The difficulty with modeling a lithium-ion (Li-ion) battery is due to its multi-domain, multi-physics nature. Vastly different length scales associated with different physics complicates the problem. When performing a thermal analysis, the goal is to determine the temperature distribution at the battery length scale. The physics governing the Li-ion transport occurs in the anode-separator-cathode sandwich layers (the electrode pair length scale). Li-ion transport in an active material occurs at the atomic length scale. The Multi-Scale Multi-Domain (MSMD) approach deals with different physics in different solution domains [[312]].
Battery thermal and electrical fields are solved in the CFD domain at the battery cell's scale using the following differential equations:
 | (19–3) |
 | (19–4) |
where 
and 
are the effective electric conductivities for the positive and negative
electrodes, 
and 
are phase potentials for the positive and negative electrodes, 
and 
are the volumetric current transfer rate and the electrochemical reaction heat
due to electrochemical reactions, respectively, 
and 
are the current transfer rate and heat generation rate due to battery internal
short-circuit, respectively, and 
is the heat generation due to the thermal runaway reactions under the thermal
abuse condition.
For normal operation, 
is set to zero. For more information, refer to Thermal Abuse Model. The source terms 
and 
are computed using an electrochemical submodel. If there is no internal
short-circuit, 
and 
are equal to zero. For more information, refer to External and Internal Electric Short-Circuit Treatment.
A wide range of electrochemical models, from simple empirically-based to fundamental physics-based, is available in the open literature. In Ansys Fluent, the following electrochemical submodels are implemented:
Newman, Tiedemann, Gu and Kim (NTGK) or direct current internal resistance (DCIR) model
Equivalent Circuit Model (ECM) model
Newman Pseudo-2D (P2D) model
In addition, you can define your own electrochemical model via user-defined functions and hook it to the Fluent MSMD battery module.
To use the MSMD approach in an arbitrary finite volume of the cell composite, the following conditions must be met:
Battery micro layers must have the same orientation
Two potential fields,
and 
, must be uniquely determined
These conditions are usually met for aligned stack cells or wound cells with extended foil-type continuous current tabs.
The MSMD solution method can resolve the potential distribution within a battery and, therefore, the detailed heat generation distribution within the battery. Since two extra transport equations are solved, the computational cost is higher compared to the previous methods.