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A Mathematical model describing the heat transfer and fluid hydrodynamics during the engagement cycles of “wet” clutches have been developed. The model equations of heat balance for the separator, friction materials, core plate, and automatic transmission oil (ATF) or air in the clearance between separators and friction materials were formulated. The momentum balance for ATF flow in the friction lining (porous medium) during the engagement was considered. Proper boundary conditions at the interface and boundary conditions at the inner and outer radius of the clutches were accounted for. The model includes the simulation of engagement cycles for both the traditional (two-sided) wet clutches and the single-sided wet clutches.