The paper studies the possibility of unifying the two branches of the irreversible engineering thermodynamics, namely finite physical dimensions thermodynamics (FPDT) and finite speed thermodynamics (FST), aiming to take into account their benefits and successes and to eliminate as much as possible their disadvantages. Actually, the two branches have the same goal, that of optimizing the performance of thermal machines and they were developed almost in parallel. Analysis of thermal machines cycles using the FPDT is based on the first and second law of thermodynamics, in the presence of the external irreversibility generated by the heat transfer at finite temperature difference at the thermal reservoirs and internal irreversibility, using the internal source of entropy considered as parameter or function to be specified. The FST is based on the mathematical expression of the first law for process with finite speed that involves three causes of internal irreversibility, namely the finite speed of the piston, internal friction and throttling. The direct method is used in the analysis of thermal machines cycles to provide analytical expression of the machine performance (efficiency and power) as a function of the speed of the process. The significant progress of these two branches of irreversible engineering thermodynamics makes their unification a desirable outcome. We hope that the new model yielded from this study will provide an even more important tool for engineers that will help their attempt to a better design and optimization of thermal machines.