The propagation speed, shape and stability of the rim generated by a liquid-curtain breakup are studied. In the experiment, a liquid curtain surrounded by a slot die, edge guides and the surface of a roller breaks at the contact point between the edge guide and roller in a low-Weber-number range, and the rim propagates in the horizontal direction. Except for the initial time, the rim is almost straight and has a nearly constant propagation speed. For an Ohnesorge number much smaller than 1, unevenness occurs on the rim and the droplets separate from it. When the Ohnesorge number is of the order of unity, the rim becomes convex vertically downward, and the liquid lump flows down. The shape, propagation speed and surface stability of the rim are discussed by analysing the equation proposed by Entov & Yarin (J. Fluid Mech., vol. 140, 1984, pp. 91–111). It is shown that the volume flow rate condition at the slot die exit is important to explain the propagation of the rim. Additionally, in the initial stage of the curtain breakup, the Plateau–Rayleigh instability causes unevenness on the rim surface, and after the rim reaches the slot die exit, the Rayleigh–Taylor instability generates a liquid lump on the rim, which grows into droplets when the Ohnesorge number is much less than 1.

In this research, the flow wave propagation, speed, and suppression of pulsation through an elastic tube were studied by using a diaphragm pump. The flow fluctuations with shocking pressure fluctuations occur through the elastic tube because the check ball is blocked to prevent reverse flow. Thus, the check ball is one of the causes of pulsating flow in diaphragm pumps, but only a few studies have analyzed the relationship among the check ball movement, pressure, and flow fluctuations. In this study, we constructed several elastic tube experiments: (i) single-tube model; (ii) two-tube model. To predict the flow wave propagation and pulsation through an elastic tube, we developed an axisymmetric theoretical model and compared it with the experimental results. Based on our study, the main results are as follows: The relationship among the check ball movement, pressure, and flow fluctuations shows that the pressure and flow rate pulsation is caused by the asymmetry of the check ball movement. Additionally, we observed that the theoretical flow wave propagation trend had good agreement with the experimental results although the flow wave speed in the urethane-tube experiment differed significantly from the theoretical prediction. Furthermore, the amplitude of the pulsation increased significantly because of the reflected wave at the tube exit, but it did not increase when the resistance was added at the exit. We also observed that the pulsation is reduced more in the silicon tubes compared with urethane tubes because the deformation of the silicon tubes is larger than that of urethane tubes.

In this paper, investigate a two dimensional unsteady Magneto hydro dynamics (MHD) free convection flow of viscous incompressible and electrically conducting fluid flow past an vertical plate in the presence of Grashof Number, Modified Grashof Number, Prandtl Number, Schamidt Number as well as Dufour effects. The governing equations of the problem contain a system of non-linear partial differential equations; have been transformed into a set of coupled non-linear ordinary differential equations which is solved numerically by applying well known explicit finite difference method. The Finite-difference method is an enormously used technique to investigate of the general non linear partial differential equation. Partial differential equations occur in many branches of applied mathematics for example, in hydrodynamics, elasticity, quantum mechanics. Hence, the proposed study is to investigate the numerical results which are performed for various physical parameters such as velocity profiles, temperature distribution and concentration profiles within the boundary layer are separately discussed in graphically.

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There exist numerous numerical methods for solving the initial value problems of ordinary differential equations. The accuracy level and computational time are not the same for all of these methods. In this article, the Modified Euler method has been discussed for solving and finding the accurate solution of Ordinary Differential Equations using different step sizes. Approximate Results obtained by different step sizes are shown using the result analysis table. Some problems are solved by the proposed method then approximated results are shown graphically compare to the exact solution for a better understanding of the accuracy level of this method. Errors are estimated for each step and are represented graphically using Matlab Programming Language and MS Excel, which reveals that so much small step size gives better accuracy with less computational error. It is observed that this method is suitable for obtaining the accurate solution of ODEs when the taken step sizes are too much small.