The slender channel equations for laminar flow are solved downstream of the entrance of curved channels of variable height. The singularities at the entrance are removed with coordinate transformations which stretch the boundary layer and shrink the core flow. Initial conditions at the entrance are obtained from the governing equations with only the streamwise velocity specified. A modified box scheme is used to develop a finite-difference method which allows the derivatives of the dependent variables across the channel to be discontinuous at the interface between the boundary layer and core flow. Numerical results are presented for several channel geometries and entry conditions.

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