  In this paper we investigate for further symmetry properties of the nonlinear
fin equations of the general form $u_t=(E(u)u_x)_x + h(x)u$ rather than recent
works on these equations. At first, we study the projective (fiber-preserving)
symmetry to show that equations of the above class can not be reduced to linear
equations. Then we determine an equivalence classification which admits an
extension by one dimension of the principal Lie algebra of the equation. The
invariant solutions of equivalence transformations and classification of
nonlinear fin equations among with additional operators are also given.
