Finite Hollow Research Articles

Investigating Thermal Deflection in a Finite Hollow Cylinder Using Quasi-Static Approach and Space-Time Fractional Heat Conduction Equation

Investigating Thermal Deflection in a Finite Hollow Cylinder Using Quasi-Static Approach and Space-Time Fractional Heat Conduction Equation

A general integration method for radiative transfer in 3-D non-homogeneous cylindrical media with anisotropic scattering

A general set of integral equations is presented to solve 3-D radiative heat transfer problems in emitting, absorbing and linear anisotropic scattering finite hollow or solid cylinders with non-homogeneous media. By tracing a ray to compute the intensity,it is much easier to handle the spatial change properties including extinction coefficient. Both the continuous change property and step-change property are dealt with without difficulties. The solid angle integration in getting the incident radiation and heat fluxes is represented by the bounding surface integration. In order to avoid the singularity problem near the bounding surface, the surface integrations are transformed to new modified integral equations by mathematical methods. By doing so, we get more flexible general integral equations applicable to all cases (3-D solid cylinders, 3-D hollow cylinders, finite cylinders or infinite cylinders). This scheme has been verified by comparing the results with published data in the literature. It is believed that this method will be useful in combined radiation and convection heat transfer problems.

Transient Brake Temperatures Found by use of Analytical Solutions for Finite Hollow Cylinders

A linear analytical model for calculating transient axisymmetric temperature distributions in finite hollow cylinders is established and adapted for practical use. A homogeneous isotropic material with temperature-independent thermal properties is assumed. Among possible applications are brake discs, brake drums and block braked railway wheels. The thermal power from braking is applied as prescribed heat influxes over parts of the lateral and radial surfaces of the cylinder. Bessel series solutions to the heat conduction equation are found where Newton's law for heat transfer is used in the boundary conditions. In addition to convection prescribed surface temperatures and insulated surfaces are also studied. Arbitrary thermal loading histories are treated by use of Duhamel's principle where step loadings are superposed. Convergence and limitations of the method and required computer times are discussed. Calculated numerical results for some typical braking operations are compared with those of other studies.

On an Axisymmetric Coupled Thermal Stress Problem in a Finite Hollow Circular Cylinder

本報は,修正されたフーリエの熱伝導方程式中の連成項を変位場を支配する関数で表示し,さらに,新しく定義した温度関数を導入することによって連成項を分離し,その温度関数に対する通常の熱伝導方程式を解く問題に帰着させることに成功したものである.さらに,具体例として,有限長の中空円筒の内外円周面が軸対称加熱される場合について解析を行い,数値計算により,その温度分布および熱応力分布を明らかにした.

Three-Dimensional Transient Thermal Stresses in a Finite Hollow Circular Cylinder Due to Partially Distributed Moving Heat Sources

Three-Dimensional Transient Thermal Stresses in a Finite Hollow Circular Cylinder Due to Partially Distributed Moving Heat Sources

Elastic behaviour of shrink-fitted forming die assemblies. Part I: Development of an analytical solution

The paper deals with the elastic behaviour of the die assemblies obtained by shrinking a thick walled ring onto a finite hollow right circular cylinder in general of different length. Displacements and stresses in the two components of the assembly are evaluated by using the theoretical general solution on the finite thick-walled hollow elastic right circular cylinder with an axially symmetrical load system in terms of Airy's stress function. Radial and axial displacement influence coefficient technique is used to solve the integral equations governing the two extreme frictionless and slipless contact modes at the mating surface.

Contact Stresses in Two Elastic Bodies : In the Case of Elastic Bodies Being Finite Hollow Cylinders

Contact Stresses in Two Elastic Bodies : In the Case of Elastic Bodies Being Finite Hollow Cylinders

Three Dimensional Analysis of a Finite Hollow Cylinder Subjected to Axiasymmetric Deformations

Three Dimensional Analysis of a Finite Hollow Cylinder Subjected to Axiasymmetric Deformations

Three Dimensional Analysis of a Finite Hollow Cylinder Subjected to Axi-Asymmetric Deformations

Three dimensional elastic analysis of a finite hollow cylinder is very important to a practical design of machine parts. A few kinds of problems on an infinite hollow cylinder subjected to axi-asymmetric loads has already been studied. But the problem of a finite cylinder subjected to axi-asymmetric loads has not yet been analyzed. In this paper, a double Fourier series solution on the analysis of a finite hollow cylinder subjected to axi-asymmetric loads has been obtained by introducing stress functions which are given as series forms. Numerical results for some boundary conditions are obtained by using a digital computer and effects of Poisson's ratio, the ratio of inner radius to outer radius, and so on are discussed.

Transient Thermal Stresses in Finite Hollow Circular Cylinder with a Heat Transfer on its Surfaces

Transient Thermal Stresses in Finite Hollow Circular Cylinder with a Heat Transfer on its Surfaces

On Shrink-Fit Stresses between an Infinite Cylinder and a Finite Hollow Cylinder

This paper is concerned with the stress distributions and the displacements arising in an infinite cylinder which is shrink-fitted to a finite hollow cylinder. The three-dimensional elastic theory and the point-matching method are used to calculate the displacements and the stresses of the infinite cylinder and the finite hollow cylinder. An individual case is worked out in which the contact is frictionless an the sufficient friction occurs to cause complete adherence between surfaces in contact. The distributions of the contact stresses and the displacements are obtained for models of various elastic moduli. These are compared with the results obtained from the two-dimensional calculation and those of the shrink-fit problem of an infinite cylinder and a flexible sleeve.

On Contact Stresses between Infinite Cylinders and Finite Hollow Cylinders

On Contact Stresses between Infinite Cylinders and Finite Hollow Cylinders

Problems on the Finite Hollow Cylinders under the Axially Symmetrical Deformations : (2nd Report, The Case of Shearing Conditions)

Problems on the Finite Hollow Cylinders under the Axially Symmetrical Deformations : (2nd Report, The Case of Shearing Conditions)

Problems on the Finite Hollow Cylinders under the Axially Symmetrical Deformations

Problems on the Finite Hollow Cylinders under the Axially Symmetrical Deformations

Problems on the Finite Hollow Cylinders under the Axially Symmetrical Deformations

In this paper, the authors consider three-dimensional elastic problems on a circular hollow cylinder under the axially symmetrical deformations. The problems on the cylinder are classified into twelve fundamental cases according to boundary conditions. The general solution to various problems was obtained by expanding each elementary formula to the condition in a form of a Fourier and Bessel series and by superposing the stress systems. As numerical examples, the stress distributions and deformations of a finite hollow cylinder subjected to uniform band pressure were calculated by the digital computer of Kanazawa University (NEAC-2230). This pressure is distributed circularly over the end-surface and over the middle zone of the inner or outer-surface.

Diffusion and chemical reaction in catalysis and absorption

The interaction between irreversible, first-order chemical reaction and diffusion has been studied in finite hollow and solid cylinders. Analytical solutions in the form of Fourier—Bessel series are given. The effects of the significant geometrical parameters, and the Thiele modulus upon the effectiveness factor are computed and presented in graphical form. Steady state expressions for reversible chemical reaction and diffusion in particles of these shapes are also given. Equations for irreversible chemical reaction and diffusion under unsteady state conditions in the particles have been obtained by means of a transformation due to Danckwerts, whereby results for unsteady diffusion are transformed to results for unsteady diffusion with chemical reaction. A transformation whereby expressions for unsteady state reversible reaction and diffusion may be obtained from the expressions for unsteady state diffusion, is derived. The method is illustrated by a number of examples. Some applications to non-isothermal reaction systems are pointed out.