The problem of unsteady laminar ¯ow and heat transfer of a particulate suspension in an electrically conducting ¯uid through channels and circular pipes in the presence of a uniform transverse magnetic ®eld is formulated using a two-phase continuum model. Two dierent applied pressure gradient (oscillating and ramp) cases are considered. The general governing equations of motions (which include such eects as particulate phase stresses, magnetic force, and ®nite particle-phase volume fraction) are nondimensionalized and solved in closed form in terms of Fourier cosine and Bessel functions and the energy equations for both phases are solved numerically since they are non-linear and are dicult to solve analytically. Numerical solutions based on the ®nitedierence methodology are obtained and graphical results for the ¯uid-phase volumetric ¯ow rate, the particle-phase volumetric ¯ow rate, the ¯uid-phase skin-friction coecient and the particle-phase skin-friction coecient as well as the wall heat transfer for plane and axisymmetric ¯ows are presented and discussed. In addition, these numerical results are validated by favorable comparisons with the closed-form solutions. A comprehensive parametric study is performed to show the eects of the Hartmann magnetic number, the particle loading, the viscosity ratio, and the temperature inverse Stokes number on the solutions.