In this work, we show the existence of zero-Hopf periodic orbits in a 10-parametric differential equation of third order
x′′′ + (a1x′ + b1x + c1)x′′ + (a2x′ + b2x + c2)x′ + (a3x′ + b3x + c3)x + k = 0,
where ai, bi, ci, k ∈ R for i = 1, 2, 3. This family is based on a generalization of the equation associated to the Hiemenz flow, when the boundary conditions are neglected, and it will be named as generalized Hiemenz equation. Our approach relies in the use of averaging method. Moreover, the kind of stability of the periodic orbits is determined according to the parameters.