Nonlinear Transient Heat Transfer Analysis

Calculates the temperature distribution in a system with respect to time.

The applied thermal loads can either be time-dependent or time-invariant; transient thermal analysis is used to capture the thermal behavior of a system over a specific period of time.

The basic finite element equation for transient heat transfer analysis is given by:(1) C T ˙ + F ( K ) + [ H ] T = P MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaC4qaiqahs fagaGaaiabgUcaRiaahAeadaqadaqaaiaadUeaaiaawIcacaGLPaaa cqGHRaWkdaWadaqaaiaahIeaaiaawUfacaGLDbaacaWHubGaeyypa0 JaaCiuaaaa@4214@
Where,
C
Heat capacity matrix
F ( K )
Internal power, due to temperature-dependent conductivity ( K )
H
Boundary convection matrix, due to free convection
T ˙
Derivative of the nodal temperature matrix with respect to time
T
The unknown nodal temperature matrix
P
Thermal loading vector

Input

Defines how to setup the nonlinear transient heat transfer subcase.

  1. Use the solution sequence identifier (ANALYSIS) in the Subcase Information Entry section to select the linear transient heat transfer analysis using: ANALYSIS=NLHEAT.
  2. The NLPARM Bulk Data and corresponding subcase entries are required to activate Nonlinear Transient Heat Transfer Analysis.
  3. Define the time step intervals at which the solutions will be calculated for transient analysis using the TSTEP Bulk Data Entry. This is referenced in the TSTEP Subcase Information Entry which is used to select the integration type (TSTEP=SID) for transient analysis.
  4. The initial conditions for transient heat transfer analysis are selected by the use of the IC Subcase Information Entry. This entry can be used in the Subcase Information section to specify the set identification number of the temperature field defined by TEMP or TEMPD Bulk Data Entries.
  5. Use the single point constraint (SPC) Bulk Data Entry to specify the fixed boundary conditions for this analysis.
  6. Use the DLOAD Subcase Information Entry to reference the set IDs of DLOAD, TLOAD1 and TLOAD2 Bulk Data Entries. Use the TLOAD1 and TLOAD2 Bulk Data Entries to specify:
    1. Time dependent thermal loading - The EXCITEID field of the TLOAD1 and TLOAD2 Bulk Data Entries should point to the ID's of QVOL and QBDY1 Bulk Data Entries or a combination of them using LOADADD.
    2. Temperature boundary condition - The EXCITEID field of the TLOAD1 and TLOAD2 Bulk Data Entries should point to the ID of the SPCD Bulk Data Entry. Also, the TYPE field in the TLOAD1 and TLOAD2 entries should be set to 1.
  7. The MAT4 and MAT5 Bulk Data Entries can be used to define thermal material properties such as thermal conductivity K, heat capacity C, density RHO, convection heat transfer coefficient H and heat generation capability HGEN used in the QVOL Bulk Data Entry.
  8. The MATT4 Bulk Data Entry can be used to define temperature-dependent thermal material properties.
  9. Heat capacity (CP) is defined on MAT4/MAT5 entries is defined per unit mass. It is multiplied by density (RHO) to calculate heat capacity matrix in transient heat transfer analysis. If RHO is not defined on MAT4/MAT5, then positive density from a structural material entry with matching MID is used. If MAT4/MAT5 entries do not have a corresponding matching structural material, then the default value of 1.0 is used.
  10. The THERMAL I/O Option Entry can be used to request nodal temperature output T for transient heat transfer analysis subcases. The FLUX I/O Options Entry can be used to request temperature gradient and flux output for transient heat transfer analysis subcases.

Apply Heat Flux Loads

In Step 6(a) of the guide above, the ability to use QBDY1 data to apply heat flux loading is illustrated. This is accomplished as explained in the following steps.

  1. The value of the heat flux load is input in the Q0 field of a QBDY1 Bulk Data Entry.
  2. The EID# field in the QBDY1 Bulk Data Entry requires the identification number of CHBDYE surface elements. These surface elements should be created on the surfaces of the model to which heat flux loads are to be applied.
  3. This is conducted in HyperMesh by creating an interface of type CONDUCTION, selecting all the relevant surfaces and then adding CHBDYE surface elements to those surfaces.
  4. These newly created surface elements via the interface group can then be referenced in the EID# field of the QBDY1 Bulk Data Entry.
    Note:
    1. Shell elements are considered to be membranes in Heat Transfer Analysis. Composite properties are homogenized (1 degree of freedom per grid). The temperature distribution through the thickness of shell elements is not calculated. Only nodal temperature is determined.
    2. Non-zero SPC will be considered as zero SPC for transient thermal analysis, except when non-zero SPC are used to specify ambient points for convection. When an ambient point is controlled by TLOAD1/TLOAD2 via SPCD, the corresponding SPC should be zero.

Transient Thermal Subcase Continuation

Nonlinear transient thermal subcase can continue from the temperature solution of a previously solved steady-state or transient thermal subcase, by pointing IC to that subcase’s subcase or TSTRU ID.

Coupled Thermal-structural Analysis

The temperature results from the final time step of a nonlinear Transient Heat Transfer Analysis can be applied to a structural subcase.

Both TEMPERATURE(LOAD) and TEMPERATURE(MATERIAL) are allowed to reference the subcase ID or temperature result sets from the Nonlinear Transient Heat Transfer Analysis for use in either material property calculations or thermal loading.

If temperature history at multiple time steps should be applied to a structural subcase, One Step Transient Thermal Stress Analysis should be used.

Comments

  1. In Nonlinear Transient Heat Transfer analysis, the Backward Euler method is used as the integration scheme.