E. Momoniat

Lie Group Solution for Free Convective Flow of a Nanofluid Past a Chemically Reacting Horizontal Plate in a Porous Media

The optimal homotopy analysis method (OHAM) is employed to investigate the steady laminar incompressible free convective flow of a nanofluid past a chemically reacting upward facing horizontal plate in a porous medium taking into account heat generation/absorption and the thermal slip boundary condition. Using similarity transformations developed by Lie group analysis, the continuity, momentum, energy, and nanoparticle volume fraction equations are transformed into a set of coupled similarity equations. The OHAM solutions are obtained and verified by numerical results using a Runge-Kutta-Fehlberg fourth-fifth order method. The effect of the emerging flow controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction have been presented graphically and discussed. Good agreement is found between analytical and numerical results of the present paper with published results. This close agreement supports our analysis and the accuracy of the numerical computations. This paper also includes a representative set of numerical results for reduced Nusselt and Sherwood numbers in a table for various values of the parameters. It is concluded that the reduced Nusselt number increases with the Lewis number and reaction parameter whist it decreases with the order of the chemical reaction, thermal slip, and generation parameters.

Exact flow of a third-grade fluid on a porous wall

The flow of a third-grade fluid occupying the space over a wall is studied. At the surface of the wall suction or blowing velocity is applied. By introducing a velocity field, the governing equations are reduced to a non-linear partial differential equation. The resulting equation is analysed analytically using Lie group methods.

Approximate conditional symmetries and approximate solutions of the perturbed Fitzhugh–Nagumo equation

We consider a perturbation of the Fitzhugh–Nagumo equation. The perturbation is proportional to the electric potential across the cell membrane. The purpose of this investigation is to determine the effects of a change in electric potential across the cell membrane. Exact solutions of the perturbed equation are easily obtained from the well-known solutions of the unperturbed Fitzhugh–Nagumo equation. The method of approximate conditional symmetries is used to obtain first-order approximate solutions of the perturbed Fitzhugh-Nagumo equation. The approximate solutions are compared with the exact solutions of the perturbed equation. The exact solutions of the perturbed equation do not indicate a change in the wave front connecting one constant state to another. There is only a proportional increase or decrease in the constant nonzero state. The approximate solutions do show a change in the shape of the wave front connecting two constant states as well as a proportional increase or decrease in the constant n...

Non-linear diffusion of an axisymmetric thin liquid drop: group-invariant solution and conservation law

The non-linear diffusion equation describing the axisymmetric spreading of a thin incompressible liquid drop under gravity on a horizontal plane is considered. A group-invariant solution is derived by finding a linear combination of the three Lie point symmetries admitted by the non-linear diffusion equation which conserves the total volume of the liquid drop and which satisfies the boundary condition of vanishing thickness at the rim. It is shown that conservation of the total volume of the liquid drop and the existence of a certain conservation law for the differential equation impose the same condition on the constants in the linear combination of the three Lie point symmetries.

Analytical Modelling of Three-Dimensional Squeezing Nanofluid Flow in a Rotating Channel on a Lower Stretching Porous Wall

A coupled system of nonlinear ordinary differential equations that models the three-dimensional flow of a nanofluid in a rotating channel on a lower permeable stretching porous wall is derived. The mathematical equations are derived from the Navier-Stokes equations where the governing equations are normalized by suitable similarity transformations. The fluid in the rotating channel is water that contains different nanoparticles: silver, copper, copper oxide, titanium oxide, and aluminum oxide. The differential transform method (DTM) is employed to solve the coupled system of nonlinear ordinary differential equations. The effects of the following physical parameters on the flow are investigated: characteristic parameter of the flow, rotation parameter, the magnetic parameter, nanoparticle volume fraction, the suction parameter, and different types of nanoparticles. Results are illustrated graphically and discussed in detail.

An implicit series solution for a boundary value problem modelling a thermal explosion

An implicit series solution admitted by a boundary value problem modelled by a Lane-Emden equation of the second kind is obtained. The boundary value problem was derived by Frank-Kamenetskii to model the steady temperature in a vessel in which a thermal explosion is taking place. The Lane-Emden equation is reduced to an autonomous second-order ordinary differential equation by means of a coordinate transformation. The autonomous second-order ordinary differential equation is reduced to a first-order Abel equation. A power series solution of the first-order Abel equation is obtained. The power series solution of the Abel equation is transformed into an implicit series solution of the original Lane-Emden equation satisfying the boundary conditions of the original problem. We show that the implicit power series solution is valid for values of the dimensionless Frank-Kamenetskii parameter @d<0.02.

Peristaltic MHD Flow of Third Grade Fluid with an Endoscope and Variable Viscosity

Abstract This investigation deals with the mechanism of peristaltic transport of a non-Newtonian, incompressible and electrically conducting fluid with variable viscosity and an endoscope effects. The magnetic Reynolds number is taken to be small. The mechanical properties of the material are represented by the constitutive equation for a third grade fluid. The fluid fills the gap between coaxial uniform tubes, such that the inner tube is rigid and outer tube with sinusoidal wave travelling down its wall. Numerical solutions are given for large wavelength at low Reynolds number.

On the Rayleigh problem for a Sisko fluid in a rotating frame

The unsteady rotating flow of a Sisko fluid bounded by a suddenly moved infinite flat plate is investigated. The fluid is electrically conducting in the presence of a transverse applied time-dependent magnetic field. A highly non-linear differential equation resulting from the balance of momentum and mass, coupled with appropriate boundary and initial conditions is solved numerically. The numerical solutions for different values of the parameters are compared and discussed.

Investigation of the effect of the Coriolis force on a thin fluid film on a rotating disk

Abstract The effect of the Coriolis force on the evolution of a thin film of Newtonian fluid on a rotating disk is investigated. The thin-film approximation is made in which inertia terms in the Navier–Stokes equation are neglected. This requires that the thickness of the thin film be less than the thickness of the Ekman boundary layer in a rotating fluid of the same kinematic viscosity. A new first-order quasi-linear partial differential equation for the thickness of the thin film, which describes viscous, centrifugal and Coriolis-force effects, is derived. It extends an equation due to Emslie et al. [J. Appl. Phys. 29, 858 (1958)] which was obtained neglecting the Coriolis force. The problem is formulated as a Cauchy initial-value problem. As time increases the surface profile flattens and, if the initial profile is sufficiently negative, it develops a breaking wave. Numerical solutions of the new equation, obtained by integrating along its characteristic curves, are compared with analytical solutions of the equation of Emslie et al. to determine the effect of the Coriolis force on the surface flattening, the wave breaking and the streamlines when inertia terms are neglected.

Effects of injection (suction) on a steady mixed convection boundary layer flow over a vertical cone

Purpose – The purpose of this paper is to study the steady mixed convection flow over a vertical cone in the presence of surface mass transfer when the axis of the cone is inline with the flow.Design/methodology/approach – In this case, the numerical difficulties to obtain the non‐similar solution are overcome by applying an implicit finite difference scheme in combination with the quasilinearization technique.Findings – Numerical results are reported here to display the effects of Prandtl number, buoyancy and mass transfer (injection and suction) parameters at different stream‐wise locations on velocity and temperature profiles, and on skin friction and heat transfer coefficients.Research limitations/implications – Thermo‐physical properties of the fluid in the flow model are assumed to be constant except the density variations causing a body force term in the momentum equation. The Boussinesq approximation is invoked for the fluid properties to relate the density changes to temperature changes and to co...