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The local heat transfer enhancement in a parallel duct by local blowing or suction slot at the heated wall has been numerically studied on adaptive grid system, which is found from new grid and adaptive grid generation methods. The flow solver employed two-dimensional k-.epsilon. turbulent model, wall function approximation on a generalized nonstaggered grid system and the SIMPLE algorithm equipped by the QUICK scheme for convective fluxes. The Sorenson and Steger elliptical grid generation method is improved to have the function of grid control along all of the boundaries. The improvement is achieved by interpolating interior control functions from those found at boundaries through transfinite interpolation, and two new elliptic grid generation methods are subsequently developed. Three new elliptic adaptive grid generation methods are also developed based on the interpretation of control functions and Anderson''s adaptive grid method. Among adaptive grid methods, the most promising one combines present elliptic grid generation, Anderson adaptive grid methods, and a new method retaining background grid clustering and stretching. Numerical test cases have illustrated the feasibility of all the grid generation and adaptive grid methods. In studying the local heat transfer enhancement, arrangements introducing a stream of injecting fluid or sucking fluid through a slot at wall are employed. Cases of uniform temperature and uniform heat flux at heated wall, where the opposite wall is adiabatic, are examined. It is found that both arrangements can enhance the local heat transfer coefficient at the downstream side of the slot. The considered situations are described by parameters of the momentum flux ratio between injected (or and main stream, slot angle measured from the upstream wall,
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