The problem of unsteady motion of an electrically conducting viscous liquid contained in a cylindrical vessel in the presence of an axially symmetric magnetic field of constant strength has been solved exactly by using concurrently two methods of operational calculus—the finite Hankel transform, and the Laplace transform. Results of these operations for general boundary conditions are presented in convolution integral form. The exact solutions of two special cases are presented in terms of tabulated functions, including those especially developed for the purposes of this paper. By examining the limiting cases of these special results, verification of results that have previously appeared in the literature and other interesting phenomena arise.

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