Free convection on a heated vertical plate: The solution for small Prandtl number

The solution of the equations for the free-convection boundary-layer flow on a vertical plate with a prescribed power-law heating is considered for small values of the Prandtl number σ. It is shown that the boundary layer divides up into two regions. There is a thin inner region, of thickness O{ie273-1}, in which, to leading order, the temperature is a constant, but which is not determined from the inner solution. This gives rise to a large temperature on the plate of O{ie273-2}. This inner region drives a flow in a much thicker inviscid outer region, of thickness of O{ie273-3}. At the outer edge of this outer region the ambient conditions are attained, and it is the matching between the two regions which determines the plate temperature.     

Wall-bounded laminar sink flows

Summary The laminar flow near an infinite plane wall perpendicular to a line sink of constant strength is investigated in the limit of large Reynolds numbers. Self-similarity requires that fluid is issuing from the boundary layer. The inviscid flow outside the boundary layer is governed by the Euler equations. A one-parametric set of solutions to the Euler equations with appropriate boundary conditions is given. Uniqueness of the inviscid flow solution is obtained from matching with the boundary layer expansion. The solution of the boundary-layer equations is given both in closed form and numerically. It is found that at the edge of the boundary layer the vorticity decays algebraically.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday     

Non-uniform slot injection into a laminar boundary layer

Summary Slot injection into a laminar boundary layer in both supersonic and subsonic flow is considered. The blowing rates are sufficiently large to provoke an interaction between the boundary layer and outer inviscid flow, and this interaction is accounted for by triple-deck theory. The non-uniform nature of the blowing velocity models the channel flow from which the injection takes place.     

An updated interactive boundary layer method for high Reynolds number flows

The quasi‐simultaneous interactive boundary layer (IBL) method is improved with the iterative correction of an inviscid operator. The updated interactive boundary layer method (UIBL) presented in this work, uses the Hess–Smith panel method (HSPM) as an inviscid operator to update the outer flow calculation and the inviscid velocity in the interaction law (IL). The discretization of the Hilbert integral (HI) from the original method is modified to reduce the error introduced by the calculation of the HI in a restricted domain. The method is tested on a flat plate with a small indentation for two‐dimensional, steady, incompressible and laminar flow. The UIBL method is capable to predict the flow separation and reattachment with good accuracy. The accuracy of the results is competitive with the numerical solution of the Navier–Stokes equations (NSE). Copyright © 2005 John Wiley & Sons, Ltd.     

Micropolar fluid jet impingement on a curved surface

This paper deals with an analysis of a normally impinging micropolar fluid jet on a curved surface. The flow near the stagnation point in the impingement region is divided into inviscid and viscous flow regions. The inviscid flow solution is governed by Euler's equations of motion expressed in curvilinear coordinate system. The viscous flow solution is governed by the zeroth and the first order boundary layer equations. These boundary layer equations are solved by assuming power series expansions for both velocity and microrotation fields which give rise to two systems of ordinary coupled differential equations. The effects of surface curvature and material parameters on boundary layer characteristics have been studied and presented graphically. The gradients of zeroth order velocity and microrotation at the wall decrease and the zeroth order displacement and momentum thicknesses increase with decrease in the value of surface curvature. The reduction in curvature results in the reduction in the gradients of first order velocity and microrotation at the wall as well as first order displacement and momentum thicknesses.     

The entrainment theorem for wall driven boundary layer flows

Boundary layer flows driven by permeable plane surfaces, stretching with power–law velocities are considered in the presence of an applied lateral mass flux. The relationship between the wall shear stress and the entrainment velocity (the transversal velocity at the outer edge of the boundary layer) as a function of the mass transfer parameter f _w is examined analytically by using the Merkin transformation method. It is shown that at the value of f _w where the wall shear stress vanishes, the entrainment velocity reaches a minimum or maximum value. This relationship between two characteristic quantities at the outer and inner edge of the boundary layer, respectively, is referred to as entrainment theorem. Its physical content is analyzed in the paper in some detail.     

Slip flow on a body of revolution

This work investigates the boundary layer development and resulting net frictional drag along a general blunt-nosed body of revolution in uniform slip flow. The curvilinear boundary layer equations are subjected to a Navier slip condition near the surface. For motion near the nose, a similarity-type solution is obtained as a double series, comprising a small velocity slip parameter, from which the non-dimensional drag coefficient is obtained. In addition, the displacement effect of the boundary layer on the outer inviscid flow is determined and interpreted by means of a dimensionless parameter. The general analysis is then applied to the special case of the Rankine half-body. Considering laminar flow along the nose and downstream regions, results are presented for prescribed slip parameters and Reynolds numbers with particular emphasis on the influence of slip on the flow.     

Linear-stability Analysis of Thermocapillary Flow in an Annular Two-layer System with Upper Rigid Wall

The linear-stability analysis of thermocapillary flow in the annular immiscible two-layer system of 5cSt silicone oil and HT-70 with a radial temperature gradient was carried out. The annular two-layer system is heated at the outer cylindrical wall and cooled at the inner wall, the bottom and top surfaces are bounded by two rigid and heat-insulated walls. The influences of the liquid layer depth and radius ratio between the cold inner wall and the hot outer wall on stability are thoroughly investigated. The critical Marangoni number, critical wave number and critical phase velocity are obtained. In addition, the mode of bifurcation for the hydrothermal wave is predicted at different liquid layer depth, and the temperature disturbance pattern of hydrothermal wave at interface is also exhibited.     

High Reynolds number flows with closed streamlines

Summary In this paper we consider high Reynolds number flows with closed streamliness within which an inviscid region of uniform vorticity is separated from the containing boundary by viscous boundary layers. From numerical solutions of the boundary-layer equations we are able to determine that value of the core vorticity for which inviscid core and boundary layer are compatible.     

硬质合金内衬的组合超高压筒体优化设计

研究了硬质合金内衬的多层组合超高压筒体的强度优化设计。以等强度理论为设计原则,建立了以各外层径比(外径与内径的比值)为变量,容器总径比为约束,弹性承压能力最大为目标的优化设计数学模型。应用Lagrange乘子法进行优化,得到了各层最优径比公式及最大内压公式。在此基础上,从叠加原理出发,推导了不同材料多层容器的层间缩套压力及过盈量的最优精确解。最后通过实际算例与分析表明,硬质合金内衬的组合容器需要更大的缩套压力,对于三层容器,中间层和内衬主要承担径向压应力,而外层主要承担周向拉应力。     

Atomistic study of structures and elastic properties of single crystalline ZnO nanotubes

The structural stability and Young's modulus of single crystalline ZnO nanotubes are investigated using atomistic simulations. Unlike the case for conventional layered nanotubes, the energetic stability of single crystalline ZnO nanotubes is related to the wall thickness. The potential energy of ZnO nanotubes with fixed outer and inner diameters decreases with increasing wall thickness, while the nanotubes with the same wall thickness are independent of the outer and inner diameters. The transformation of single crystalline ZnO nanotubes with a double layer from wurtzite phase to graphitic phase suggests the possibility of wall-typed ZnO nanotubes. The size-dependent Young's modulus of ZnO nanotubes is also investigated. The wall thickness plays a significant role in the Young's modulus of single crystalline ZnO nanotubes, whereas the variation of outer and inner diameters slightly affects the Young's modulus of nanotubes with same wall thickness.     

Failure Analysis of T12 Boiler Re-Heater Tubes During Short-Term Service

The failure of T12 re-heater tubes that had been in service only for 3000 h was investigated. The wall thickness of the tubes was visibly reduced by heavy oxidation corrosion on the outer and inner walls. The original pearlite substrate completely decomposed. Uniform oxide scale appearance on the inner wall shows obvious vapor oxidation corrosion characteristics. Corrosion originated in the grain boundary, and selective oxidation occurred due to ion diffusion in the substrate. The layered oxide scale formed on the inner wall is related to the different diffusion rates for different cations. Exposure to high temperature corrosive flux accelerated the corrosion on the outer wall. The microstructure degradation and corrosion characteristics of the tubes indicate that the tubes failed primarily because of overheating, as evidenced by calculations.     

Viscous vortex core generation

Summary The unsteady flow of a viscous incompressible fluid between two porous co-axial circular cylinders is analysed when the outer cylinder is impulsively set into rotation. When there is radial inflow, vorticity is transferred from an unsteady boundary layer initially over the outer cylinder to a steady boundary layer over the inner cylinder.With 1 Figure     

一类非均布荷载作用下双层厚壁圆筒光滑接触时的应力解析解

采用复变函数方法,给出了双层厚壁圆筒外壁受有一类两向不等压非均布径向压力,内壁受有均布压力作用时平面问题的应力求解方法。在两层圆筒光滑接触的假定下,获得双层厚壁圆筒的应力解析解。通过算例分析了不同弹性模量组合时圆筒内不同截面的切向应力与径向应力分布规律,研究结果表明:当内壁均布压力较小时,两层圆筒的内壁处切向应力沿环向均呈余弦分布,且都在内壁的最小地应力方向承受最大压应力,在最大地应力方向承受最大拉应力;径向应力沿径向在圆筒0#x000b0;、45#x000b0;、90#x000b0;截面处分别呈近似#x0201c;M#x0201d;状、#x0201c;菱形#x0201d;、#x0201c;W#x0201d;状分布;随着内外层弹性模量比值的增大,内层圆筒内壁附近切向应力增大,径向应力在最小地应力方向增大,在最大地应力方向减小,而在外层筒分布规律相反。采用内软外硬的弹性模量组合,能有效的减小圆筒内层内壁处的应力集中程度。     

Effect of magnetic fields on heat convection inside a concentric annulus filled with Al2O3–water nanofluid

In the current study, forced convective heat transfer of an MHD fully developed laminar nanofluid between two concentric horizontal cylinders is investigated in the presence of a radial magnetic field. In contrast to a conventional no-slip condition at the surfaces, the Navier’s slip condition is considered at the surface to represent the non-equilibrium region near the surfaces. Employing the modified Buongiorno model, the conservative partial differential equations have been collapsed to two-point ordinary boundary value differential equations before being numerically solved. To consider the effects of thermal boundary condition on nanoparticle migration, two distinctive cases including constant heat flux at the outer wall and adiabatic inner wall (Case A) and constant heat flux at the inner wall with adiabatic outer wall (Case B) have been considered. Our results indicate that due to thermophoresis force, the distribution of nanoparticles was denser at the adiabatic wall for the case A which affects the local and the universal fluid flow and heat transfer characteristics. Moreover, inducing a radial magnetic field on the system, heat transfer rate was increased for the case A which had a decreasing effect on the case B. Finally, slip velocity at the walls enhances heat transfer rate for both cases.     

Numerical analysis of the zeta potential regarding the characteristics of a ring-type electro-osmotic mixer

The micromixer that is applied for the electro-osmotic effect in this study, which is a passive type, takes two fluids from different inlets and combines them into a single channel. The fluids then enter the mixing chamber with different inner and outer radii. Four microelectrodes are positioned on the outer wall of the mixing chamber. The electric potentials on the four microelectrodes are sinusoidal for certain values of the time, voltage, zeta potential, and frequency. In order to check the validity of the two-dimensional numerical analysis that already has been performed, we performed a three-dimensional numerical analysis using a commercial code, COMSOL. The incompressible Navier-Stokes equation is solved in this model, with a slip boundary condition on the inner and outer walls of the mixing chamber. The results of two- and three-dimensional models are graphically depicted and compared from the viewpoint of streamlines and concentration.     

湍流边界层激励下加筋平板振声响应特性研究

船舶、汽车和飞机等高速运动时,其外壳受湍流边界层壁面脉动压力激励而产生的内场声辐射成为该类交通工具自噪声的重要成分。基于模态叠加法计算结构振动响应。采用湍流壁面脉动压力功率谱Corcos模型,计算了外侧气流或水流湍流边界层激励下简支平板振动及内场辐射声,计算值与解析解和试验值吻合良好,验证了算法的有效性。采用湍流壁面脉动压力功率谱改进型Corcos模型,研究了外侧水流湍流边界层激励下平板及板格的振声响应特性,结果表明:水流马赫数低,壁面脉动压力迁移波数大于平板结构弯曲波数,壁面脉动压力波数-频率谱的迁移脊对平板的激励作用可以忽略;横向或纵向加筋对板格振动速度自功率谱级基本无影响;减小板格宽度与长度之比,适当增大板格流向长度可使平板振动辐射声功率在2 000 Hz以上明显降低。     

锻后身管壁厚方向力学性能变化实验研究

目的 针对传统身管材料30SiMn2MoVA,研究精锻工艺和热处理工艺对身管壁厚方向力学性能的影响。方法 采用线切割方式沿身管内表层、中间层和外表层分层取样,通过拉伸实验和胀形实验,分别获取身管材料经精锻成形工艺后壁厚方向纵向力学性能和横向力学性能的变化规律,同时获得残余应力对锻后身管壁厚方向力学性能的影响。结果 身管毛坯壁厚方向各层材料力学性能基本相同,精锻后内表层材料强度性能明显高于中间层和外表层,外表层和中间层伸长率要高于内表层;去应力后,身管材料强度性能和伸长率基本得到恢复,但横向伸长率恢复不明显。结论 精锻工艺对身管材料内表层的强度性能提升最大,同时塑性消耗也最大,锻后热处理工艺能使身管强度性能得到恢复,提高身管材料的纵向伸长率。     

Optimum design method for double-layer thick-walled concrete cylinder with different modulus

The stress state of thick-walled cylinder will be improved when it is composed of multi-layer concrete with different Young’s modulus of elasticity. The optimum design method for double-layer concrete cylinders is discussed in this paper. When the modulus of the inner-layer concrete is less than the outer one, the stress concentration on the cylinder inner surface will be relieved and the maximum tangential stress may be transferred from the inner surface of inner-layer to the inner surface of outer-layer, where is in triaxial stress state. The elastic limit bearing capacity of double-layer concrete cylinder will be improved due to the high compressive strength of concrete in triaxial stress state. Compared with the conditional single-layer thick-walled cylinder, the thickness of the double-layer cylinder can be reduced evidently. On the basis of stress solution of double-layer cylinder and by using the mixed penalty function method, the minimum wall thickness required, the best thickness ratio and the modulus ratio of inner layer to outer layer are calculated for cases in which the external load and uniaxial compressive strength are known already. If the thickness and uniaxial compressive strength is given, the best thickness ratio and modulus ratio of inner layer to outer layer can also be proposed by using the mixed penalty function method.     

The cyclically symmetric anti-plane fracture analysis for the arc-shaped interface in a non-homogeneous bimaterial cylindrical structure

A hollow cylinder, which consists of an inner functionally graded elastic substrate and an outer functionally graded elastic layer with cyclically symmetric cracks (a special case of multiple cracks), is considered under anti-plane shear load. The method of variable separation is employed to reduce the mixed boundary value problems to a Cauchy singular integral equation, which is solved numerically by the Lobatto–Chebyshev quadrature technique. Numerical results are presented to show the effects of geometrical and physical quantities on the stress intensity factors (SIFs). Parametric studies are conducted on the SIFs, and practical guidelines are given for the optimization of the fracture performance: (a) the SIFs depend on the ratio between the outer and inner radii, and the ratio should be at least 1.1; (b) the outer elastic layer should be stiffer than the inner elastic substrate; (c) large non-homogeneity parameter of the outer graded layer and small non-homogeneity parameter of the inner graded substrate are beneficial to SIFs reduction; (d) there is a strong interference between the stress fields around multiple cracks when the cyclically symmetric parameter increases.