Explicit Multipole Formula for the Local Thermal Resistance in an Energy Pile—The Line-Source Approximation

This paper presents a closed-form quite handy formula for the local thermal resistance Rb between the temperature of the bulk heat-carrier fluid in the pipes, equally spaced on a concentric circle inside a circular energy pile, and the mean temperature at the periphery of the pile. The so-called multipole method is used to calculate the temperature field. An important improvement of the multipole method is presented, where Cauchy’s mean value theorem of analytical functions is used. The formula for thermal resistance Rb0 for the zero-order approximation (J = 0), where only line heat sources at the pipes are used, is presented. The errors using zeroth-order approximation (J = 0) are shown to be quite small by comparisons with eight-order approximation (J = 8) with its accuracy of more than eight digits. The relative error for the local thermal resistance Rb0 for the zero-order approximation (J = 0) lies below 5% for a wide range of input parameter values. These ranges are judged to cover most practical cases of application. The smallest local thermal resistance Rbmin is, with some exceptions, obtained when the pipes lie directly in contact with the pile periphery. A neat formula for this minimum is presented.

On the Dynamics of Canyon–Flow Interactions

This paper explores the dynamical origin and physical characteristics of flow disturbances induced by ocean currents in interaction with shelf-incised submarine canyons. To this end, a process-oriented hydrodynamic model is applied in a series of case studies. The focus of studies is the canyon-upwelling process in which seawater is moved from the upper continental slope onto the shelf within a shelf-break canyon. Results reveal that the generation of canyon upwelling, to zero-order approximation, is a barotropic and friction-independent quasi-geostrophic process. Hence, the principle of conservation of potential vorticity for such flows is sufficient to explain the fundamental physical properties of the canyon-upwelling process. For instance, this principle explains the direction-dependence of the canyon-upwelling process. This principle also explains the formation of stationary topographic Rossby waves downstream from the canyon that can lead to far-field effects. Density effects, being of secondary influence to the canyon-upwelling process, result in the intensification of canyon-upwelling flows via the formation of narrow near-bottom density fronts and associated baroclinic geostrophic frontal flows. Findings of this work reveal that the apparently complex canyon-upwelling process is much more basic than previously thought.

LOW-TEMPERATURE EQUATION OF STATE OF SOLID METHANE

The theoretical equation of state for solid methane, developed within the framework of perturbation theory, with the crystal consisting of spherical molecules as zero-order approximation, and octupole – octupole interaction of methane molecules as a perturbation, is proposed. Thermodynamic functions are computed on the sublimation line up to the triple point. The contribution of the octupole – octupole interaction to the thermodynamic properties of solid methane is estimated.

Dynamic Analysis of Planar 3-RRR Flexible Parallel Robots with Dynamic Stiffening

In consideration of the second-order coupling quantity of the axial displacement caused by the transverse displacement of flexible beam, the first-order approximation coupling model of planar 3-RRR flexible parallel robots is presented, in which the rigid body motion constraints, elastic deformation motion constraints, and dynamic constraints of the moving platform are considered. Based on the different speed of the moving platform, numerical simulation results using the conventional zero-order approximation coupling model and the proposed firstorder approximation coupling model show that the effect of “dynamic stiffening” term on dynamic characteristics of the system is insignificant and can be neglected, and the zero-order approximation coupling model is enough precisely for catching essentially dynamic characteristics of the system. Then, the commercial software ANSYS 13.0 is used to confirm the validity of the zero-order approximation coupling model.

Optimal design of ring-stiffened cylindrical shells using homogenization approach

We propose a modification of the homogenization method for computational model of an axially symmetric cylindrical shell supported by rings having different stiffness properties governed by arbitrary analytical functions. The mentioned functions serve as control for an associated inverse problem. The latter is solved through a zero-order approximation corresponding to the structurally orthotropic solution being formulated for the first-order approximation of the location of discrete rings.

Influence of Helix Angle in Low Immersion Milling Forces and Stability Analysis: down-Milling, up-Milling and Slotting

Chatter is the most obscuring phenomenon and significant amount of research has been documented regarding prediction, control and elimination of chatter. Chatter is still a main hindrance in achieving good surface finish and productivity. This paper presents the influence of helix angle of milling cutter in down-milling, up-milling and slotting operation. Altintas multi-frequency solution (MFS) is advanced by adding the impact of helix angle in milling forces. A comparison is made for stability lobes diagram based on the helix angle model for different helix angles against the Altintas multi-frequency solution model (MFS) and zero order approximation (ZOA) model. The comparison shows that for small helix angle the stability lobes follow the Altintas (MFS) model and for high helix angle the stability lobes follow the Altintas (ZOA) model. The experimental results prove the simulations. Introduction

HETEROCLINIC ORBITS ARISING FROM COUPLED CHUA'S CIRCUITS

In this paper, we study the existence of heteroclinic orbits for ordinary differential equations which arise from a one-dimensional array of Chua's circuits. By using the upper and lower solutions method, and a zero-order approximation we show that for a certain set of parameters there exist traveling wave solutions for some given wave speeds.