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 nonlinear transient heat transfer analysis is given by:

$C \dot{T} + [K_{C} + H] T + R {(T - T_{a b s})}^{4} = f$

Where,

$C$: Heat capacity matrix.
$K_{C}$: Temperature-dependent conductivity.
$H$: Temperature-dependent boundary convection matrix, due to free convection.
$\dot{T}$: Derivative of the nodal temperature matrix with respect to time.
$T$: The unknown nodal temperature matrix.
$R$: Radiation exchange matrix.
$T_{a b s}$: Absolute temperature scale defined via PARAM, TABS.
$P$: Thermal loading vector.

Thermal load vector can be expressed as:

$f = f_{B} + f_{H} + f_{Q} + f_{R}$

$f_{B}$: Power, due to heat flux at boundary specified by QBDY1.
$f_{H}$: Boundary convection vector, due to convection specified by CONV (automatic free convection definition can be activated via CONVG Bulk/Subcase pair).
$f_{Q}$: Power vector, due to internal heat generation specified by QVOL.
$f_{R}$: Boundary radiation vector, due to radiation specified by RADBC.

Note:

For Nonlinear Heat Transfer Analysis, Conductivity ( $K_{C}$ ), and/or Free Convection Coefficient ( $H$ ) are temperature-dependent.
The differential equation is solved by backward Euler method to find nodal temperature $T$ at the specified time steps. The difference between this equation and the Linear Steady-State Heat Transfer Analysis equation is the term, $C \dot{T}$ , that captures the transient nature of the analysis.