Compact thermal models

A compact thermal model (CTM) replaces the resolved interior of an electronic package with one junction node and thermal-resistance paths to selected package faces. The surrounding fluid and conducting solids remain part of the resolved thermal domain.

For each active face \(i\), Vanellus uses its area-averaged temperature \(T_i\) and a junction-to-face resistance \(R_i\):

\[ Q_i = \frac{T_J - T_i}{R_i}, \qquad P = \sum_i Q_i. \]

The resulting junction temperature is

\[ T_J = \frac{P + \sum_i T_i/R_i} {\sum_i 1/R_i}. \]

Each resistance describes heat transfer between the junction and an entire package face, in \(\mathrm{K/W}\). Vanellus distributes that heat flow uniformly over the meshed face area.

Two-resistor model

two_resistor_ctm has two active paths:

• resistance_jc connects the junction to case_side;
• resistance_jb connects the junction to the face opposite case_side.

The other four cuboid faces are adiabatic. This representation is appropriate when package data separates heat flow toward the case and board and side losses can be neglected.

Both active faces must completely touch the solved thermal domain. The board face normally touches a conducting board, while the case face can exchange heat with fluid or another conducting region.

Star-resistor model

star_resistor_ctm retains the board and case paths and activates all four remaining faces. Each side face receives a separate branch with resistance resistance_js.

The four side branches act in parallel; resistance_js is not divided among them. When their temperatures are equal, their combined side conductance is therefore four times the conductance of one branch.

All six faces must completely touch fluid or conducting cells. Use the STAR model when side heat transfer is significant to the package balance (e.g. for taller chips) and the available resistance data supports it.

Explicit coupling

With ctm_coupling: "explicit", Vanellus:

1. area-averages the solved temperature over each active face;
2. under-relaxes those face temperatures using the CTM’s relaxation_factor;
3. calculates the junction temperature and face heat rates; and
4. applies those rates as heat-flux conditions for the next energy solve.

The lag between the solved temperature and the next heat-flux update can oscillate when the package is strongly coupled to its surroundings. Relaxation can stabilize it but slows the response.

Implicit coupling

With ctm_coupling: "implicit", each active path is represented as a mixed heat-transfer-coefficient condition. The current face temperature is included implicitly in the energy equation, while the effective temperature derived from the other CTM faces is updated between iterations.

This removes the direct lag in each face’s own heat-flux response and is normally more stable. The CTM relaxation_factor is not used with implicit coupling.

Both formulations represent the same resistance network and should converge to the same physical balance. They differ in how that balance is coupled into the iterative energy solution.

Reported temperature

The CTM produces one junction temperature, recorded as junction_temperature_<tag> in iteration_info.csv. The same final value is written uniformly into the component cells in solid.vtu for visualization. It is not a resolved temperature distribution through the package.

See also

• Model an electronic package with a compact thermal model shows how to configure both models.
• Conducting and insulating domains explains how CTMs relate to the energy domain.
• Monitors and derived quantities explains the junction-temperature history.
• How simulations stop explains CTM convergence criteria.
• API reference lists exact CTM fields and limits.