The aim of this paper is to present a developed detailed model for the simulation of automotive fin-and-tube heat exchangers (Compact Heat Exchanger Simulation Software, CHESS). The simulation strategy and the mathematical methodology are described in detail. The model is based on a 3D discretization around the tubes as small heat exchangers, where the appropriate governing equations (mass, momentum and energy) are applied for each control volume on the air-side, the solid elements, and the coolant side. Some verification and illustrative results are also provided to show the features of the model. A comparison between numerical simulation results and experimental data is presented in a companion paper (Part 2).