Li-ion battery is growing in popularity for many engineering applications due to its advantages of high energy density, little or no memory effect, and low self-discharge. In spite of many desirable features of Li-Ion (Li-I) battery, it has one rare but severe failure mode of fire/explosion for the electric vehicles (EVs). Thus, for further growth of Li-ion battery business, the safety problem should be taken care.

Most failure modes of Li-ion battery are related to temperature increase. Increased temperature causes another side reaction in the battery which again causes further increase in temperature, resulting in thermal runaway. It is thus important to keep the temperature below a certain temperature limit for prevention of the battery failure due to thermal runaway. Even if not related to battery failure directly, temperature increase may degrade battery performance significantly. Such battery issues necessitate temperature monitoring as the size of battery system increases.

Moreover, temperature uniformity across the battery cell and battery pack is important, in order to avoid short circuit or local degradation due to hot spots. Considering, the temperature dependence of the battery cell voltage, a large temperature variation in the battery pack generates unbalanced battery voltage, leading to safety issue. Therefore, it is prescribed to keep the temperature difference from cell to cell and module to module below 5 ^oC.

Different numerical and analytical models have been used to simulate the Li-I batteries taking account for their material properties, size, operating conditions and etc. This includes both semi-coupled and fully coupled electrochemical-thermal models, from cell to pack level. It is of great importance to reduce the temperature magnitude as well as temperature gradient on the cell level, as this will lead to larger temperature gradients in the cell surface and bigger degradation values, especially for the larger batteries. Most of the models use differential equations to solve for the energy balance in the energy storage systems (ESS).

The idea of this study is to solve the energy balance equation in battery cell as a porous medium with the internal heat generation in the ESS, which is related to the temperature-current dependent overpotential heat generation and state of charge (SOC) dependent change in entropy heat generation. Overpotential heat generation is normally attributed to the internal resistance within the battery, kinetic aspects and mass transport associated with electrochemical reactions. Heat generation due to entropy change on the other hand can be caused by the reversible electrochemical reactions within the battery. Heat generation from the enthalpy of mixing is also another source of internal heat generation but it is normally neglected in many models.

The energy equation with the proper heat generation (as a source term) will be discretised on a two-dimensional (2D) domain using finite difference method (FDM). The developed 2D model is then will be used to optimise the internal configuration of the cell material, i.e. porosity and/or thermos-physical properties, in order to reach the lowest level of temperature as well as the temperature gradient.