The two‐dimensional mixed convection in a horizontal sinusoidal corrugated channel (CC) is investigated. The two‐phase mixture model (2PMM) is implemented in Ansys Fluent software to simulate the nanofluid (NF) flow. The mathematical formulation of the 2PMM shows the limitation of the single‐phase mixture model linked to the absence of the slip particle‐fluid velocity and, consequently, the parameters that depend on this factor, particularly the diffusion and the drag coefficients. The laminar mixed convection regime is studied, where the NF copper–water is considered under a uniform temperature wall. The simulation results agree with three published works on mixed laminar convection and forced laminar convection in horizontal CC. The effects of nanoparticles volume fraction (ϕ), Richardson number (Ri), wavelength (λ), and wave amplitude (α) are investigated. The results showed that for a mixed flow, the improvement of heat transfer in a horizontal CC could essentially be obtained for a low Ri, where for a given λ, the trueNu ¯ $\bar{{Nu}}$ submits an apparent increase with the increase of λ, that is, for Ri = 0.05 (λ = 3, α = 0.3, ϕ = 3%), the enhancement is 29.7% for trueNu ¯ $\bar{{Nu}}$ and 128.5% for average entropy production compared to the smooth channel. The effect of ϕ on trueNu ¯ $\bar{{Nu}}$ or trueS g ¯ $\bar{{S}_{g}}$ is weakly dependent on Ri. The use of a Cu–water NF with a volume fraction of 5% (α = 0.2, λ = 2) leads to an increase in the trueNu ¯ $\bar{{Nu}}$ of 17.6% for Ri = 0.05 and 16.4% for Ri = 10 compared to conventional water fluid.