This work is focused on the analytical modeling of the problem concerning steady, laminar, natural convection fully developed flow of a particulate suspension through an infinitely long vertical circular pipe in the presence of a transverse magnetic field and fluid heat generation or absorption effects. The wall of the pipe is maintained at a uniform constant temperature. The analytical solutions for the velocity and temperature profiles of both phases are given in terms of Bessel functions. A parametric study of the physical parameters involved in the problem is performed and the obtained results are presented graphically to show special trends of the solutions.