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The paper investigates a planar hydraulic jump during a thin film flow over a two-dimensional obstacle spanning the entire width of a horizontal channel. The shallow water analysis supported by numerical simulations identifies a hydraulic drop and simultaneous jump-drop-jump phenomenon under certain flow conditions. A hydraulic drop although observed for flow over obstacles in the macro-domain has never been reported for a thin film flow. The study, thus, establishes the efficacy of shallow water analysis which, with a novel solution methodology, predicts jump and drop characteristics over obstacles with much less computational effort compared to computational fluid dynamics based simulations. In addition, analytical expressions for jump efficiency and head loss across jump along with energy dissipation analysis are provided for a viscous jump. The numerical simulations reveal recirculation zones close to the channel floor and at the free surface, and the energy dissipation analysis provides a quantitative criterion for formation of recirculation zone pair. The observations are consolidated as a phase diagram which characterizes a myriad of free surface profiles based on operating and geometrical parameters.

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Abstract

The article deals with visualization of heatlines and isotherms during cooling of a hot moving steel plate numerically. The cooling of the plate is assumed using single spray-water jet. The visualization process is carried out by forming and discretizing the governing energy equation based on finite volume method. The linear algebraic equations are solved by tri-diagonal matrix algorithm (TDMA). Accordingly, a numerical code is developed on FORTRAN platform. In the computational domain, a suitable heat transfer region for cooling is identified analyzing the heatline distribution in the domain and depends on the process parameters. Accordingly a parametric study is performed and reveals that effective heat transfer region increases with increasing jet velocity and cooling methods, and decreases with increasing plate velocity.