Nonlinear Steady-State Heat Transfer Analysis

Nonlinear steady-state heat transfer analysis can be used to calculate the temperature distribution in a system, in which material properties are a function of temperature.

The basic finite element equation for nonlinear heat transfer can be written as:

Where, T is unknown temperature, f is the global power vector, and L(T) is the global response (nodal power).

The system of equation (shown above) is solved using the Newton’s method. Solution control is provided by defining parameters on the NLPARM bulk data entry. TEMPERATURE (INITIAL) can be used to provide an initial temperature distribution. The temperature results from the nonlinear heat transfer analysis can be used in subsequent structural analysis.

Nonlinear Steady-State Heat Transfer Analysis Setup

The following steps can be considered as a guide to setup a nonlinear steady-state heat transfer analysis:

1.	Use the solution sequence identifier (ANALYSIS) in the subcase information section to select the nonlinear steady-state heat transfer analysis using: ANALYSIS=NLHEAT.

2.	The likely initial temperature distribution can be defined using the TEMPERATURE subcase information entry (type=INITIAL). A good initial temperature estimate improves the convergence of the solver.

3.	The MATT4 bulk data entry can be used to define temperature dependent thermal material properties.

4.	To indicate that a nonlinear solution is required for any subcase, a NLPARM subcase information entry is required. This subcase entry points to a NLPARM bulk data entry that specifies convergence tolerances and other nonlinear parameters.

5.	Loads and boundary conditions are defined in the bulk data section of the input deck. These should be referenced in the subcase information section using SPC and LOAD entries in a subcase. Each subcase defines a load vector.

Example

An example solver deck section showing the usage of ANALYSIS and NLPARM is shown below:

SUBCASE 5

ANALYSIS=NLHEAT

SPC=10

LOAD=20

NLPARM=30

…

BEGIN BULK

…

NLPARM, 30

…

ENDDATA

Note:

1.	Optimization based on nonlinear heat transfer analysis is currently not supported.

2.	CNTNLSUB is currently not supported for nonlinear heat transfer analysis.

3.	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.