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The flux density pattern on the disc face of a magnetic clutch is analysed by conformal mapping of the coil-gap configuration. The suspension rheology of iron/silicone mixtures is used to derive the viscous torque transmitted by the clutch disc rotating in a non-Newtonian medium in a narrow enclosure. Since disc Reynolds numbers are small for normal operating slips of fluid clutches, only Couette-type laminar flow occurs without boundary layer in the clutch gap. This viscous torque cannot be predicted by theories based on the shear failure of dry masses. Experimental measurements on a disc-type clutch using torque, speed and temperature transducers show that the theory based on apparent viscosity of the fluid mixture under various shear rates, magnetic inductions and volume fractions is more pertinent to the fluid magnetic clutch.