Solvers Background: Transient Heat

Description

The Transient Heat solver uses a time stepping scheme to calculate the temperature variation in a structure as a function of time. The solver considers three modes of heat transfer: conduction, convection and radiation. The output from a transient heat analysis at every time step is a single value of temperature for each node (analogous to displacement in a structural solution), from which nodal thermal flux (analogous to node reaction in a structural solution) and element thermal flux (analogous to stress in a structural solution) can be calculated.

Two types of transient heat solutions are possible:

Linear

The linear option can be used for problems that involve conduction and convection modes of heat transfer and where the material properties are independent of temperature, but the temperature varies with time.
Nonlinear

Any problem that includes radiation heat transfer, temperature dependent material properties, or variable time steps, requires the nonlinear option.

Procedure

The Transient Heat solver executes the following steps:

Calculates and assembles the element conductivity matrices, the element damping matrices and the element and nodal thermal load vectors. The load vectors are derived from the convection and radiation coefficients, the applied nodal temperatures and the applied element flux attributes. At the end of this assembly, the following system of equilibrium equations is formed:

where

= global conductivity matrix (also called stiffness matrix as an analogy to the structural formulation),

= global heat capacity matrix (also called damping matrix as an analogy to the structural formulation),

= unknown nodal temperature vector,

= rate of change of with respect to time, and

= applied heat load vector, which may be time dependent.
Solves the equations of equilibrium for the unknown nodal temperatures at each time step.
Calculates the node and element flux and temperature gradients as requested at each time step.

Notes

For linear transient heat problems where the time step is not constant, the nonlinear option is required with the matrix updated whenever the time step changes.
The update of the element stiffness matrices (SOLVERS Parameters: ITERATION (Heat)) for nonlinear problems can be performed at every step, at every saved step or after a certain number of steps.
The solution at any time step in a transient heat analysis (i.e., nodal temperatures), can be used in any of the structural solvers, as a temperature distribution for thermal stress analysis. The complete thermal transient result file can be used directly by the Quasi-static and Nonlinear Transient Dynamic solvers for problems involving time-dependent, thermal stress analysis.