Mixed convection boundary-layer on a vertical cylinder embedded in a saturated porous medium

Summary The mixed convection boundary layer on a vertical circular cylinder embedded in a saturated porous medium is considered. It is found that the flow depends on the parameter =R _a /P _e whereR _a andP _e are the Rayleigh number and Peclet number respectively. gives the ratio of the velocity scale for free convection to that for the forced convection. When is small the solution is, to a first approximation, obtained by a known heat conduction problem. The flow near the leading edge is considered and it is shown that a solution is possible only for ₀, ₀–1.354, and that a stable finite-difference solution away from the leading edge can be obtained only if –1; with <–1 there is a region of reversed flow near the cylinder. The finite-difference scheme is unable to give a satisfactory solution at very large distances from the leading edge, and to overcome this difficulty a simple approximate solution is developed. This solution shows that at large distances along the cyclinder, forced convection eventually becomes the dominant mechanism for heat transfer. This is also confirmed by an asymptotic solution of the full boundarylayer problem.Nomenclature a radius of cylinder - g acceleration of gravity - K permeability of the porous medium - N _u non-dimensional Nusselt number - r radial coordinate - non-dimensionalr=r/a - R _a Rayleigh number=(g T)Ka/ - P _e Peclet number=U ₀ a/ - T temperature - T _w temperature of the cylinder (constant) - T ₀ temperature of the ambient fluid (constant) - T temperature difference=T _w –T ₀ - u Darcy's law velocity in thex direction - U ₀ velocity of the outer flow - v Darcy's law velocity in ther-direction - x coordinate measuring distance along the cylinder - X non-dimensionalx,=x(aP _e )^–1 - equivalent thermal diffusivity - coefficient of thermal expansion - ratio of free to forced convection=R _a /P _e - viscosity of the convective fluid - density of the ambient fluid - non-dimensional temperature - stream function With 2 Figures     

A note on the resistance to brittle fracture in various ceramic materials

The square of the ratio of the abraded bending strength, _d, to the unabraded bending strength, , is proposed as a measure of the resistance to crack propagation in ceramic materials. Data for various porcelains, glass-ceramics, and glasses showed that _d is essentially constant and that (_d/)² decreased rapidly with increase of the unabraded strength.     

On the Universal Curve in Superplasticity Mechanics

We have carried out a series of tests (tensile, compression, torsion, and tension+torsion) of a superplastic titanium alloy VT9 at 950°C, with strain-rate intensity _e = 5 10^-4 - 1 10^-2 s ^-1 . By plotting and analyzing the stress intensity vs strain-rate intensity curves for this material, we justified the validity of the universal curve hypothesis for finite strains with an accuracy acceptable in engineering practice.     

Combined heat and mass transfer in natural convection flow from a vertical wavy surface

Summary In the present paper, effects of combined buoyancy forces from mass and thermal diffusion by natural convection flow from a vertical wavy surface have been investigated using the implicit finite difference method. Here we have focused our attention on the evolution of the surface shear stress,f(0), rate of heat transfer,g(0), and surface concentration gradient,h(0) with effect of different values of the governing parameters, such as the Schmidt number Sc ranging from 7 to 1500 which are appropriate for different species concentration in water (Pr=7.0), the amplitude of the waviness of the surface ranging from 0.0 to 0.4 and the buoyancy parameter,w, ranging from 0.0 to 1.Notation C species concentration in the boundary layer - C species concentration of the ambient fluid - C _w species concentration at the surface - D chemical molecular diffusivity - f dimensionless stream function - g acceleration due to gravity - Gr _x local modified Grashof number - N ratio of the buoyancy forces due to the temperature difference and the concentration difference - p pressure of the fluid - T temperature of the fluid in the boundary layer - T temperature of the ambient fluid - T _w temperature at the surface - u, v thex- andy-components of the velocity field - x, y axis in the direction along and normal to the plate Greek symbols thermal diffusivity - _T volumetric coefficient of thermal expansion - _C volumetric coefficient of expansion with concentration - stream function - nondimensional similarity variable - x/L - density of the ambient fluid - v kinematic coefficient of viscosity - stream function - dimensionless skin friction - fluid viscosity     

Forced convection over a continuous sheet with suction or injection moving in a flowing fluid

Summary The analysis of forced convection flow and heat transfer about a flat sheet with suction or injection continuously moving in a quiescent or flowing fluid has been carried out. This kind of problem finds applications in a variety of manufacturing processes such as hot rolling, extrusion of plastic sheets, continuous casting, and cooling of a metallic plate in a cooling bath. The governing differential equations are reduced to nonlinear ordinary differential equations by similarity transformations. These equations are solved numerically based on a finite difference algorithm. Representative velocity and temperature profiles within the boundary layer are presented at selected values of free stream velocity and injection parameter. The friction factor and Nusselt number are illustrated for a wide range of governing parameters. For the same injection parameter, Prandtl number, and normalized velocity difference |U _w–U |, higher values of the Nusselt number and friction factor result fromU _w>U than fromU _w<U . Also, an increase in the velocity ratioU /U _w results in an increase in the heat transfer rate, but a decrease in the friction factor. Furthermore, the heat transfer is enhanced due to increasing the values of the free stream velocity, the injection parameter, and Prandtl number; while it is reduced due to increasing the velocity difference.Nomenclature C _f friction factor, _w/(u_r ²/2) - F dimensionless stream function - F _w injection parameter - h local heat transfer coefficient - k thermal conductivity - Nu Nusselt number,hx/k - Pr Prandtl number, / - q _w wall heat flux - Re Reynolds number,u _rx/ - T temperature - T _w temperature at the fluid-sheet interface - T free stream temperature - U _w normalized velocity of the sheet,u _w/u_r - U normalized free stream velocity,u /u _r - u fluid velocity component inx-direction - u _r reference velocity, Eq. (8) - u _w velocity of the continuous sheet - u free stream velocity - v fluid velocity component iny-direction - v _w fluid velocity component iny-direction at the fluid-sheet interface - x streamwise coordinate - y cross-stream coordinate Greek symbols thermal diffusivity - boundary-layer thickness - dimensionless cross-stream coordinate - dimensionless temperature - kinematic viscosity - _w wall shear stress - stream function     

Developing combined convection of non-Newtonian fluids in an eccentric annulus

Summary Laminar combined convection of non-Newtonian fluids in vertical eccentric annuli, in which the inner and outer walls are held at different constant temperatures is considered and a new economical method of solution for the three-dimensional flow in the annulus is developed. Assuming that the ratio of the radial to the vertical scale, , is small, as occurs frequently in many industrial applications, then the governing equations can be simplified by expanding all the variables in terms of . This simplification gives rise to the presence of a dominant cross-stream plane in which all the physical quantities change more rapidly than in the vertical direction. The solution trechnique consists of marching in the vertical streamwise direction using a finite-difference scheme and solving the resulting equations at each streamwise step by a novel technique incorporating the Finite Element Method. The process is continued until the velocity, pressure and temperature fields are fully developed, and results are presented for a range of the governing non-dimensional parameters, namely the Grashof, Prandtl, Reynolds and Bingham numbers.List of symbols Bn Bingham number, - d ^* difference between the radii of the outer and inner cylinders,r _o ^*–r_i ^* - e ^* distance between the axes of the inner and outer cylinders - e eccentricity,e ^*/d^* - F ^* external force acting on the fluid - g ^* acceleration due to gravity - g ^* gravitational vector, (0,0,g ^*) - Gr Grashof number, _m *² g**(T ₀*–T _e*)d*³/ _m *² - K ^* consistency of the fluid - L ^* height of the cylinders of the annulus - n flow behaviour index - p ^* dimensional pressure - P dimensionless pressure gradient - Pr Prandtl number, _m */ _m ** - r _i ^* radius of the inner cylinder of the annulus - r _o ^* radius of the outer cylinder of the annulus - r _T wall temperature difference ratio,(T _i ^*–T_e ^*)/(T_o ^*–T_e ^*) - Re Reynolds number, _m d*w _m */ _m * - T dimensionless temperature of the fluid,(T ^*–T_e ^*)/(T_o ^*–T_e ^*) - T _dif ^* temperature difference between the walls of the annulus - T _e ^* temperature at the fluid at the entrance of the annulus - T _i ^* temperature at the inner cylinder of the annulus - T _o ^* temperature at the outer cylinder of the annulus - u dimensionless transverse velocity in thex direction,u ^*/(w_m ^*) - U dimensionless transverse velocity in the annulus,Reu - u ^* fluid velocity vector, (u ^*, v^*, w^*) - v dimensionless transverse velocity in they direction,v ^*/(w_m ^*) - V dimensionless transverse velocity in the annulus,Rev - w dimensionless vertical velocity,w ^*/w_m ^* - w _m scaling used to non-dimensionalise the vertical velocity - x dimensionless transverse coordinate,x ^*/d^* - y dimensionless transverse coordinate,y ^*/d^* - z dimensionless vertical coordinate,z ^*/L^* - Z dimensionless vertical coordinate,z/Re - Z _r dimensionless distance in the vertical direction where the final wall temperatures are attained,Z _r ^*/L^* - * dimensional molecular thermal diffusivity - * coefficient of thermal expansion, - dimensional rate of strain tensor - dimensionless ratio of the length scales in the annulus,d ^*/L^* - * dimensional apparent non-Newtonian viscosity - _m * mean viscosity, - * dimensional fluid density - _m * dimensional reference fluid density - * dimensional stress tensor - yield stress     

Characterization of the microstructure of a commercial Al-Cu alloy (2 0 1 1) by differential scanning calorimetry (DSC)

In this work the microstructure of a commercial Al-Cu alloy (2 0 1 1) in several metallurgical states has been studied by means of differential scanning calorimetry (DSC). The metallurgical states were chosen in such a way that the alloy contained predominantly one of the four possible phases in these alloys (i.e. GP zones and, and phases). The commercial tempers T3 and T6 have also been considered. The interpretation of the DSC curves was aided by measuring the changes in Vickers hardness and conductivity during a linear heating similar to that provided by the DSC apparatus; these studies allow, for instance, a clearer distinction between the GP (Guinier-Preston) zone dissolution peak and the phase dissolution peak. The results are compared with those obtained by other authors.     

Viscous oscillating cascade aerodynamics and flutter by a locally analytical method

A mathematical model is developed to analyze the viscous aerodynamics of an harmonically oscillating flat plate airfoil cascade in an incompressible laminar flow. The steady flow field is described by the Navier-Stokes equations, with the unsteady viscous flow modeled as a small perturbation to this steady flow. Solutions for both the steady and the unsteady viscous flow fields are then obtained by developing locally analytical solutions. The significant effects of Reynolds number, elastic axis, interblade phase angle and incidence angle on the oscillating cascade unsteady aerodynamics and torsional flutter characteristics are then demonstrated.List of symbols C airfoil chord - C _M unsteady moment coefficient - k reduced frequency, U/U - Re Reynolds number, U C/v - S cascade spacing - U free-stream velocity magnitude - x _ea elastic axis location - x mean flow direction coordinate - y normal flow direction coordinate - y _m mean airfoil position - x x-direction step size - y y-direction step size - (x ₀, y ₀) center of grid element - ₀ mean flow incidence angle - amplitude of airfoil oscillation - interblade phase angle - nondimensional unsteady stream function - nondimensional steady stream function - nondimensional unsteady vorticity - nondimensional steady vorticity - cascade stagger angle     

Melting of the flux line lattice observed by specific heat experiments in YBa2Cu3O7−δ

High resolution adiabatic specific heat experiments on YBa₂Cu₃O₇– (00.05) are performed in magnetic fields from 0 to 14 T (Bc and Bc). In a 0.3 gram, twinned crystal with strong pinning, a step is consistently observed at the melting temperature T_m of the vortex solid up to a critical point that depends on . The field B_m and step temperature T_m obey the relation B_m=B_mo()(1–T_m/Tc)^4/3. The anisotropy of B_m and that of the upper critical field B_c2 are found to be equal. Alternatively, in a 18 mg, twinned crystal of high purity with low pinning, first-order-like specific heat peaks are observed on the melting line from 8 to 14 T. The entropy under these peaks is 0.5 kB /vortex/bilayer. These characteristic features are attributed to the melting of a vortex glass in the former case and that of a vortex lattice in the latter case.     

Temperature dependence of electrical resistivity of deformed and undeformed V-rich V3Si single crystals

The electrical resistivity (T) of V-rich V₃Si single crystals (T _c-11.4 K) was measured from 4.2 to 300 K along the directions of [1 0 0] and [1 1 1] before and after plastic deformation at 1573 K. Anisotropy of (T) was observed although V₃Si has the cubic A15 structure. Plastic deformation does not affect the normal-state (T) behaviour but changes the normal-superconducting transition width T_c. At low temperatures (T _c<T 40 K), (T) varies approximately as T ⁿ where n-2.5 and this behaviour does not contradict the (0)- phase-diagram plot proposed by Gurvitch, where is the electron-phonon coupling constant and (0) is the residual resistivity.     

Die Entwicklung von Längswirbeln in zeitlich anwachsenden Grenzschichten an konkaven Wänden

Zusammenfassung Messungen des Anwachsens von Längswirbeln in zeitlich anwachsenden Grenzschichten an konkav gekrümmten Wänden (Görtler-Taylor-Wirbel) ergaben drei deutlich getrennte Bereiche: Es traten zunächst Wirbel mit der Wellenläge 0,9 auf (=Grenzschichtdicke, =Höhe einer Zelle, die zwei gegensinnig drehende Wirbel enthält). Je nach Größe der mit der Verdrängungsdicke ₁ der Grenzschicht gebildeten Reynolds-Zahl erschienen dann kurze Zeit später Wirbel mit 2,5, wenn war. Im Bereiche dagegen traten stattdessen bei den hier durchgeführten Versuchen immer Wirbel mit der Wellenlänge 6,5 auf. Bei werden die ersten Tollmien-Schlichting-Wellen mit der Wellenlänge _TS 6· angefacht. In ihren wandnahen Bereichen der Wellentäler könnten sich dann die oben genannten Längswirbel der Wellenlänge 6,5· ausbilden, die die zwei-in eine dreidimensionale Störung allseits gleicher Größenordnung verwandeln können.

---

The development of longitudinal vortices in boundary layers growing with time along concave walls

Summary Measurements of the growth of longitudinal vortices in boundary layers growing with time along concave walls (Görtler-Taylor vortices) rendered three distinctly separated regions. First, vortices with a wave-length 0.9 appeared (-boundary layer thicness, =height of a cell containing two counterrotating vortices). Then, depending on the Reynolds number R _{a 1}/v ₁=displacement thickness), vortices with 2.5 appeared shortly afterwards, provided . In the region , however, the wave-length was 6.5. For the first Tollmien-Schlichting waves with _TS 6 were excited. In the wave-throughs close to the wall the abovementioned longitudinal vortices with wave length 6.5 may then be formed. This might transform the two-dimensional into a three-dimensional flow of equal order of magnitude in all directions.

---

Zeichenerklärungen R _a Innenradius - Re _a Reynolds-Zahl gebildet mit dem InnenradiusR _a - Reynolds-Zahl gebildet mit der Verdrängungsdicke ₁ - kritische Taylor-Zahl - h Standhöhe der Flüssigkeit im Zylinder - t Zeit - z Anzahl - Steigungswinkel der Geraden - Grenzschichtdicke - ₁ Verdrängungsdicke - Wellenlänge (enthält ein gegensinnig rotierendes Längswirbelpaar) - v kinematische Zähigkeit - Winkelgeschwindigkeit Indizes K Knickpunkt der Geradensteigung - L unterhalb des Knickpunktes der Geradensteigung - TS Tollmien-Schlichting - e Einsatz der Wirbelentstehung     

Heat conduction in a multilayer composite wedge

A new method for analytically solving a problem of steady-state heat conduction for multilayer composite wedge-shaped bodies is suggested based on a generalization of the integral Mellin transform.Notation T temperature - _rr, thermal conductivity coefficients - thickness of composite material layers (1) - N₁(), N ₂ ⁽¹⁾ (), N ₂ ⁽²⁾ () auxiliary local functions from the rapid variable =r/ - m(r, p) auxiliary function entering the core of the generalized integral Mellin transform - ₀ half of the wedge aperture angle Moscow Institute of Chemical Engineering. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 4, pp. 487–491, April, 1993.     

Dielectric properties of hydrothermally grown gallium orthophosphate single crystals

GaPO₄ single crystals of the low-temperature form were hydrothermally grown in 4M H₃PO₄ solution at 180 ° C. Single crystals 5.0×5.2×3.7mm³ in size could be grown in a silica glass vessel of 10 mm inner diameter. The dielectric properties of grown crystals were measured with the electric field parallel (E c) and perpendicular (E c) to thec-axis. The values of dielectric constant (ie2800-01) ofE c andE c are about 10.3 and 7.8, respectively, at frequencies from 10 kHz to 1 MHz, and these are nearly independent of frequency at room temperature. However, these values increase with temperature in the temperature range about 310 to 500 K and in the frequency region below 1 MHz. Dielectric loss (ie2800-02) increases with increasing temperature at around 300 K (E c) and 310 K (E c). From the log (conductivity) against 1/T plot in the intrinsic region at higher temperatures, the values of activation energy (E) for conduction are calculated to be about 0.17 and 0.33eV, forE c andE c, respectively.     

Statistical analysis of the failure stresses of ceramic fibres: Dependence of the Weibull parameters on the gauge length, diameter variation and fluctuation of defect density

The strength distribution of ceramic fibres is commonly described using a two-parameter Weibull distribution function. This study shows that the determination of these parameters from around 30 tensile tests obtained at one single gauge length (L ₀) does not allow the strength distribution at other gauge lengths to be correctly predicted. The reliability in the Weibull parameter determination is lowered by variations in fibre diameter (D) and the insufficient number of fibres tested. An effective failure stress _E = · ( D · L ₀)^1/m is first introduced to take into account fibre diameter variations and to extract the two Weibull parameters from the 180 tests obtained at 6 gauge lengths. It is then shown that the linear size effect, which is expected from the standard Weibull model, is not appropriate to fit correctly this experimental strength distribution. The length dependence follows a power law (L ₀ ) leading to an effective failure stress _E = · ( D · L ₀ )^1/m . Diameter variations along the gauge length cannot be responsible for this non linear variation with the length, which is attributed to a large scale fluctuation of the density of defects. The value of can bring valuable information about fluctuations in the fibre processing conditions.     

Types of superplasticm-δ curves of Ti-6Al-4V alloy and their intertransformation

The superplasticm- curves of Ti-6Al-4 alloy have been determined at different temperatures and strain rates; all were of them _L=m _max type, and were of either fundamental, descending or ascending types. The latter two types were transformed from the former through the processes ofm _Lm _O, _LO andm _Lm _F, _LF, respectively. The highest total elongation, _F, was 1150% obtained at 950C and 1.55×10^–3 s^–1. The Chin Liu equation has been applied to all types ofm- curves. The parameters characteristic of all types ofm- curves have been obtained and were found to vary with temperature and strain rate. The total elongation, _F, is determined by the resultant effects of all other parameters, not by a singlem value, theoretically considered to be constant and determined practically by a tensile strain of about 30%–50% (m _30%–50%) as usual.Nomenclature C (=k/k _o ) the normalized slope ofm- curve corresponding to - a material constant corresponding to - m strain-rate sensitivity index corresponding to - m _max maximum on them- curve corresponding to _L - m _min minimum on them- curve corresponding to _L - crosshead speed during the tensile test - the strain of the entire stretching process (has same significance as ordinarily adopted ) - _F total elongation at fracture chosen for the present work - _I intermediate strains including _I1, _I2, _I3, ..., _I(i–1), _Ii , _I(i+1), ..., chosen for the present work - _L limit strain separatingm- curves into sections - _O (=0) starting strain - strain rate - flow stress     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

Method for heat transfer calculation using isothermal coordinates

Equations for steady-state heat transfer are considered in curvilinear coordinates. The equations are shown to be simplest when one of the families of coordinates are isotherms. Conditions are obtained for which these coordinate systems and some exact solutions of the heat conduction equations must satisfy.Notation a ₁, a₂, ..., a_n coefficients determining the temperature dependence of thermal conductivity (see formula (8)) - f() function of the -coordinate (see formula (4)) - H ₁,H ₂,H ₃ coefficients of the first differential form (Lamé coefficients) (see formula (2)) - n number of a term of the series in formula (8) - q heat flux - Q power of volume heat release - x, y, z Cartesian coordinates - , , general curvilinear orthogonal coordinates - ₁, ₂ coordinates of the boundary surfaces on which the temperatures are prescribed - x ₀₁ thermal conductivity att=0 - () function of the -coordinate (see formula (4)) - () -function determining temperature distribution in the case of constant heat flux along the coordinate lines Scientific-Research and Design-Technological Institute of Machine Manufacture, Scientific-Production Subbranch Novator, Kramatorsk, Ukraine. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 651–659, July–August, 1995.     

Theory of the Surface Tension Maximum of Liquid 3He

Recently Matsumoto et al. performed very precise measurements of the surface tension of liquid ³He, (T), at low temperatures and found that (T) exhibits a small maximum at about 100 mK. Existing theories are unable to explain this anomaly. On the basis of a local approximation for the entropy in which the Fermi liquid effect is included, we can evaluate the variation of (T), (T)=(T)–(0), as a function of T and of the number density (or the interaction strength). It is found that (T) consists of two terms; a T² term and T⁴ ln T term. We predict that, for the density of real liquid ³He, exhibits a tiny minimum and a small but relatively larger maximum. This prediction explains qualitatively and quantitatively all salient features of the observed (T).     

Microstructural study of ε-iron-carbonitrides formed by a glow discharge technique

The microstructure and phase transformations occurring in-iron-carbonitrides have been studied by means of X-ray and electron diffraction, electron microscopy and Mössbauer spectrometry. Ordering of the interstitial atoms, N or C, results in a hexagonal unit cell for Fe₃(C, N) with parametersa=a3 andc=c wherea andc are the lattice parameters of the hexagonal close-packed (h c p) iron unit cell. Stacking faults on (0001) planes and partial dislocations with Burgers vector b=1/31 0 ¯1 0 are observed in quenched-Fe₄ (C, N). After quench-aging, the carbonitrides show a structural hardening due to the precipitation of a metastable phase. Slow cooling of-carbonitrides with less than 25 at% interstitials leads to the precipitation of-carbonitride and ferrite in-phase grains which allows the orientation relationships between the-,- and-phases to be defined and a model of the-phase--phase transformation to be proposed.     

Thermal Expansion of La1.85Sr0.15CuO4 in Magnetic Fields up to 14 Tesla

We present thermal expansion measurements on a La_1.85Sr_0.15CuO₄ single crystal in external magnetic fields. Clear anomalies of the thermal expansion are observed at the superconducting transition. We have studied in detail the anisotropic influence of external fields on the anomalies. As expected, the field dependence is maximum for B c and minimum for B c. The measured angular dependence corresponds to that of an anisotropic 3d superconductor with an anisotropy parameter 18.