For co-current flow, according to Section 5, the roots of 𝒫 ́3 are positive and distinct real numbers and, therefore, the AS Eqs. ( )-( ), is applicable. Table shows the values of 𝑥 𝑒𝑝(1,2) by solving Eq. (32) by a hybrid numerical method, considering the bisection and secant methods, and Eq. ( ) by successive substitutions (except for the adiabatic case, which was calculated using the exact expression Eq. ( ), given by Bertoli et al. ). Table shows the results for 𝑥 𝑠𝑝(2) by solving Eq. ( ) by the hybrid numerical method and Eq. ( ) by successive approximations.