nastran SOL 400: RCNS, RCNT, HSTAT, HTRAN

Element type CQUAD4 for surface

Numerical results Temperature results:

Heat Flux: 500 W/m2 Convection to T = 25oC

1 m x 1 m x 0.001 m

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Heating and Convection on a Plate

IntroductionThis problem demonstrates the applications of MD Nastran SOL 400 Thermal Solver (RCNS, RCNT, HSTAT, and HTRAN).

Modeling DetailsThis problem introduces the basic steps to use MD Nastran SOL 400 Thermal Solver (RCNS, RCNT, HSTAT, and HTRAN) by a simple rectangular surface model. In this problem, you will see how to change the cards to run different solvers. This model has only one Quad element. A constant heat flux load is imposed onto the surface while cooling the surface with uniform convection to a constant ambient temperature. Then you will analyze the model by running different solvers for both steady and transient analysis. You will see how easy to switch between RC Network Solver and FEM solver.

Surface Dimension = 1.0 m x 1.0 m x 0.001 mNormal Heat Flux = 500 W/m²Ambient Temperature = 25ºCThe material is Aluminum 6061 T6 Thermal Conductivity = 167 W/m.K Specific Heat = 880 W/Kg Density = 2700 Kg/m³Top Surface Convection Coefficient = 6.5

Figure 57-1 Heating and Convection on a Plate

Heat Flux: 500 W/m2 Convection to T = 25oC

1 m x 1 m x 0.001 m

MD Demonstration Problems

CHAPTER 571134

Solution HighlightsThe BDF files are pretty much similar, except some cards change in the Case Control Section and Bulk Data Post Section. The main part of the BDF file is exactly the same.

MD Nastran SOL 400 RC Network Solver: RCNS (Steady State)$# Case Control SectionTEMPERATURE (INITIAL)= 21SUBCASE 1$ Subcase name : NewLoadcase_RCNS$LBCSET SUBCASE1 DefaultLBCSet

TITLE=NewLoadcase_RCNSTHERMAL(SORT1,PRINT)=ALLANALYSIS = RCNSNLSTEP = 1SPC = 23LOAD = 24

……$# Bulk Data Post SectionTEMPD 21 0.0SPCADD 23 2DLOAD 24 1. 1. 1NLSTEP 1+ RCHEAT SNSOR 0.001 0.001 0.0 0.0 9.81+ 5000……

MD Nastran SOL 400 FEM Solver: HSTAT (Steady State)$# Case Control SectionTEMPERATURE (INITIAL)= 21SUBCASE 1$ Subcase name : NewLoadcase_RCNS$LBCSET SUBCASE1 DefaultLBCSet

TITLE=NewLoadcaseTHERMAL(SORT1,PRINT)=ALLANALYSIS = HSTATSPC = 23LOAD = 24NLSTEP = 1

……$# Bulk Data Post SectionTEMPD 21 0.0SPCADD 23 2LOAD 24 1. 1. 1NLSTEP 1

1135CHAPTER 57

Heating and Convection on a Plate

As you can see, if you have a BDF file for RCNS, or HSTAT, it is very easy to manually modify the files to run with another solver. The NLSTEP entry for RC Network Solver has more control parameters, but actually most of them are default parameters. The minimum requirement is as follows:

$# Bulk Data Post SectionTEMPD 21 0.0SPCADD 23 2LOAD 24 1. 1. 1NLSTEP 1+ RCHEAT

MD NASTRAN SOL 400 RC Network Solver: RCNT (Transient)$# Case Control SectionIC = 21SUBCASE 1$ Subcase name : NewLoadcase_RCNT$LBCSET SUBCASE1 DefaultLBCSet

TITLE=NewLoadcase_RCNTTHERMAL(SORT1,PRINT)=ALLANALYSIS = RCNTNLSTEP = 1SPC = 23DLOAD = 24

……$# Bulk Data Post SectionTEMPD 21 0.0SPCADD 23 2DLOAD 24 1. 1. 1NLSTEP 1 2400.+ RCHEAT FWDBKL 0.001 0.001 0.0 0.0 9.81 1.+ 5000 100 0.0

MD NASTRAN SOL 400 FEM Solver: HTRAN (Transient)$# Case Control SectionIC = 21SUBCASE 1$ Subcase name : NewLoadcase_NTTR$LBCSET SUBCASE1 DefaultLBCSet

TITLE=NewLoadcase_NTTRTHERMAL(SORT1,PRINT)=ALLANALYSIS = HTRANSPC = 23DLOAD = 24NLSTEP = 1

……$# Bulk Data Post SectionTEMPD 21 0.0SPCADD 23 4DLOAD 24 1. 1. 1 1. 2NLSTEP 1 2400.+ ADAPT 100

MD Demonstration Problems

CHAPTER 571136

It is also easy to manually modify the files to switch to another solver. The NLSTEP entry for RC Network Solver has more control parameters, but again most of them are default parameters. The minimum requirement is as follows:

$# Bulk Data Post SectionTEMPD 21 0.0SPCADD 23 2DLOAD 24 1. 1. 1NLSTEP 1 2400.+ RCHEAT FWDBKL + 100.

1137CHAPTER 57

Heating and Convection on a Plate

NLSTEP specifies the convergence criteria, step size control between coupled loops and step/iteration control for each physics loop in MD Nastran SOL 400. Additional fields were included in this pre-existing entry to provide control for Resistance-Capacitor method of Heat Transfer Analysis.

Format

Example: Steady State

Example: Transient

NLSTEP Control Parameters for Mechanical, Thermal, and Coupled Analysis (MD Nastran SOL 400 only)

1 2 3 4 5 6 7 8 9 10NLSTEP ID TOTTIME +

“GENERAL” MAXITER MINITER MAXBIS CREEP +

+ “FIXED” NINC NO +

+ “ADAPT” DTINITF DTMINF DTMAXF NDESIR SFACT INTOUT NSMAX +

+ ... +

“RCHEAT” SOLVER DRLXCA ARLXCA BALENG DAMPC GRVCON CSGFAC +

+ NRLOOP OUTINV DTIMEI

1 2 3 4 5 6 7 8 9 10

NLSTEP 1 +

+ RCHEAT SNSOR 0.001 0.001 0.001 0.0 0.0 9.81 +

+ 5000

1 2 3 4 5 6 7 8 9 10

NLSTEP 1 1000 +

+ RCHEAT SNDUFR 0.001 0.001 0.0 0.0 9.81 1.0 +

+ 5000 100.0 10.0

Field Contents Type Default

ID Identification number. I 0

TOTIM Total time for the load case R 1.0

“GENERAL” Keyword for parameters used for overall analysis.

... ...

“COUP” Keyword for parameters used for coupled analysis.

“RCHEAT” Keyword to indicate that RC Heat Transfer Analysis is to be performed. See Remark 10.

SOLVER The Relaxation scheme to be used. C SNSOR - See Remark 12.

DRLXCA Diffusion node convergence criterion. R 0 1.0e-3 - See Remark 11.

MD Demonstration Problems

CHAPTER 571138

Remarks

1. Only one of FIXED, ADAPT, or ARCLN load time stepping scheme can be used on a specific NLSTEP entry. FIXED or ADAPT may be used for a single physics STEP or for a coupled physics STEP/SUBSTEP. ARCLN is only valid for a single physics STEP. If no FIXED, ADAPT, or ARCLN appear on a NLSTEP entry, then the default is FIXED, with 50 increments.

2. The desired number of recycles is only used in static mechanical and heat transfer, not in dynamic mechanical. In a coupled analysis, the time step change is calculated separately for heat and mechanica,l and the smallest of the two is used.

3. When the time step is increased due to desired number of recycles, the previous time step is multiplied with SFACT. When the time step is decreased, the factor is calculated internally based upon the minimum time step.

4. User criteria can be given in the TABSCTL entry via CRITTID. These criteria include rotation, displacements, stresses, strains, creep strains. The time step is decreased if the current value of the value is larger than the user specified limit. If LIMTAR is equal to 1 (“target”), it also increases the time step for the next increment if the current value is smaller than the target value given.

5. If MAXITER is given a negative value and the MAXITER number of iterations are obtained, convergence is assumed and the analysis will continue with the next increment.

6. The “ARCLN” entry is applicable to “MECH” analysis only and is ignored for creep analysis. The available constraint types are as follows.

TYPE = “CRIS”:

TYPE = “RIKS”:

TYPE = “MRIKS”:

where:

ARLXCA Arithmetic node convergence criterion. R 0.0 1.e-3 - See Remark 11.

BALENG Allowable system energy imbalance. R 0.0 1.0e-3° - See Remark 11.

DAMPC Damping constant. R 0.0 0.0 nondimensional

GRVCON Gravitation constant. R 0.0 9.81 length/time2.

CSGFAC Time step control factor. R 0.0 1.0 non dimensional. See Remark 13.

NRLOOP Number of relaxation loops allowed. I 0 5000 loop

OUTINV Output interval. R 0.0 60.0 time. See Remark 13.

DTIMEI Time step. R 0.0 0.0 time. See Remark 13.

Field Contents Type Default

Uni

UnO

– T

Uni

UnO

– w2 i O– 2+ ln2

=

Uni Un

i 1–– T

Uni Un

O– w2 i+ 0=

Uni Un

i 1–– TUn

i 1– UnO– w2 i i 1– O– + 0=

1139CHAPTER 57

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The constraint equation has a disparity in the dimension by mixing the displacements with the load factor. The scaling factor is introduced as user input so that the user can make constraint equation unit-dependent by a proper scaling of the load factor ( ). As the value of is increased, the constraint equation is gradually dominated by the load term. In the limiting case of infinite, the arc-length method is degenerated to the conventional Newton’s method.

7. The MINALR and MAXALR fields are used to limit the adjustment of the arc-length from one increment to the next by:

The arc-length adjustment is based on the convergence rate (i.e., number of iterations required for convergence) and the change in stiffness. For constant arc-length during analysis, use:

MINALR = MAXALR = 1

8. The arc-length l for the variable arc-length strategy is adjusted based on the number of iterations that were required for convergence in the previous increment ( ) and the number of iterations desired for convergence in the current increment (NDESIRA) as follows:

9. If a negative value is given to MAXCLP, the coupled analysis will proceed to the next increment even if the coupled loop has not converged when the maximum number of coupled loops, |MAXCLP|, has been reached.

10. This entry is used for a nonfinite element, Resistance-Capacitor network method of analysis for heat transfer.

11. Convergence is determined by the combination of DRLXCA, ARLXCA, and BALENG. DRLXCA and ARLXCA determine if relaxation is met on a node by node basis, rather than a residual vector length.

12. If, in Case Control, the ANALYSIS=RCNS, then valid values are:

If, in Case Control, the ANALYSIS=RCNT, then valid values are:

= user specified scaling factor (SCALEA)

= load factor

= the arc-length

SNSOR (Default) Successive over-relaxation method

SSQMR Steady state Quasi Minimal Residual method

SSSPM Steady state sparse matrix solver method

STDSTL An iterative solver aimed at the fourth root of a quartic for the network equations (good for strong radiation dependence)

SNDUFR (Recommended) An unconditionally stable, explicit method based on a modified Dufort-Frankel scheme

SNFRDL Fast, accurate explicit forward differencing transient method

FWDBKL Implicit forward/backward differencing Crank Nicolson method

w

l

w

MINALR lnew l old MAXALR

MIMAR MAZALR 1= =

Imax

lnew lold NDESIRA Imax 1 2=

MD Demonstration Problems

CHAPTER 571140

If SOLVER is left blank or set to SNSOR and ANALYSIS=RCNT, then internally the RC code will select SNDUFR.

13. About the time step:

a. The default computed time step (DTIMEU) = CSGMIN* CSGFAC. CSGMIN is based on the conductance in the model and can be checked in the .sot file. If CSGFAC is not specified, it is internally set to 1.0.

b. In a normal sized model, CSGMIN is usually small enough for the time step which will assure a convergent transient run.

c. CSGFAC is used to adjust the time step. It is recommended to determine the best CSGFAC to the model while maintaining acceptable temperature errors.

d. If OUTPUT < CSGFAC*CSGMIN or OUTPUT < DTIMEI, then OUTPUT becomes the time step. All the OUTPUT points are automatically required to be calculated.

e. DTIMEI is the forced time step which will ignore any other factors. Sometimes it may lead to inaccurate answer if it is too large. DTIMEI does not affect the automatic time step solvers.

f. If the model size is very small, CSGMIN may be too big for the time step. A small CSGFAC or DTIMEI should be used to adjust the time step.

g. CSGFAC*CSGMIN or DTIMEI should be small enough to “catch” any details in time fields, temperature fields, or orbital flux arrays.

SNADE Alternating direction explicit method

ATSDUF SNDUFR with automatic time step based on ERRMIN/ERRMAX

ATSFBK FWDBKL with automatic time step based on ERRMIN/ERRMAX

SNTSM Weighted implicit forward/backward differencing method

SNTSM3 Weighted implicit forward/backward differencing method

SNTSM1 Weighted implicit forward/backward differencing method

SNTSM4 Weighted implicit forward/backward differencing method

TRSPM Transient sparse matrix solver method

ATSSPM TRSPM with automatic time step based on ERRMIN/ERRMAX

TRQMR Transient Quasi Minimal Residual

ATSQMR TRQMR with automatic time step based on ERRMIN/ERRMAX

1141CHAPTER 57

Heating and Convection on a Plate

Results

Figure 57-2 Temperature Contour of Plate (Steady State)

Figure 57-3 Temperature Curves of Plate (Transient State)

MD Demonstration Problems

CHAPTER 571142

RCNS and HSTAT have the same steady state result. RCNT and HTRAN have the same transient temperature curves. These curves are drawn in SimXpert/Result/Chart. The curves from RCNT/FWDBKL and HTRAN fit perfectly. The total time (end tine) is 2400 seconds. The output interval is 100 seconds.

Modeling TipsSimXpert uses ATSDUF as the default solver, and Sinda for Patran uses SNDUFR as the default solver. RC Network Solver has other solvers available. For this specific model which has only one element and the thickness is very thin,

therefore CSGMIN is very small (CSGMIN is the minimum value of CSG for each node in the model. ,

where is the capacitance, and is the conductors for this node), a very small time step will be required. We need to set up some control parameters for ATSDUF or SNDUFR to make sure they have small enough time step to start the transient analysis. For more information, please reference the MSC Sinda User's Guide or Sinda for Patran User's Guide. The solver FWDBKL is an implicit solver which does not have this problem. FWKBKL is one of the implicit transient solvers of RC Network Solver.

Input File(s)

VideoClick on the image or caption below to view a streaming video of this problem; it lasts approximately 30 minutes and explains how the steps are performed.

Figure 57-4 Video of the Above Steps

Files Description

QT34_conv_rcns.dat MD Nastran SOL400/RC Network Solver thermal input file

QT34_conv_ntss.dat MD Nastran SOL400/FEM Solver thermal input file

QT34_conv_rcnt.dat MD Nastran SOL400/RC Network Solver thermal input file

QT34_conv_nttr.dat MD Nastran SOL400/FEM Solver thermal input file

CSG C Gi=

C Gi

Heat Flux: 500 W/m2 Convection to T = 25oC

1 m x 1 m x 0.001 m