The present paper presents a validation of momentum boundary-layer integral solution and finite-volume Reynolds-Averaged Navier Stokes (RANS) Computational Fluid Dynamics (CFD) results for skin friction around airfoils NACA 8H12 and MMB-V2 as well as heat transfer around an isothermal cylinder with rough surface. The objective is to propose a two-equation integral model and compare its predictions to results from a robust CFD tool, to experimental data and to results from a one-equation integral solution. The latter is the mathematical model used by classic 2D icing codes. All proposed model predictions are compared to CFD results for verification and, whenever possible, to experimental data for validation. The code-to-code verification brings reliability to both the proposed code and the CFD tool when there is no test data available. The present authors implemented a numerical code that solves a set of integral equations of laminar and turbulent momentum boundary layer that was not yet applied to icing or ice protection problems. Before implementing the proposed model into icing and thermal ice protection numerical codes, it is necessary to validate the momentum boundary layer and CFD results separately. The present authors propose the use of mathematical models and correlations for transition not yet applied to flows over rough or clean surfaces subjected to icing conditions. Traditionally, to simulate icing or anti-icing cases, the codes use one-equation models and consider an abrupt transition process, i.e., zero transition length not a transition region with a finite length. The proposed model assumes that a rough surface or laminar separation as well as natural - low turbulence level as in the atmosphere - or by-pass mechanisms - high turbulence level as inside icing tunnels - can trigger laminar-turbulent transition. The more accurate the predictions of transition onset and length, the more accurate the predicted heat and mass transfer will be, for future application in icing simulations. In addition, the pressure gradient and its variation are relevant at high angles of attack and for flow around thick or even ice contaminated airfoils. However, those pressure variation effects on velocity profile are also taken into account by the two-equation models proposed herein. Therefore, the present paper includes some effects not considered by the literature on icing in order to validate results against experimental data and to verify integral code predictions with regards to CFD tool results.