The sole irreversibility considered in an endo-reversible Carnot heat-engine model is the loss of heat-resistance between the engine and its surrounding heat reservoirs. This paper presents a new steady-state-flow irreversible Carnot heat-engine model by taking additional account of several internal irreversibilities of the heat engine, such as heat leakage, friction, turbulence and other undesirable irreversibility factors. This is done by means of a constant parameter and a constant coefficient, together with the loss of heat-resistance. Analysis and optimisation of the model were carried out to investigate the effect of the various irreversibilities on the performance of the model. Numerical examples illustrate the effectiveness of the model.