In this study, Prandtl's transposition theorem is used to stretch the ordinary coordinate system in certain direction. The wavy surface can be transferred into a calculable plane coordinate system. The governing equations of laminar-forced convection along wavy surface are derived from complete Navier–Stokes equations. A simple transformation is proposed to transform the governing equations into the boundary layer equations and solved numerically by the cubic spline collocation method. Meanwhile, we derive an expression for the dimensionless entropy generation equation, which takes into account both heat-transfer irreversibility and fluid friction irreversibility. The distribution of both entropy generation number and Bejan number is studied. It shows that irreversibility is periodically dominated by the heat transfer and the friction in laminar-forced convection.