Numerical solution of laminar boundary layer flow over a flat plate in a nonuniform stream

The laminar flow and heat transfer over an isothermalflat plate in a free stream with nonuniform velocity havebeen analysed. The governing equations are transformed withFalkner-Skan transformations into a nondimensional formwhich is more appropriate for numerical solution. A fullyimplicit numerical method (with a hybrid representation forthe convective term normal to the streamwise direction) isused for solving the governing equations. This leads to asystem of linear algebraic equations of the tridiagonal typewhere a factorization method is used to obtain the solution.Two practical cases are considered. In the first case,a flat plate is located in the laminar wake of an upstreamplate. In the second case, a flat plate is inserted in thelaminar shear layer joining a uniform stream and a quiescentfluid. The dependence of the boundary-layer parameters on thelateral and the downstream shifts of the plate have beeninvestigated. It was found that the nonuniformity of thefree stream velocity causes reductions in both the wallshear stress and heat transfer relative to the correspondingvalues for· uniform free stream. These relative reductionsdecrease with increasing downstream distance along the platein the upper half of the wake. In the lower half of the