In this paper, the techniques of the calculus of variations are used to study the general problems in magnetohydrodynamic lubrication when two or more control variables are bounded. The load integral, in the case of a magnetohydrodynamic slider bearing, is maximized with film thickness and conductivity functions as bounded control variables. It is shown that if the conductivity of a bearing surface is of step-type function then uniformly applied magnetic fields are more advantageous.

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