  In this communication we deal with the exact solutions called
"pseudosimilarity" of a steady free convection problem studied by by Kumaran
and Pop (2006). They showed that there is no similarity solution for the case
of a wall temperature as $T_{w}(x)\sim x^{-{1/2}}$ (resp. a wall heat flux as
$q_{w}(x)\sim x^{-{3/2}},$ and a dimensionless heat transfer coefficient
$h_{w}(x)\sim x^{-1}$). We shall present some results about existence and
asymptotic behaviour of new exact solutions of the resulting boundary value
problem for each case.
