Articles written in Pramana – Journal of Physics

    • Electro-osmotic flow and heat transfer of a non-Newtonian nanofluid under the influence of peristalsis


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      This paper investigates the electro-osmotic flow of non-Newtonian nanofluid through a peristaltic microchannel by considering the influence of electro-osmotic phenomenon. The effects of the Brownian and thermophoresis parameters are taken into account. The problem is modulated and its governing equations are solved analytically by assuming long wavelength and low Reynolds number. The distributions of the axial velocity, temperature, nanoparticles volume fraction and volumetric flow rate are achieved and plotted under the influence of various parameters. In addition, the expressions for the skin friction, Nusselt number and Sherwood number are obtained and illustrated through a set of graphs. Furthermore, the trapping phenomenon is examined with the Rayleigh, Brownian and thermophoresis parameters. The present results are useful in medical and biological applications, especially in cancer therapy, which involves suspended nanoparticles of gold in blood (nanofluid)passing through a peristaltic tube (artery).

    • A novelty to the nonlinear rotating Rayleigh–Taylor instability


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      This paper presents a novel approach for studying the nonlinear Rayleigh–Taylor instability (RTI). The system deals with two rotating superposed infinite hydromagnetic Darcian flows through porous media under the influence of a uniform tangential magnetic field. The field allows the presence of currents on the surface of separation. The appropriate linear governing equations are solved and confirmed with the corresponding nonlinear boundary conditions. A nonlinear characteristic of the surface deflection is deducted. Away from the traditional techniques of the stability analysis, the work introduces a new one. The analysis depends mainly on the homotopy perturbation method (HPM). To achieve an analytical approximate periodic solution of the surface deflection, the secular terms are removed. This cancellation resulted in well-known amplitude equations. These equations are utilised to achieve stability criteria of the system. Therefore, the stability configuration is exercised in linear aswell as nonlinear approaches. The mathematical procedure adopted here is simple, promising and powerful. The method may be used to treat more complicated nonlinear differential equations that arise in science, physics andengineering applications. A numerical calculation is performed to graph the implication of various parameters on the stability picture. In addition, for more convenience, the surface deflection is depicted.

    • Nonlinear stability analysis of coupled azimuthal interfaces between three rotating magnetic fluids


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      The current work deals with the nonlinear azimuthal stability analysis of coupled interfaces between three magnetic fluids. The considered system consists of three incompressible rotating magnetic fluids throughout the porous media. Additionally, the system is pervaded by a uniform azimuthal magnetic field. Therefore, for simplicity, the problem is considered in a planar configuration. The adopted nonlinear approach depends mainly on solving the linear governing equations of motion with the implication of the corresponding convenient nonlinear boundary conditions. The linear stability analysis resulted in a quadratic algebraic equation in the frequency of the surface waves. Consequently, the stability criteria are theoretically analysed. A set of diagrams is plotted to discuss the implication of various physical parameters on the stability profile. On the other hand, the nonlinear stability approach revealed two nonlinear partial differential equations of the Schrödinger type. With the aid of these equations, the stability of the interface deflections is achieved. Subsequently, the stability criteria are theoretically accomplished and numerically confirmed. Regions of stability/instability are addressed to illustrate the implication of various parameters on the stability profile.

    • EHD instability of two rigid rotating dielectric columns in porous media


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      The present work analyses the linear azimuthal stability of a single interface between two cylindrical dielectric fluids. The theoretical model consists of two incompressible rotating electrified fluids throughout the porous media. The system is influenced by a uniform azimuthal electric field. The inner cylinder is filled with a viscous liquid. The outer one is occupied by an inviscid gas. The problem meets its motivation from a geophysics point of view. Therefore, for more convenience, the problem is considered in a planar configuration. Typically, the normal mode analysis is used to facilitate the stability approach. The examination resulted in a stream function, which is governed by a fourth-order ordinary differential equation with complicated variable coefficients. By means of the Mathematica software along with the special functions, the distribution of the stream function is written in terms of the modified Bessel functions. A non-dimensional procedure exposes some non-dimensional numbers, for instance, Weber, Ohnesorg, Taylor, Rossby and Darcy numbers. These numbers are considered with regard to the temporal and spatial increase of both frequency and modulation. The linear stability theory generated a very complicated transcendental dispersion equation. The influences of various physical parameters in the stability profile were studied as well.

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