Abstract:The effect of compressibility of fluids on the linear electrohydrodynamic instability of a dielectric liquid sheet issued from a nozzle into an ambient dielectric stationary gas in the presence of a horizontal electric field is investigated. It is found that increasing the Mach number from subsonic to transonic causes the maximum growth rate and the dominant wavenumber of the disturbances to increase, and the increase is higher in the presence of the electric field. Liquid compressibility has been found to hav… Show more
“…Equations (14) to (25) are the linearized equations. The normal mode solutions of the governing equations can be written as ðu 0 , v 0 , p 0 , g , p g , 0 g , Þ ¼ ðuð yÞ, vð yÞ, pð yÞ, g ð yÞ, p g ð yÞ, g ð yÞ, 0 Þ Á expðikx þ !tÞ ¼…”
This article presents the linear stability analysis of an electrified liquid sheet injected into a compressible ambient gas in the presence of a transverse electric field. The disturbance wave growth rates of sinuous and varicose modes were determined by solving the dispersion relation of the electrified liquid sheet. It was determined that by increasing the Mach number of the ambient gas from subsonic to transonic, the maximum growth rate and the dominant wave number of the disturbances were increased, and the increase was greater in the presence of the electric field. The electrified liquid sheet was more unstable than the non-electrified sheet. The increase of both the gas-to-liquid density ratio and the electrical Euler number accelerated the breakup of the liquid sheet for both modes; while the ratio of distance between the horizontal electrode and the liquid-sheet-to-sheet thickness had the opposite effect. High Reynolds and Weber numbers accelerated the breakup of the electrified liquid sheet.
“…Equations (14) to (25) are the linearized equations. The normal mode solutions of the governing equations can be written as ðu 0 , v 0 , p 0 , g , p g , 0 g , Þ ¼ ðuð yÞ, vð yÞ, pð yÞ, g ð yÞ, p g ð yÞ, g ð yÞ, 0 Þ Á expðikx þ !tÞ ¼…”
This article presents the linear stability analysis of an electrified liquid sheet injected into a compressible ambient gas in the presence of a transverse electric field. The disturbance wave growth rates of sinuous and varicose modes were determined by solving the dispersion relation of the electrified liquid sheet. It was determined that by increasing the Mach number of the ambient gas from subsonic to transonic, the maximum growth rate and the dominant wave number of the disturbances were increased, and the increase was greater in the presence of the electric field. The electrified liquid sheet was more unstable than the non-electrified sheet. The increase of both the gas-to-liquid density ratio and the electrical Euler number accelerated the breakup of the liquid sheet for both modes; while the ratio of distance between the horizontal electrode and the liquid-sheet-to-sheet thickness had the opposite effect. High Reynolds and Weber numbers accelerated the breakup of the electrified liquid sheet.
“…The second condition is called the reproducing property and a Hilbert space which possesses a reproducing kernel is called a reproducing kernel Hilbert space (RKHS). More details can be in [7][8][9][10][11][12][13][14]. A description of the RKM for discretization of the linear fractional Fredholm integrodifferential equations problem (4)-(5) is presented in Section 2.…”
This article is devoted to both theoretical and numerical studies of nonlinear fractional Fredholm integrodifferential equations. In this paper, we implement the reproducing kernel method (RKM) to approximate the solution of nonlinear fractional Fredholm integrodifferential equations. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the solution of the nonlinear fractional Fredholm integrodifferential equation. Uniformly convergence of the approximate solution produced by the RKM to the exact solution is proven.
“…Fractional derivatives have many applications, such as diffusion problems, liquid crystals, proteins, mechanics structural control, and biosystems [1][2][3][4][5][6][7][8][9]. Several analytical and numerical methods are used to solve fractional boundary and initial value problems, such as generalized differential transform, the Adomian decomposition method, the homotopy perturbation technique, fractional multistep methods, the spline approximation method, and the collocation method [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”
In this article, a modified implicit hybrid method for solving the fractional Bagley-Torvik boundary (BTB) value problem is investigated. This approach is of a higher order. We study the convergence, zero stability, consistency, and region of absolute stability of the modified implicit hybrid method. Three of our numerical examples are presented.
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