Natural convection is important in systems of large dimensions where h
eated sections may develop over a significant length of the vertical b
oundary. In superconducting magnetic energy storage (SMES) systems the
postulated design includes baths 20 m high housing superconductive co
ils. It is of interest to determine how natural circulation evolves in
such a bath when a significant number of turns become normal, and wha
t additional heat capacity is afforded by natural circulation. In this
paper the circulation velocity resulting from the natural convection
process is evaluated. A coupled set of energy, mass and momentum equat
ions is solved in two dimensions. These equations are formulated using
the two-fluid model, which describes He II as consisting of two inter
penetrating fluids, the normal and superfluid. They are also solved fo
r a one-fluid model treating He II as a single fluid. The two models a
re compared to show that the two-fluid model illustrates the existence
of a counterflow resulting from the motion of the two fluids with or
opposite to the applied heat flux. A well established single-fluid num
erical method, the marker and cell (MAC) method, has been adapted to s
olve the two-fluid equations. Results indicate that natural convection
cells in superfluid helium evolve in a fundamentally different way th
an those in ordinary fluids, because of the counterflow that develops
in the presence of temperature gradients.