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The paper is focused on magnetorheological (MR) clutches applied in industrial drive systems working in a steady continuous-duty state. The main goal of the carried out numerical and analytical analyses oriented towards electrical power consumption, copper losses (Joule heat) in an excitation coil, spatial temperature distributions and the highest temperature possible for an MR fluid is to compare MR clutches due to a different number of discs. The authors considered selected representative MR multi-disc clutches with one, two, three or four discs, developing clutching torque $T_c$ equal to 20, 35 and 50 Nm. These clutches were constructed based on the in-house design that integrates analytical and field methods (further in the paper referred to as the integrated analytical-field design method) described in the literature. The thermal computer simulation results obtained with the help of the AGROS2D program, combined with findings achieved with the use of simplified physical reasonings, allow one to draw the conclusion that the most advantageous, recommended number of discs for a magnetorheological clutch from the viewpoint of various (both constructional and thermal) criteria is the number of discs: N = 2. This conclusion takes into account the results presented earlier in the literature: the choice is a compromise between decreasing the mass (volume) of the MR clutches and increasing both the electrical power consumption and the maximum temperature of MR fluids in a clutch working region as the number of discs, N, increases. Full article