About:2-Node Thermal
Internal Temperature (2-node) Model - resolve bulk and surface temperature for improved voltage prediction
Overview
The Internal Temperature (2-node) thermal model extends the About:Lumped 0D thermal model by resolving the temperature difference between the interior of a cylindrical cell and its surface. The model predicts the volume-average (bulk) temperature, which governs the electrical response of the cell, together with the temperature of the cooled surface.
The thermal problem is divided by the surface node into two thermal resistances. The internal thermal resistance \(R_\text{int}\) is a property of the cell and is supplied with the model. The external thermal resistance \(R_\text{ext}\) is a property of the surrounding thermal environment and is defined by the user. Resolving the surface temperature between the two separates the cell-controlled and environment-controlled parts of the thermal problem.
Coupling the equivalent circuit model (ECM) to the bulk temperature, rather than to a single lumped temperature, improves voltage prediction accuracy under high-rate and low-temperature operation, where the cell develops a significant internal-to-surface temperature gradient. Separately resolving the bulk and surface temperatures also allows model calibration against measurable surface temperatures while the bulk temperature is predicted independently; a 0D lumped model does not support this.
The model is included with the Simulink implementation of About:ECM for supported cylindrical form factors.
Technical Description
The model represents the cell as two thermal nodes connected by a single internal thermal resistance (Figure 1).
Figure 1: Thermal network of the 2-node model. Components beyond the cell model boundary represent the user-defined cooling environment.
- A bulk node carrying the entire cell thermal mass (total heat capacity \(m C_p\)). Its temperature is the volume-average jelly-roll temperature. It is this temperature that is coupled to the ECM.
- A surface node, which is massless: it has no heat capacity of its own and mediates heat exchange between the bulk and the external cooling boundary.
The bulk node represents a volume average rather than the geometric centre used in core-shell models. \(R_\text{int}\) is defined to reproduce the volume-average-to-surface temperature difference for the selected cooling configuration.
Heat generated by the ECM enters the bulk node, conducts through \(R_\text{int}\) to the surface, and passes across the external thermal resistance \(R_\text{ext}\) to the environment. Because the surface node is massless, the surface temperature responds instantaneously to the heat flow through it. In the limit \(R_\text{int} \to 0\) the two nodes coincide and the model reduces to the 0D lumped model.
Heat leaves the cell through the surfaces defined by the selected cooling configuration (Figure 2): Base-cooled (cell base), Radial surface-cooled (cylindrical surface), or Convection chamber (all exposed surfaces).
Figure 2: Cooled surfaces for the three supported cooling configurations.
Key features
- Predicts bulk (volume-average) and surface temperature from a single internal thermal resistance.
- Bulk temperature is coupled to the ECM; surface temperature is provided as an output.
- \(R_\text{int}\) is computed by the model from the selected form factor, can material, cooling configuration, and jelly-roll conductivities. No cell-specific thermal parameterisation is required.
- Reuses the cell mass and specific heat capacity supplied in the ECM parameter set.
- Selectable alongside the default Lumped (0D) thermal model.
Key applications
- Improved voltage prediction accuracy under high C-rate or high-power duty cycles.
- Internal temperature estimation where only surface temperature is measurable.
- Comparison of cooling strategies (base, surface, convection).
- Comparison of cell thermal properties (form factor, can material, jelly-roll thermal conductivity).