In the design of flow geometries consisting of channels such as high-temperature gas heat exchangers, a great number of design parameters can be chosen, why solving the turbulent Reynolds Averaged Navier-Stokes (RANS) equations by CFD coupled with other physics can become computational demanding. Therefore, we here propose a method for a significant reduction of computational resources and consequent high speed. This is done by using the less computational demanding Darcy's Law (DL) to approximate the laminar and turbulent flows in channels with circular and arbitrary cross-sections. To obtain the right velocity profile, an artificial permeability variation across the cross-section of the channel is determined. This is obtained based on the analogy of the DL and Darcy–Weisbach equation (DW). Results demonstrate that the DL approximations predict velocities and pressures distributions from the laminar and turbulent flows in the channels with circular and arbitrary cross-sections very well. At the same time, the models with DL approximations reduce the runtime up to ~40 times as compared to RANS, and improve the stability and convergence of the model. Lastly, a cross-flow heat exchanger is studied as an application of the DL approximations.