  Starting with generic stationary axially symmetric spacetimes depending on
two spacelike isotropic orthogonal coordinates $x^{1}, x^{2}$, we build
anisotropic fluids with and without heat flow but with wanishing viscosity. In
the first part of the paper, after applying the transformation $x^1\rightarrow
J(x^1)$, $x^2\rightarrow F(x^2)$(with $J(x^1), F(x^2)$ regular functions) to
general metrics coefficients $g_{ab}(x^1,x^2)\rightarrow g_{ab}(J(x^1),
F(x^2))$ with $G_{x^1 x^2}=0$, being $G_{ab}$ the Einstein's tensor, we obtain
that ${\tilde{G}}_{x^1 x^2}=0\rightarrow G_{x^1 x^2}(J(x^1),F(x^2))=0$.
Therefore, the transformed spacetime is endowed with an energy-momentum tensor
$T_{ab}$ with expression $g_{ab}Q_{i}+heat\;term$ (where $g_{ab}$ is the metric
and $\{Q_{i}\}, {i=1..4}$ are functions depending on the physical parameters of
the fluid), i.e. without viscosity and generally with a non-vanishing heat
flow. We show that after introducing suitable coordinates, we can obtain
interior solutions that can be matched to the Kerr one on spheroids or
Cassinian ovals, providing the necessary mathematical machinery. In the second
part of the paper we study the equation involving the heat flow and thus we
generate anisotropic solutions with vanishing heat flow. In this frame, a class
of asymptotically flat solutions with vanishing heat flow and viscosity can be
obtained. Finally, some explicit solutions are presented with possible
applications to a string with anisotropic source and a dark energy-like
equation of state.
