Linear 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:

C \dot{T} + [K_{C} + H] T = f

Where,

$C$: Heat capacity matrix
$K$: Conductivity matrix
$H$: 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
$f$: Thermal loading vector

Thermal load vector can be expressed as:

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

Where,

$f_{B}$: Power due to heat flux at boundary specified by QBDY1 card.
$f_{H}$: Boundary convection vector due to convection specified by CONV card.
$f_{Q}$: Power vector due to internal heat generation specified by QVOL card.

Automatic free convection definition can be activated via CONVG Bulk/Subcase pair.

The differential equation is solved to find nodal temperature $T$ at the specified time steps. The difference between the equation and the Linear Steady-State Heat Transfer Analysis equation is the term, $C \dot{T}$ , that captures the transient nature of the analysis.