Effect of heat transfer on compressible boundary layer flow over a circular cylinder

Summary The effect of heat transfer on the steady laminar compressible boundary layer flow past a horizontal circular cylinder has been studied. The resulting coupled nonlinear partial differential equations have been solved numerically using a very efficient finite-difference scheme. Specific results are given for the boundary layer separation parameter and the skin friction and heat transfer coefficients.     

The asymptotic boundary layer on a circular cylinder in axisymmetric micropolar fluid flow

An asymptotic boundary layer analysis is presented using the theory of micropolar fluids due to Eringen. The laminar boundary layer induced on the outside of a long, slender cylinder due to the flow of an incompressible micropolar fluid parallel to the axis of the cylinder is investigated. For reasons of both analytical and practical interests the boundary layer characteristics far down stream from the leading edge are analyzed on the basis of their asymptotic nature. Asymptotic series solutions for the velocity and micro-rotation fields are obtained. An expression for the new micropolar boundary layer thickness is derived. Central to the present investigation is the result that while calculating the skin friction one should take into account the total surface stress effects, not only due to the usual shear stresses but also due to the couple stresses. As a result, it is shown that the micropolar theory does predict a reduction in skin friction as is observed in experiments thus confirming Eringen's well known conjecture.     

Heat transfer characteristics of a micropolar boundary layer in a crossflow over a non-isothermal circular cylinder

A boundary layer analysis has been presented for the heat transfer characteristics of a micropolar fluid flowing past a circular cylindrical surface with non-isothermal boundary conditions. The solution of the energy equation is obtained in the form of a power series of the distance measured from the stagnation point. The results for the Nusselt number have been obtained for several values of the material parameters of the fluid. A discussion has been provided for the effect of non-isothermal wall on the heat transfer rate.     

On a boundary layer phenomenon in Mindlin-Reissner plate theory for laminated circular sector plates

Summary In this article, the edge-zone equation of Mindlin-Reissner plate theory, for composite plates laminated of transversely isotropic layers is studied. Analytical solutions are obtained for both circular sector and completely circular plates with various boundary conditions. The boundary-layer function and its effect on the stresses are numerically studied. Effects of plate thickness and boundary conditions are investigated. The results for circular and completely circular plates are exactly the same as those of rectangular plates in our previous work. Therefore, this boundary layer phenomenon seems to be geometry independent.     

Plane steady problem of heat-conduction theory for a hyperbolic cylinder with boundary conditions of the third kind

Fredholm integral equations of the second kind are obtained for the temperature distribution at the surface of a hyperbolic cylinder which is cooled in accordance with Newton's law. The integral equations permit solution by the successive-approximation method at small values of the Biot number.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 1, pp. 150–153, January, 1980.     

On a boundary layer theory for non-Newtonian fluids

Theoretical support for the existence of a boundary layer theory, similar ⁺o the classical boundary layer theory for linearly viscous fluids, is offered in the case of the non-Newtonian fluid of second grade. It is also pointed out that unless certain assumptions are made regarding the flow, assumptions which are not alluded to in earlier work in this area, in addition to the assumptions usually made in the case of the linearly viscous fluid, the theory so developed might have inherent flaws.     

The torsion problem for a circular cylinder with radial edge cracks

Summary A finite Mellin transform technique reduces the torsion problem for a circular cylinder with radial edge cracks to that of solving some integral equations. Expressions are found for the stress intensity factors and crack formation energy. Three particular cases are considered in detail and numerical results given.     

Saint-Venant's problem for a micropolar elastic circular cylinder

In the present paper Saint-Venant's problem in the linear theory of micropolar elasticity is solved for a circular cylinder. Expressions for the macrodisplacement vector and microrotation vector are obtained.     

Approximate solution of an internal problem in laminar boundary layer theory

Laminar flow of a liquid in a channel of arbitrary shape is examined with account for interaction of the boundary layer with the core. A simple approximate method is described for calculating the boundary layer in a channel with arbitrary generator.     

Approximate solution of the internal problem for a turbulent boundary layer

The development of a turbulent boundary layer in an axisymmetric channel is analyzed with an an account of the mutual effects of the boundary layer and the core of the flow. The coordinates of the separation point, the coordinates of the junction, and other characteristics are found as functions of the Reynolds number and the channel geometry. A simple approximate method is proposed for calculating the boundary layer in a channel with an arbitrary curvilinear generatrix.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 18, No. 2, pp. 224–232, February, 1970.     

Axial eigenfunctions for the axisymmetric problem of an elastic circular cylinder

Constructing a biorthogonality relation it is shown how solutions can be obtained for the stress, displacement and mixed problems associated with the axisymmetric deformations in a cylinder whose plane faces are either stress-free or displacement-free. Numerical results are presented for the reproduction of the boundary stresses when a self-equilibrating load is prescribed on the circular boundary of the cylinder whose plane faces are stress-free.     

Diffraction theory of an anisotropic circular cylinder

A fully analytical theory is developed to derive the field diffracted by an infinitely long circular cylinder made of an arbitrary anisotropic homogeneous material, illuminated by an arbitrary plane wave.     

Axisymmetric thermal boundary layer of a micropolar fluid on a cylinder

The laminar micropolar thermal boundary layer in axial flow along a long, thin circular cylinder is investigated using the theory of micropolar fluids formulated by Eringen. The governing energy equation has been solved numerically by the power series approach. Missing values of the thermal functions are tabulated for a wide range of the material parameters, the transverse curvature parameter, and Prandtl number of the fluid.     

Transient thermal contact problem for axial crack in a hollow circular cylinder

The transient behavior of an axial-cracked hollow circular cylinder subjected to a sudden heating is investigated. It is shown that surface heating may induce compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, this problem can be divided into two parts and solved by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without a crack are obtained by finite element/implicit time integration method. The calculated temperature and thermal stress distributions are in good agreement with the values predicted by the analytical method. Secondly, the opposite senses of the stress distributions along the cracked surfaces, which are obtained previously, are treated as the traction boundary conditions, and the contact length and contact pressure of the real cracked cylinder are obtained by a modified elimination finite element scheme. In this scheme, the concepts of contact-node-pairs' penetration, contact-double-forces and compliance matrix are introduced. The calculated results indicate that the contact length ratio becomes smaller when the crack length ratio increases, and becomes larger as the radius ratio increases. Finally, the normalized stress intensity factor for the crack tip of the cylinder is obtained. It is shown that the larger the crack length ratio the higher the stress intensity factor.     

Heat of a layer transversely flowing past a cylinder with circular finning

Results of investigations and generalized relations for calculating heat transfer of a dense layer with transversely finned cylinders are presented. Thermal efficiency is determined and recommendations are given for selecting the geometric parameters of developed surfaces of this type.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.18, No. 1, pp. 52–58, January, 1970.     

Axisymmetric compressible boundary layer on a long thin moving cylinder

Summary All equations of motion well-known in classical mechanics can be written in a unified contravariant algebra form and possess a Lie admissible algebra structure as well as a Lie algebra structure under certain conditions. The application of Poisson's integration theory to these equations is given.     

The axisymmetric micropolar boundary layer on a long thin cylinder

The laminar micropolar boundary layer in axial flow along a long, thin cylinder is investigated using the theory of micropolar fluids due to Eringen. The governing equations are solved numerically by expanding the velocity and angular velocity functions in the form of power series. Wall values of the momentum and angular momentum functions are tabulated for a wide range of values of the material parameters and the transverse curvature parameter.     

A free boundary problem in the theory of lubrication

The theory of variational inequalities is applied to a free boundary problem arising in the hydrodynamic lubrication. We deal mainly with the properties of the pressure distribution in the clearance space and with the shape of the cavitated region.     

Plane contact thermoelasticity problem for a two-layer circular hollow cylinder with heat generation

We consider a contact thermoelasticity problem for a two-layer hollow cylinder. One of the layers rotates with respect to the other with a constant angular velocity. Constant stresses on the interface of cylindrical layers are caused by (a) compressive radial stresses or displacements on the side surfaces of the body and (b) a positive difference between ambient temperatures inside and outside the two-layer cylinder. Heat is generated as a result of friction on the contacting surfaces of the layers. We study the effects of the intensity of heat generation and physicomechanical properties of the cylinders on the distributions of stresses, displacements, and temperatures in the body.Franko L'viv State University, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 6, pp. 24–30, November – December, 1994.