  In this paper we apply classical and recent techniques from quaternionic
analysis using parabolic Dirac type operators and related Teodorescu and
Cauchy-Bitzadse type operators to set up some analytic representation formulas
for the solutions to the time depedendent incompressible viscous
magnetohydrodynamic equations on some conformally flat manifolds, such as
cylinders and tori associated with different spinor bundles. Also in this
context a special variant of hypercomplex Eisenstein series related to the
parabolic Dirac operator serve as kernel functions.
