Cylinder Of Elliptic Cross Section Research Articles

Non-Newtonian effect on natural convection flow over cylinder of elliptic cross section

The non-Newtonian effect in the boundary layer flow over a horizontal elliptical cylinder is investigated numerically. A modified power-law viscosity model is used to correlate the non-Newtonian characteristics of the fluid flow. For natural convection flows, the surface of the cylinder is maintained by the uniform surface temperature (UST) or the uniform heat flux (UHF) condition. The governing equations corresponding to the flow are first transformed into a dimensionless non-similar form using suitable transformations. The resulting equations are solved numerically by an efficient finite difference scheme. The numerical results are presented for the skin friction coefficient and the local Nusselt number with the eccentric angle for different values of the power-law index n. The local skin friction coefficient and the local Nusselt number are found to be higher and lower, respectively, for the shear thickening fluids (n > 1) than the other fluids (n ⩽ 1). The effects of different elliptical configurations on the average Nusselt number are also presented and discussed for both conditions of the surface temperature.

Deepening subwavelength acoustic resonance via metamaterials with universal broadband elliptical microstructure

Slow sound is a frequently exploited phenomenon that metamaterials can induce in order to permit wave energy compression, redirection, imaging, sound absorption, and other special functionalities. Generally, however, such slow sound structures have a poor impedance match to air, particularly at low frequencies and consequently exhibit strong transmission only in narrow frequency ranges. This therefore strongly restricts their application in wave manipulation devices. In this work, we design a slow sound medium that halves the effective speed of sound in air over a wide range of low frequencies (hence our referral to the microstructure as “broadband”), whilst simultaneously maintaining a near impedance match to air. This is achieved with a rectangular array of acoustically rigid cylinders of elliptical cross section, a microstructure that is motivated by combining transformation acoustics with homogenization. Microstructural parameters are optimized in order to provide the required anisotropic material properties as well as near impedance matching. We then employ this microstructure in order to halve the size of a quarter-wavelength resonator (QWR) or equivalently to halve the resonant frequency of a QWR of a given size. This provides significant space savings in the context of low-frequency tonal noise attenuation in confined environments where the absorbing material is adjacent to the region in which sound propagates, such as in a duct. We employ the term “universal” since we envisage that this microstructure may be employed in a number of diverse applications involving sound manipulation.

Effect of thermal radiation on unsteady mixed convection flow near forward stagnation point over a cylinder of elliptic cross section

The effect of thermal radiation on unsteady mixed convection flow near a forward stagnation point over a cylinder of elliptic cross section is investigated in this paper. The governing equations are transformed into dimensionless partial differential equations by using a suitable transformation and then are solved numerically by using an implicit finite difference scheme known as Keller Box method. The accuracy of the results is verified by comparing the obtained results with the previous studies available in the literature. It is shown that the results are highly accurate and are in good agreement. The separation times for both blunt and slender orientations in the presence of thermal radiation are shown in tabular forms. Moreover, the effects of pertinent parameters including Prandtl number Pr, mixed convection parameter ?, thermal radiation parameter Rd, surface temperature parameter qw and blunt/slender orientation parameter w on the velocity profile, the temperature profile and the Nusselt number are shown graphically. From the present study, it is observed that boundary layer separation occurs early due to thermal radiation and Nusselt number increases for both blunt and slender orientations.

Analytical theory of the dipole-exchange oscillations in long ferromagnetic nanowires of elliptical cross-section in a transverse external magnetic field

The analytical theory of the dipole-exchange spin-wave excitations of ferromagnetic cylinders of elliptical cross section with the bias magnetic field perpendicular to the axis of the cylinder is presented. Explicit analytical expressions for the frequency spectrum and the magnetization spatial distribution are derived. Their evolution as a function of cross-section's aspect ratios has been investigated. The developed formalism allows successful interpretation of experimental Brillouin Light Scattering spectra obtained previously for Ni nano-wires both qualitatively and quantitatively. It also provides a tool for comprehensive analysis of phenomena, in which spatial distribution and polarization of high-frequency magnetization play crucial role.

Acoustic scattering by elastic cylinders of elliptical cross-section and splitting up of resonances

The scattering of a plane acoustic wave by an infinite elastic cylinder of elliptical cross section is studied from a modal formalism by emphasizing the role of the symmetries. More precisely, as the symmetry is broken in the transition from the infinite circular cylinder to the elliptical one, the splitting up of resonances is observed both theoretically and experimentally. This phenomenon can be interpreted using group theory. The main difficulty stands in the application of this theory within the framework of the vectorial formalism in elastodynamics. This method significantly simplifies the numerical treatment of the problem, provides a full classification of the resonances, and gives a physical interpretation of the splitting up in terms of symmetry breaking. An experimental part based on ultrasonic spectroscopy complements the theoretical study. A series of tank experiments is carried out in the case of aluminium elliptical cylinders immersed in water, in the frequency range 0 ≤ kr ≤ 50, where kr is the reduced wave number in the fluid. The symmetry is broken by selecting various cylinders of increasing eccentricity. More precisely, the greater the eccentricity, the higher the splitting up of resonances is accentuated. The experimental results provide a very good agreement with the theoretical ones, the splitting up is observed on experimental form functions, and the split resonant modes are identified on angular diagrams.

PRESSURE DROP IN LIQUEFIED PETROLEUM GAS LAMINAR FLOW IN CYLINDRICAL ELLIPTIC PIPES

This work investigated Liquefied Petroleum Gas (LPG) flow in cylinders of elliptic cross-section. The LPG found in Nigeria contains mainly butane with varying percentages of propane. Commercial code FLUENT, which uses the finite volume method, was used to solve fluid flow governing equations. Very little attention has been paid to LPG flow in cylindrical elliptic pipes. Results of flow parameters of velocity and pressure were presented. Results showed that the pressure drop for LPG flow in elliptic pipes was higher than the ones of the circular pipes for the same cross-sectional area. This finding is relevant because the pressure drop is related to the power needed to drive the flow. Results showed that the velocity increased towards centre of the pipe at all cross-sections, and also increased towards the outlet of the pipe.

Hamiltonian bifurcation theory for a rotating flow subject to elliptic straining field

A weakly nonlinear stability theory is developed for a rotating flow confined in a cylinder of elliptic cross-section. The straining field associated with elliptic deformation of the cross-section breaks the SO(2)-symmetry of the basic flow and amplifies a pair of Kelvin waves whose azimuthal wavenumbers are separated by 2, being referred to as the Moore–Saffman–Tsai–Widnall (MSTW) instability. The Eulerian approach is unable to fully determine the mean flow induced by nonlinear interaction of the Kelvin waves. We establish a general framework for deriving the mean flow by a restriction to isovortical disturbances with use of the Lagrangian variables and put it on the ground of the generalized Lagrangian-mean theory. The resulting formula reveals enhancement of mass transport in regions dominated by the vorticity of the basic flow. With the mean flow at hand, we derive unambiguously the weakly nonlinear amplitude equations to third order for a nonstationary mode. By an appropriate normalization of the amplitude, the resulting equations are made Hamiltonian systems of four degrees of freedom, possibly with three first integrals identifiable as the wave energy and the mean flow.

Unsteady Mixed Convection Flow over a Cylinder of Elliptic Cross Section near Forward Stagnation Point

The unsteady mixed convection flow over a cylinder of elliptic cross section when the major axis is horizontal (blunt orientation) or vertical (slender orientation) near forward stagnation point is studied. The unsteadiness is due to an impulsive motion on the free stream. The governing boundary layer equations are first reduced into a non-dimensional form, and then transformed into a set of non-similar boundary layer equations, which are solved numerically using an efficient implicit finite-difference method known as Keller-Box method. The numerical results are obtained for various values of the Prandtl number, Pr, the mixed convection parameter, and parameter for blunt and slender orientation, !. The effects of these parameters on velocity profiles, temperature profiles as well as Nusselt number are presented through graphs and tables. The results show that as the mixed convection parameter, is increased, the velocity of the fluid is increased but the temperature of the fluid is decreased, for both blunt and slender orientations. Furthermore, the slender orientation gives earlier separation times for opposing flow while there is no separation of flow detected for the assisting flow. Keywords: unsteady flow; mixed convection; cylinder of elliptic cross section; forward stagnation point. 2010 Mathematics Subject Classification: 76B99; 76R99.

Free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid

This work studies the free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A coordinate transformation is performed, and the obtained nonsimilar governing equations are then solved by the cubic spline collocation method. The effects of the Brownian motion parameter and thermophoresis parameter on the profiles of the temperature, nanoparticle volume fraction and velocity profiles are presented. The local Nusselt number is presented as a function of the thermophoresis parameter, Brownian parameter, Lewis number and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). Results show that the local Nusselt number is increased as the thermophoresis parameter or the Brownian parameter is decreased. The local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased. Moreover, the local Nusselt number of the elliptical cylinder with slender orientation is higher than those of the elliptical cylinder with blunt orientation over the lower half cylinder.

Double diffusion from a horizontal cylinder of elliptic cross section with uniform wall heat and mass fluxes in a porous medium

This work studies the double diffusion near a horizontal cylinder of elliptic cross section with uniform wall heat and mass fluxes in a fluid-saturated porous medium. A coordinate transformation is used to obtain the non-similar governing boundary layer equations. The transformed equations are solved numerically by an efficient cubic spline collocation method. Results for the local surface temperature and the local surface concentration are presented as functions of the Lewis number, the buoyancy ratio, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). As the Lewis number is increased, the local surface concentration decreases while the local surface temperature increases. Moreover, an increase in the buoyancy ratio tends to decrease both the local surface temperature and the local surface concentration.

Lagrangian approach to weakly nonlinear stability of elliptical flow

Rotating flows with elliptically strained streamlines suffer from parametric resonance instability between a pair of Kelvin waves whose azimuthal wavenumbers are separated by two. We address the weakly nonlinear amplitude evolution of three-dimensional (3D) Kelvin waves, in resonance, on a flow confined in a cylinder of elliptic cross-section. In a traditional Eulerian approach, derivation of the mean flow induced by nonlinear interaction of Kelvin waves stands as an obstacle. We show how a topological idea, or the Lagrangian approach, facilitates calculation of the wave-induced mean flow. A steady incompressible Euler flow is characterized as a state of the maximum of the total kinetic energy with respect to perturbations constrained to an isovortical sheet, and the isovortical perturbation is handled only in terms of the Lagrangian variables. The criticality in energy of a steady flow allows us to calculate the wave-induced mean flow only from the linear Lagrangian displacement. With the mean flow at hand, the Lagrangian approach provides us with a shortcut to enter into a weakly nonlinear amplitude evolution regime of 3D disturbances. Unlike the Eulerian approach, the amplitude equations are available directly in the Hamiltonian normal form.

Effect of Fluctuating Surface Temperature on Natural Convection Flow Over Cylinders of Elliptic Cross Section~!2009-09-14~!2009-12-05~!2010-05-11~!

Effect of Fluctuating Surface Temperature on Natural Convection Flow Over Cylinders of Elliptic Cross Section~!2009-09-14~!2009-12-05~!2010-05-11~!

Natural convection heat transfer from a horizontal isothermal elliptical cylinder with internal heat generation

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature dependent internal heat generation. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. Results show that both the heat transfer rate and skin friction of the elliptical cylinder with slender orientation are higher than the elliptical cylinder with blunt orientation. Moreover, an increase in the heat generation parameter for natural convection flow over an isothermal horizontal elliptic cylinder leads to a decrease in the heat transfer rate from the elliptical cylinder and an increase in the skin friction of the elliptical cylinder.

Ultrasonic scattering by a fluid cylinder of elliptic cross section, including viscous effects

This paper analyzes acoustic scattering by a viscous compressible fluid cylinder of elliptic cross section submerged in an unbounded viscous nonheat-conducting compressible fluid medium. The classical method of eigenfunction expansion along with the appropriate wave field expansions and the pertinent boundary conditions are used to develop a solution in the form of infinite series involving Mathieu and modified Mathieu functions of complex arguments. The complications arising due to the nonorthogonality of angular Mathieu functions corresponding to distinct wave numbers in addition to the problems associated with the appearance of additional angular-dependent terms in the boundary conditions are all avoided in an elegant manner by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. A multiprecision code was developed for computing the Mathieu functions of complex argument in terms of complex Fourier coefficients that are themselves calculated by numerically solving appropriate sets of eigen-systems. The numerical results point to the imperative influence of fluid viscosity in notable reduction of pressure amplitudes at intermediate and high frequencies. They also reveal the central role of the cross sectional ellipticity in conjunction with the angle of incidence in altering the pressure directivities. Limiting cases are considered, and fair agreements with well-known solutions are obtained.

Free Convection Heat Transfer from a Confined Horizontal Elliptic Cylinder

The laminar free convection heat transfer from an isothermal horizontal cylinder of elliptical cross-section confined between two adiabatic walls is investigated by the Mach-Zehnder interferometry technique. The ellipse major axis is vertical, and the minor to major axis ratio is kept constant to 0.53. This paper focuses on the effect of wall spacing and Rayleigh number variation on the local and average free convection heat transfer coefficient from the cylinder surface. The local and average Nusselt numbers were determined for the Rayleigh number range of 9 × 10 2 to 3.2 × 10 3 and wall spacing to cylinder minor axis ratios of 1.9, 2.3, 2.67, 3.17, 3.8, 4.6, 6.12, 8, 13, ∞. Results are indicated with a single correlation that gives the average Nusselt number as a function of the ratio of the wall spacing to cylinder minor axis and the Rayleigh number. There is an optimum distance between the walls in which the Nusselt number is maximum. The experiment was also carried out on a cylinder of circular cross-section with the same periphery and length of the elliptic cylinder to allow a comparison with the results of other research.

Natural Convection Heat and Mass Transfer From a Horizontal Cylinder of Elliptic Cross Section with Constant Wall Temperature and Concentration in Saturated Porous Media

AbstractThis work studies the natural convection heat and mass transfer near a horizontal cylinder of elliptic cross section with constant wall temperature and concentration in a fluid-saturated porous medium. A coordinate transformation is used to obtain the nonsimilar governing boundary layer equations. The transformed governing equations are then solved by the cubic spline collocation method. Results for the local Nusselt and Sherwood numbers are presented as functions of the Lewis number, the buoyancy ratio, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). The heat and mass transfer rates of the elliptical cylinder with slender orientation are higher than those with blunt orientation.

The effect of temperature-dependent viscosity on the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature-dependent viscosity. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of viscosity-variation parameter, aspect ratio, and Prandtl number. The total heat transfer rate and the total skin friction of the elliptical cylinder with slender orientation are higher than those of the elliptical cylinder with blunt orientation. Moreover, increasing the viscosity-variation parameter tends to enhance the heat transfer rates from a horizontal elliptical cylinder.

Free convection heat and mass transfer from a horizontal cylinder of elliptic cross section in micropolar fluids

This work examines the natural convection heat and mass transfer near a horizontal cylinder of elliptic cross section with constant wall temperature and concentration in a micropolar fluid. The transformed governing equations are then solved by the cubic spline collocation method. Results for local Nusselt and Sherwood numbers are presented as functions of vortex viscosity parameter and aspect ratio. The heat and mass transfer rates of the elliptical cylinder with slender orientation are higher than those of the elliptical cylinder with blunt orientation. Moreover, the heat and mass transfer rates from an elliptical cylinder in Newtonian fluids are higher than those in micropolar fluids.

Virus transmission through compromised synthetic barriers: part II--influence of pore geometry.

When stressed during normal use, synthetic barriers such as gloves and condoms can develop tears that are undetectable by the user. It is of considerable public-health importance to estimate the quantity of virus transmitted through the tear, in the event of viral contamination of the fluid medium. A mathematical model that accounts for virus adsorption to the barrier material was used to compute the quantity of virus transmitted through defects of various geometries. Slits were modeled as cylinders of elliptic cross section, and upper and lower bounds for the transmission rate of HIV and Hepatitis B virus (HBV) were calculated for barrier-use scenarios such as coitus and gripping of surgical instruments. For a 1-microm high slit, HIV transmission was found to be negligible for all likely use scenarios. HIV transmission became potentially significant for a 5-microm slit. Due to its high titer, HBV transmitted at potentially important levels even through the 1-microm slit. The dependence of the transmission rate upon pore aspect ratio was determined and found to be very strong for high-adsorption situations and near-circular pores. Numerical predictions of virus transport through a laser-drilled hole in a condom matched experimental measurements well, even when the tapered nature of the geometry is ignored.

A neural-network approach to the electromagnetic imaging of elliptic conducting cylinders

A neural-network approach is presented for the electromagnetic imaging of conducting cylinders of elliptical cross section. Simulation results are presented which demonstrate that a properly trained neural network is capable of accurately identifying the shape and location of unknown elliptic cylinders in inaccessible domains. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 28: 303–306, 2001.