Fully developed turbulent and laminar flows through symmetric planar and axisymmetric expansions with heat transfer were modeled using a finite-difference discretization of the boundary-layer equations. By using the boundary-layer equations to model separated flow in place of the Navier-Stokes equations, computational effort was reduced permitting turbulence modeling studies to be economically carried out. The continuity and momentum equations were solved in a coupled manner. The validity of the once-through calculation scheme utilizing the FLARE approximation was studied by using a multiple sweep procedure in which the FLARE approximation is removed after the first sweep;For laminar constant property flow, the equations were nodimensionalized so that the solution was independent of Reynolds number. Two different dependent hydrodynamic variable sets were tried: the primitive variable set (u-v), and the streamwise velocity stream function variable set (u-(psi)). The predictions of the boundary-layer equations were identical regardless of the variable set used. The predictions of the boundary-layer equations for parameters associated with the trapped eddy compared well with the predictions of the Navier-Stokes equations and experimental measurements for laminar isothermal flow when the Reynolds number was above 200 and the ratio of inlet to outlet channel diameter(width) was less than 1/3. The reattachment length and the flow field outside of the trapped eddy were well predicted for Reynolds numbers as low as twenty for laminar flow;The Boussinesq assumption was used to express the Reynolds stresses in terms of a turbulent viscosity. Near-wall algebraic turbulence models based on Prandtl's-mixing-length model and the maximum Reynolds shear stress were compared. The near-wall models were used with the standard high-Reynolds-number k-(epsilon) turbulence model. A low-turbulent-Reynolds-number k-(epsilon) model was also investigated but found to be unsuitable for separated flow. The maximum-shear-stress near-wall model gave better predictions than the Prandtl-mixing-length models, especially for heat transfer. The predicted turbulent heat transfer is primarily dependent on the turbulence model used in the near-wall region. Globally iterating over the flow field had a more pronounced effect on the heat transfer solution than on the hydrodynamic solution.