The recovery of precious metals is necessary for environmental and economic reasons. Spent catalysts from automotive industry containing precious metals are very attractive recyclable material as the devices have to be periodically renovated and eventually replaced. This paper presents the method of removing platinum from the spent catalytic converters applying lead as a collector metal in a device used to wash out by using mangetohydrodynamic stirrer. The article includes the description of the methods used for modeling of magnetohydrodynamic phenomena (coupled analysis of the electromagnetic, temperature and flow fields) occurring in this particular device. The paper describes the general phenomena and ways of coupling the various physical fields for this type of calculation. The basic computational techniques with a discussion of their advantages and disadvantages are presented.