  We study shear-free spherically symmetric relativistic gravitating fluids
with heat flow and electric charge. The solution to the Einstein-Maxwell system
is governed by the generalised pressure isotropy condition which contains a
contribution from the electric field. This condition is a highly nonlinear
partial differential equation. We analyse this master equation using Lie's
group theoretic approach. The Lie symmetry generators that leave the equation
invariant are found. The first generator is independent of the electromagnetic
field. The second generator depends critically on the form of the charge, which
is determined explicitly in general. We provide exact solutions to the
gravitational potentials using the symmetries admitted by the equation. Our new
exact solutions contain earlier results without charge. We show that other
charged solutions, related to the Lie symmetries, may be generated using the
algorithm of Deng. This leads to new classes of charged Deng models which are
generalisations of conformally flat metrics.
