Hollow Circular Cylinder Research Articles

Estimation of Effective Thermal Conductivity of Two-Phase Material for Hollow Circular Model

Two-phase materials are commonly used in engineering application because of its various properties like strength, thermal conductivity, durability and toughness etc. Effective thermal conductivity (ETC) of two-phase material is the fundamental property to predict its thermal performance. Various geometry (spheres, cylinders, irregular particles) have been considered by researchers for calculating ETC of two-phase materials. Due to complex structure, hollow circular cylinder geometry is not reported yet. In this paper, two-dimensional periodic two-phase system, with hollow circular cylinder shape is considered for calculating ETC. In present work unit cell approach method is used to derive collocated parameters model for estimation of ETC. Hollow circular cylinder model with Ψ = 0.2 gives good result for estimating ETC with average percentage error of 6.46%.

Calculation of Stress Intensity Factor for an Internal Circumferential Crack in a Rotating Functionally Graded Thick-Walled Hollow Circular Cylinder under Thermal Shock

Abstract In this article, the fracture behavior of functionally graded thick-walled cylinder under thermo-mechanical shock is investigated. For this purpose, classical coupled thermoelastic equations are used in calculations. First, these equations are discretized with extended finite element method (XFEM) in the space domain and then they are solved by the Newmark method in the time domain. The most general form of interaction integral is extracted for axially symmetric circumferential crack in a cylinder under thermal and mechanical loads in functionally graded materials and is used to calculate dynamic stress intensity factors (SIFs). The problem solution has been implemented in MATLAB software.

MATHEMATICAL MODELS AND METHODS OF SOLVING SPATIAL GENERALIZED BOUNDARY VALUE PROBLEM HEAT ROTATING HOLLOW PIECEWISE HOMOGENEOUS CYLINDER

Context. The phenomenological theory of heat conduction speed of heat propagation is assumed infinitely large. However, the high intensity of the observed transient processes such as explosions, supersonic flow, high speeds of rotation of the use of this assumption leads to errors, so it is necessary to take into account that the distribution of heat takes place at a finite rate.Objective. Development of a new generalized mathematical model of the temperature distribution in the hollow piecewise uniform cylinder in the form of a boundary value problem of mathematical physics for the heat equation and the solution of the resulting boundary value problem.Method. The use of known integral Laplace transforms, Fourier series, and developed a new integral transformation for piecewise homogeneous space.Results. Found Polga transient temperature field of a circular cylinder in a cylindrical coordinate system, a piecewise homogeneous polar radius direction, which rotates at a constant angular velocity about the axis OZ, with the ultimate heat propagation speed. Thermal properties of each layer does not depend on the temperature at an ideal thermal contact between the layers, and there are no internal sources of heat.Conclusions. For the first time developed a mathematical model of the temperature distribution in the empty piecewise uniform cylinder, which rotates at a constant angular velocity about the axis OZ, taking into account the finite speed of propagation of heat in the form of mathematical physics boundary value problem for hyperbolic partial differential equations of heat conduction with boundary conditions of the first kind. Thermal properties are in each layer does not depend on the temperature at an ideal thermal contact between the layers, and there are no internal sources of heat.Created a new integral transform of a piecewise-homogeneous space, with which found the temperature field of the hollow piecewise homogeneous circular cylinder in the form of convergent orthogonal series of Bessel functions and of Fourier. The obtained analytical solution of a generalized boundary value problem of heat transfer cylinder, which rotates, given a finite amount of heat propagation velocity can be used for modeling of temperature fields, which occur in many technical systems (satellites, forming rolls, turbines, etc.).

Thermal and friction characteristics of a circular tube fitted with perforated hollow circular cylinder inserts

The objective of the present work is to measure the heat transfer and pressure drop in a circular tube integrated with the perforated hollow circular cylinder (PHCC) inserts with air as the working medium. The experiments are performed with PHCC inserts of three different diameter ratios (DR = 0.5, 0.65, and 0.8) and three perforation index (PI = 8%, 16%, and 24%) in a circular tube turbulent flow regime, where the Reynolds number is varied from 6000 to 27,000. A fixed value of pitch ratio (PR = 2) is considered in all the experiments. The experimental results demonstrated that the Nusselt number (Nu) and friction factor (f) are increased with the decrease of pitch ratio. The results also reveal that the heat transfer rate in the tube fitted with PHCC inserts is significantly increased with the corresponding marginal increase in pressure drop. In the range of the present work, heat transfer rate and friction factor are obtained to be around 150–230% and 160–450% higher than those of the plain tube values, respectively. Thermal enhancement factor (TEF) in the present study is in the range of 1.21–1.47 with a maximum value for DR = 0.65 and PI = 8%, respectively. In addition, the empirical correlations for the Nusselt number and friction factor are also developed, based on the experimental data.

Overall Heat Transfer Coefficient of Functionally Graded Hollow Cylinder

This paper presents how to calculate the overall heat transfer coefficient of a very long functionally graded hollow circular cylinder subjected to steady state heat transfer. Thermal conductivity coefficient of the functionally graded cylinder (FGC) vary radially and continuously according to an exponential form, which is supposed to be independent of the temperature. Overall heat transfer coefficient is found analytically in terms of the radial coordinate, thermal conductivity, material parameter, inner surface and outer surface temperatures of the cylinder. Once the overall heat transfer coefficient is found, calculation of the heat transfer rate across the cylinder wall is quite straightforward. The equation derived for the overall heat transfer coefficient can be applied to any type of functionally graded hollow circular cylinder playing with the material parameter term.

Stress and active control analysis of functionally graded piezoelectric material cylinder and disk under electro-thermo-mechanical loading

The purpose of this article is to investigate the active control behavior and stress analysis of functionally graded piezoelectric material circular hollow cylinder and disk under electro-thermo-mechanical loading. Also, this research presents a new compact formula for analysis of cylinder and disk that could be useful for engineers and designers to get insight into behavioral change of structures by geometry. The exact solutions of the functionally graded piezoelectric material structures could be found based on Lame’s solution. For a radially polarized cylinder and disk with continuously graded properties, it is assumed that material properties are varied by a power-law function, and inner surface and outer surface of these structures are considered to be sensor and actuator, respectively. Based on the exact solution, extensive numerical analyses are carried out to provide an insight into the effect of non-homogeneity constant and control factor on electro-thermo-mechanical behaviors and active control analysis of structures. The results show how the electro-thermo-mechanical behaviors change by non-homogeneity and control factor.

Forced vibration of the elastic system consisting of the hollow cylinder and surrounding elastic medium under perfect and imperfect contact

The bi-material elastic system consisting of the circular hollow cylinder and the infinite elastic medium surrounding this cylinder is considered and it is assumed that on the inner free face of the cylinder a point-located axisymmetric time harmonic force, with respect to the cylinder\'s axis and which is uniformly distributed in the circumferential direction, acts. The shear-spring type imperfect contact conditions on the interface between the constituents are satisfied. The mathematical formulation of the problem is made within the scope of the exact equations of linear elastodynamics. The focus is on the frequency-response of the interface normal and shear stresses and the influence of the problem parameters, such as the ratio of modulus of elasticity, the ratio of the cylinder thickness to the cylinder radius, and the shear-spring type parameter which characterizes the degree of the contact imperfectness, on these responses. Corresponding numerical results are presented and discussed. In particular, it is established that the character of the influence of the contact imperfection on the frequency response of the interface stresses depends on the values of the vibration frequency of the external forces.

Analysis of the Yield Condition of Porous Bone-implant Fixation

In this paper a theoretical analysis of porous bone-implant coupling is performed. The cancellous bone is described as a hollow circular cylinder formed of isotropic poroelastic material filled with viscous intraosseous fluid. The conical metallic implant, axially compressed, is assumed to be undeformable in comparison to cancellous bone. The Biot's formulation of theory of poroelasticity is used and by means of the modified Huber-Mises yield criterion the new yield condition (constitutive equation) has been determined as a function of strain. From this criterion it is possible the maximum permissible displacement of implant seating in bone to determine.

Experimental and Analytical Examination in Mortar Hollow Circular Cylinder Block for Heat Storage

Experimental and Analytical Examination in Mortar Hollow Circular Cylinder Block for Heat Storage

The radially nonhomogeneous thermoelastic axisymmetric problem

The plane axisymmetric thermoelastic problem with axisymmetric geometry, loading and temperature field is studied. Considering the radial dependence of the stress, displacement fields, of the stiffness matrix and the linear thermal expansion coefficient, after a series of admissible functional manipulations, the general differential system solving the radially nonhomogeneous circular cylinder results. The exact thermoelastic solution is proposed for a radially nonhomogeneous hollow circular cylinder of exponential shear modulus and constant Poisson ratio and also for a radially nonhomogeneous hollow circular cylinder of power law shear modulus and constant Poisson's ratio. For the isotropic elastic axisymmetric thermoelastic problem, a general solution is derived. Defining the elastic reduced stress, strain and displacement fields and using the nonhomogeneous compatibility equations of strain and the equilibrium equations of the thermoelastic problem, a nonhomogeneous differential equation in terms of the reduced displacements field, results. In the cases that the shear modulus is expressed by an exponential or a power law form, the displacements and stress fields are deduced analytically. Two applications have been performed for a radially nonhomogeneous hollow cylinder where the stress and displacements fields are determined for thermal loading.

Reissner mixed variational theorem-based finite cylindrical layer methods for the static analysis of functionally graded piezoelectric circular hollow cylinders under electro-mechanical loads

ABSTRACTA unified formulation of Reissner's mixed variational theorem-based finite cylindrical layer methods is developed for the static analysis of simply-supported, multilayered functionally graded piezoelectric material (FGPM) circular hollow cylinders. The material properties of the cylinder are assumed to obey an exponent-law exponentially varying through the thickness coordinate of this. The trigonometric functions and Lagrange polynomials are used to interpolate the in-surface and thickness variations of the primary variables of each individual layer, respectively. The coupled electro-elastic effects on the static behaviors of multilayered FGPM cylinders are closely examined.

Bifurcation of pressurized functionally graded elastomeric hollow cylinders

Various bifurcation behaviors, including asymmetric axial buckling induced by end thrust, bifurcation under external pressure, and eversion without any loading, of a soft circular hollow cylinder (or cylindrical shell) composed of functionally graded incompressible elastomeric material are considered in a unified way. Based on the nonlinear elasticity theory of a deformable continuous body undergoing large deformation and the linearized incremental theory for a superimposed infinitesimal deformation, an efficient approach for buckling analysis is developed and applied to the cylinder subjected to a combination of axial end thrust and internal/external pressure. It is based on the state-space formalism, which naturally avoids the derivatives of instantaneous material constants, enabling a convenient and accurate numerical implementation. Along with the layerwise method, an analytical characteristic equation (i.e. the bifurcation criterion) governing the general asymmetric buckling of the cylinder is derived. Detailed parametric studies are then carried out for a pressurized soft functionally graded hollow cylinder using an incompressible Mooney-Rivlin material model. The effects of material gradient on bifurcation induced either by end thrust or external pressure are discussed through numerical examples. Not only does this study provide an efficient tool for buckling analysis of soft cylinders, some findings that are unique to a functionally graded material are also highlighted. All in all, it is found highly possible to tune the bifurcation behavior of soft elastomeric cylindrical shells by tailoring material composition and/or adjusting the pressures acting on the surfaces of the cylinder.

Three-dimensional stress analysis of thin structures using a boundary element method with sinh transformation for nearly singular integrals

In this work a three dimensional (3D) boundary element method was established with an efficient nonlinear coordinate transformation scheme, namely sinh transformation, to evaluate nearly singular integrals in boundary integral formulations. Second-order quadrilateral surface elements were developed based on this method to accurately describe the geometry of thin structures. The elastic behaviors of selected thin structures were then computed by using the 3D boundary element model to demonstrate the accuracy and efficiency of this approach. A number of testing examples, i.e., the 3D Kirsch problem, the thin spherical shell problem, the ellipsoidal vessel problem with non-uniform thickness and the hollow circular cylinder problem, were numerically studied to test the established method. Remarkable accuracy and efficiency were found in the developed approach through the comparison to the numerical results and analytical solutions reported in the literature.

Thermoelastic Equilibrium of a Three-Layer Circular Hollow Cylinder Weakened by a Crack

We solve plane problems of stationary heat conduction and thermoelasticity for a hollow three-layer cylinder weakened by a crack by the method of singular integral equations. The cross section of the cylinder is a circular concentric ring with similar rings of a different material inserted into this ring. The inner ring contains an edge radial crack. The surfaces of the cylinder are free of loads and temperature conditions of the first kind are satisfied on these surfaces. On the interface of the media, we impose the conditions of perfect thermal and mechanical contact. The numerical solution is obtained for the case where unequal constant temperatures are given on the inner and outer surfaces of the cylinder. The stress intensity factors at the tip of an edge crack are found for different values of thermal and mechanical parameters of the components of the cylinder.

On the dispersion of the axisymmetric longitudinal wave propagating in a bi-layered hollow cylinder made of viscoelastic materials

The paper deals with the study of axisymmetric longitudinal fundamental wave propagation (dispersion) in the bi-layered hollow circular cylinder made of linear viscoelastic materials. The investigations are made by utilizing the exact equations of linear viscoelasto-dynamics. The corresponding dispersion equation is derived for an arbitrary type of hereditary operator and the algorithm is developed for its numerical solution. Concrete numerical investigations are made for the case where constitutive relations of the layers’ materials of the cylinder are described through fractional exponential operators. The influence of the viscosity of the layers’ materials of the hollow cylinder on the wave dispersion is studied through the rheological parameters which indicate the characteristic creep time and long-term values of the elastic constants of these materials. Dispersion curves are presented for certain selected dispersive and non-dispersive attenuation cases under various values of the problem parameters and the influence of the aforementioned rheological parameters on these curves is discussed. As a result of the numerical investigations, in particular, it is established that in the case where the rheological parameters of the layers are the same, the viscosity of the layers’ materials causes the axisymmetric wave propagation velocity to decrease.

Bending analysis of piezoelectric exponentially graded fiber-reinforced composite cylinders in hygrothermal environments

The closed-form solutions of a piezoelectric exponentially graded fiber-reinforced hollow cylinder in hygrothermal environment conditions are investigated. The interaction of electric displacement and electric potentials as well as the elastic deformations is discussed. The present piezoelectric fiber-reinforced circular cylinder is subjected to a mechanical load as well as an electric potential at its lateral surfaces. The resultant constitutive equations of the piezoelectric fiber-reinforced composite cylinder are analytically investigated. The thermal conductivity and the moisture diffusivity coefficient are supposed to change continuously in the radial direction by a simple exponential law. The hygrothermoelastic responses of piezoelectric exponentially graded fiber-reinforced hollow circular cylinders are presented. The significant of influence of the graduation of material, temperature, moisture, pressures and electric parameters is investigated. Concluding remarks and appropriate discussions are presented.

Agglomeration effects on electro‐magneto‐thermo elastic behavior of nano‐composite piezoelectric cylinder

Agglomeration effect on the electro‐magneto‐thermo elastic response of a hollow piezoelectric circular cylinder reinforced with carbon nanotubes (CNTs) is the main contribution of present work. The cylinder is subjected to an internal pressure, a distributed temperature field due to steady state heat conduction with convective boundary condition, a magnetic field in axial direction and a constant electric potential difference between its inner and outer surfaces or combination of these loadings. All the equivalent mechanical, thermal and piezoelectric properties of nano‐composite cylinder are obtained using Mori–Tanaka model considering agglomeration effects. The governing equation in polarized form is shown to reduce to a second‐order ordinary differential equation for the radial displacement. Considering mechanical boundary condition, this differential equation is analytically solved. The electro‐magneto‐thermo‐mechanical stresses, the electric potential and radial displacement distributions in the structure are discussed in detail. The presented results indicate that the agglomeration and volume percent of CNTs have significant influences on the electro‐magneto‐thermo‐mechanical behavior of the nano‐composite cylinder. POLYM. COMPOS., 39:1594–1603, 2018. © 2016 Society of Plastics Engineers

Investigation on sound transmission through thick-wall cylindrical shells using 3D- theory of elasticity in the presence of external and mean air-gap flow

This paper studies the effects of an external mean flow and an internal air-gap mean flow on sound transmission through a double-wall thick cylindrical shell. Due to the major influence of some effective terms such as membrane, bending, transverse shearing and rotational inertia on thick-walled shell, three-dimensional theory of elasticity is used to obtain the governing equations of motion. Therefore, Newton’s second law is utilized to develop the equilibrium equations for an infinitesimal element in cylindrical coordinates. Then, the equations of motion related to the circular hollow cylinders are solved using Helmholtz potentials for arbitrary values of physical and geometrical parameters. In addition, by coupling of both inner and outer shells, a modal transfer matrix is created. This modal matrix stands for the global dynamic equilibrium of the double-wall cylinder. Moreover, the sound transmission Loss of the double-wall cylinder excited by an acoustic oblique plane wave with two angles of incident (i.e. elevation and azimuth angles) is predicted. Due to lack of studies in the field of sound transmission through the thick-walled shell, the results obtained in this study are compared with those from other researchers for a thin cylindrical shell. These results indicate an excellent agreement in comparison with each other. Furthermore, the results reveal that with thickening of the shell, critical and coincidence frequencies are getting closer to ring frequency. Moreover, the effects of external and air-gap flows on TL behave in similar way whereas the Mach number is positive. In addition, an improvement of transmission loss can be found whereas the Mach number is negative; particularly this enhancement is more specified for the external flow. Finally, the results indicate that where both external and air-gap fluids simultaneously flow in opposite directions the TL is significantly enhanced. However, for the case where these two fluids flow in the same direction the TL is decreased.

On the problem of free deceleration of a rigid body in a resisting medium

A mathematical model of the influence of a medium on a rigid body with some part of its external surface being flat is considered with due allowance for an additional dependence of the moment of the medium action force on the angular velocity of the body. A full system of equations of motion is given under quasi-steady conditions; the dynamic part of this system forms an independent third-order system, and an independent second-order subsystem is split from the full system. A new family of phase portraits on a phase cylinder of quasi-velocities is obtained. It is demonstrated that the results obtained allow one to design hollow circular cylinders (“shell cases”), which can ensure necessary stability in conducting additional full-scale experiments.

The effects of vent channels and metal conductive base on thermal characteristics of the active graphite-composite cylindrical heat sink

This study proposed a novel configuration of active LED graphite-composite heat sink and experimentally investigated the effects of vent channels and metal conductive base on the fluid flow and heat transfer characteristics of this active heat sink. The heat sink was made of the graphite powders, aluminum-alloy powders, and adhesive mixed in specific proportion by the vacuum-pressure injection technique. The cost and weight of this graphite-composite material are much lower than those of aluminum alloy. The configuration of heat sink is a hollow circular cylinder with multiple radial fins. Different motor fans can be put in the chamber of heat sink, with various vent-channel positions and orientations (vertical vent channels, horizontal upper-row vent channels, and horizontal bottom-row vent channels) and numbers of channels (24, 36, 48, and 72) in the heat sink to enhance overall cooling performance by driving through airflow. The results indicate that the overall Nusselt number (Nu) of the graphite-composite heat sink with motor fan was 2.23–2.50 times that without motor fan. The numbers of vent channels in heat sink were positively related to the total flow rate of through air. Thus, the heat sink with the most vent channels had the maximum Nu in the motor-fan mode. When an additional annular aluminum-alloy conductive base was mounted in the graphite-composite heat sink with the most vent-channel configuration, the Nu was 35% higher than that without conductive base in motor-fan mode, proving the metal conductive base was effective. The optimal vent-channel configuration in this study was also used for the full aluminum-alloy heat sink, the corresponding Nu of the models without/with motor fan were compared with the full aluminum-alloy heat sink without vent channel, the heat transfer enhancements were about 13% and 127%, respectively.