A multi-geometry and multi-physics model is developed for a Li-ion battery module which includes three cells connected in series by electrical busbars. The model can be used to predict the 3D profiles of the electrical potentials and temperature in the battery. The physics-based porous electrode (P2D) model is used to predict the electrochemical behavior of the cells, and the coupling between the P2D model and the electrical/thermal equations is simplified through a linear approximation method. This approximation is useful at rates of at least 5C and reduces the computation time significantly. The anisotropic conductive properties for the regions where conductors are separately arrayed are discussed in detail, and the model predictions are presented and discussed.