Lithium-ion batteries are one of the most common energy storage systems which are widely used as a power source in portable electrical and electronic products, especially in electric and hybrid electric vehicles (HEVs) due to low self-discharge and high energy/power density. However, as a drawback, thermal instability is recognized as one of the major safety concerns and challenges in performance improvement of lithium ion battery which requires an in-depth understanding of the thermal behavior during charge and discharge cycles to improve the safety and increase the life-cycle of lithium-ion batteries. Mathematical modeling of thermal behavior as well as cooling strategy has proven to be an efficient and cost effective tool to improve the performance and extend durability of lithium-ion batteries. The thermal-electrochemical transport equations of lithium-ion battery are a set of highly coupled non-linear partial differential equations (PDEs) with non-linear source terms and Neumann type of boundary conditions in all boundaries which causes the system of equations to be highly stiff. Due to these difficulties, the procedure of numerical solution using computational fluid dynamic (CFD) techniques is highly time-consuming.

In the present study, the combination of CFD techniques and electric circuit theories (Kirchhoff laws) is used to efficiently simulate thermal behavior of a lithium-ion cell both accurately and quickly. For this purpose, the whole cell regions is treated as a ladder electric circuit in which KCL and KVL equations are solved for each computational electric cell and the Butler-Volmer equation is used to find the potential difference between solid and electrolyte phases.  By this approach, a set of linear system of finite difference equation can be obtained for each computational cell in which the conservation of charge equation, known as compatibility condition, is automatically satisfied. By solving this system of equations iteratively, one can obtain the distribution of electric potential and concentration throughout the cell quickly, which includes the most time consuming part of the numerical procedure. At the next step, the whole battery cell is considered as a heat source and then the specific thermal management strategy is applied to calculate temperature distribution throughout the lithium-ion cell. With the new obtained temperature field, all properties of the cell are updated and this procedure is repeated until the convergence criteria are achieved. The obtained numerical results show good agreement with P2D model by a significant improvement in computational time compared to the previous CFD techniques. It should be mentioned that, this method include the advantages of CFD techniques (accurate results) and equivalent circuit models (low computational time), simultaneously. it is obvious that, this approach is completely different compared with impedance based models— because of using exact PDEs instead of imperial base calculation of local impedances— and create very flexible platform for modeling different lithium-ion battery. It is worth noting that this numerical approach can be simply extended for 3D simulation of cell and battery pack. In addition this can be applied for thermal management of Hybrid electric vehicles with standard battery power demand profiles like US06 driving cycle.