  As a follow up to articles dealing firstly with a convective variational
formulation in a Milne-Cartan framework for non-dissipative multi fluid models,
and secondly with various ensuing stress energy conservation laws and
generalised virial theorems, this work continues a series showing how
analytical procedures developed in the context of General Relativity can be
usefully adapted for implementation in a purely Newtonian framework where they
provide physical insights that are not so easy to obtain by the traditional
approach based on a 3+1 space time decomposition. The present article describes
the 4-dimensionally covariant treatment of various dissipative mechanisms,
including viscosity in non-superfluid constituents, superfluid vortex drag,
ordinary resistivity (mutual friction) between relatively moving non-superfluid
constituents, and the transvective dissipation that occurs when matter is
transformed from one constituent to another due to chemical disequilibrium such
as may be produced by meridional circulation in neutron stars. The
corresponding non dissipative limit cases of vortex pinning, convection, and
chemical equilibrium are also considered.
