Furthermore, the length of the tubes is 10 m, and an ambient temperature of 25 °C is assumed. For this set of parameters, the roots of 𝒫 ́3 are real and distinct (𝜆 ́0 = -1.3067, 𝜆 ́1 = 0.6829, 𝜆 ́2 = 8.6988) and the solution in the form of Eqs. ( )-( ) -with the sign change given by Eq. ( ) -, is applicable. However, as discussed in Sections 1 and 7, to achieve solution generalization for this flow arrangement, it is necessary to analyze the character of the roots. Given the complexity and extension of this analysis (see Bertoli et al. ), it is delegated to future work.