Summary: Two-dimensional steady boundary layer equations, for simultaneous heat and fluid flow within ducts, are handled through the generalized integral transform technique. The momentum and energy equations are integral transformed by eliminating the transversal coordinate and by reducing the PDE’s to an infinite system of coupled nonlinear ordinary differential equations for the transformed potentials. An adaptively truncated version of this ODE system is numerically handled through well-known initial value problem solvers, with automatic precision control procedures. The explicit inversion formulae are then recalled to provide analytic expressions for velocity and temperature fields and related quantities of practical interest. Typical examples are presented in order to illustrate the hybrid numerical analytical approach and its convergence behaviour.