Convective heat transfer in the entrance region of a rectangular duct with two indented sides

This study presents a numerical solution to convective heat transfer in laminar flow in the thermal entrance region of a rectangular duct with two indented sides. The flow is considered to be hydrodynamically fully developed and thermally developing laminar flow of incompressible, Newtonian fluids with constant thermal properties. The ducts are subjected to a constant wall temperature. An algebraic technique is used to discretize the solution domain and a boundary-fitted coordinate system is numerically developed. The governing equations in the boundary-fitted coordinates are solved by the control volume-based finite difference method. Distribution of the bulk temperature and the Nusselt number along the direction of flow is calculated and presented graphically. Also calculated is the thermal entrance length of the rectangular ducts with two indented sides. The parameters, such as the friction factor times the Reynolds number, and the Nusselt number for the fully developed flow and thermally developing flow are obtained.List of symbols a half-width of duct [m] - A cross-sectional area [m²] - b half-height of duct [m] - C _p specific heat [kJ kg^-1 K^-1] - D _h hydraulic diameter [m] - f skin friction factor = - h _z local heat transfer coefficient [Wm^–2 K^–1] - h _T asymptotic heat transfer coefficient [Wm^–2 K^–1] - J Jacobian matrix of transformation, Eq. (20) - k thermal conductivity [Wm^–1 K^–1] - L thermal entrance length [m] - L ^* dimensionless thermal entrance length =L/D _h RePr - L1 maximum number of grids in direction - M1 maximum number of grids in direction - Nu _T asymptotic Nusselt number =h _T D _h /k - p pressure [n m^–2] - P circumferential length [m] - Pr Prandtl number = /_T - Re Reynolds number =w _m D _h / - T temperature [K] - T _b bulk temperature [K] - T _i inlet temperature - T _w circumferential duct wall temperature [K] - w velocity [ms^–1] - w _m mean velocity [ms^–1] - W dimensionless velocity = – - W _m dimensionless mean velocity - x, y transveral coordinates [m] - X,Y dimensionless transversal coordinates =      

Complexation and Disproportionation of Np(V) in K10P2W17O61 Solutions

Complexation of NpO₂ ⁺ and NpO₂ ^{2 +} with unsaturated K _n P₂W₁₇O₆₁ ^{n - 1 0} (L ^x-) heteropolyanion and disproportionation of Np(V) in the presence of L ^x- were studied spectrophotometrically. The logarithms (logK) of the formation constants of NpO₂ ^VL and NpO₂ ^{V I}L are 3 and 7, respectively. The K⁺ and Na⁺ cations bind the L ^x- anions, thus decreasing the yield of the complexes. Neptunium(V) disproportionation in K₁₀P₂W₁₇O₆₁ solutions containing 1 M (HClO₄ + NaClO₄) (pH from 0 to 4) and free from NaClO₄ (pH 2-6.5) was studied. The disproportionation rate is described by the equation -d[Np(V)]/dt = k[Np(V)][L ^x-]. The pH dependence of the rate constant passes through a maximum at pH 1. The rate constant decreases with increasing [Na⁺]. The reaction is inhibited by its product, Np(IV). The Np(V) complex is not involved in disproportionation; the reactive species is NpO₂ ⁺ aqua ion, which is probably converted into NpO^{3 +}L ^x-. Then NpO^{3 +}L ^x- rapidly reacts with NpO₂ ⁺, which occurs simultaneously with, or is preceded by release of the second oxygen atom.     

Strong Nonequilibrium Coherent States in Mesoscopic Superconductor-Semiconductor-Superconductor Junctions

A biased superconductor-normal metal-superconductor junction is known to be a strong nonequilibrium system, where Andreev scattering at the interfaces creates a quasiparticle distribution function far from equilibrium. A manifestation of this is the well-known subgap structure in the I/V characteristic, with peaks in the conductance at V = 2/ne. We study an SNS structure consisting of highly doped diffusive GaAs with superconducting electrodes of aluminum with one electrode configured as a flux-sensitive interferometer. This enables us to probe the coherent nature of the quasiparticle states at subgap bias voltage. Oscillations in the conductance as a function of flux are seen at zero bias voltage and disappear below experimental resolution as the bias voltage exceeds the Thouless energy E _t = D/L ², where L is the junction length. The oscillations reappear at higher bias in a region around the superconducting energy gap V = /e corresponding to the subgap conductance peak n = 2.     

Study on ZnGa2O4:Cr a.c. powder electroluminescent device

An a.c. powder electroluminescent (EL) device using ZnGa₂O₄:Cr³⁺ phosphor was fabricated by the screen printing method. Optical and electrical properties of the device were investigated. The fabricated device shows a red emission at 695 nm driven by the a.c. voltage. The emission is attributed to the energy transfer from hot electrons to Cr³⁺ centers via self-activated Ga-O groups. Luminance (L) versus voltage (V) matches the well-known equation of L = L₀exp(− bV ^− 1 / 2) and luminance increases proportionally with frequency due to the increase of excitation probability of host lattice or Cr³⁺ centers. The diagram of the charge density (Q) versus applied voltage (V) is based on a conventional Sawyer-Tower circuit. At 280 V and 1000 Hz, the luminance and the luminous efficiency of the fabricated powder EL device are about 1.0 cd/m² and 13 lm/W, respectively. And under the high field, the device fabricated with the oxide-based phosphor of ZnGa₂O₄:Cr³⁺ shows excellent stability in comparison with the conventional sulfide powder EL device.     

Electrical-thermal switching effect in high-density polyethylene/graphite nanosheets conducting composites

The nonlinear response in high-density polyethylene/graphite nanosheets conducting composites under increasing applied voltage is investigated. Under sufficient applied constant voltage, the resistance increases initially due to Joule heating effect and then eventually reaches a steady value with a characteristic thermal relaxation time τ _h , which decreases as the applied field increases. The switch value, namely the ratio of the resistance under steady condition to the resistance of sample in linear regime, gradually increases with the increasing applied field. The threshold voltage (V ₀) at which the resistance start to increase with time scales with linear regime resistance (R ₀) of the sample as with the exponent x = 0.78 ± 0.05. All the curves of R/R ₀ vs. V/V ₀ collapse to a similar curve with the function R/R ₀ = 1 + α(V/V ₀) ^θ . The results reveal that the threshold voltage value decreases with increasing graphite nanosheets content in the composites.     

An assessment of expressions for the apparent thermal conductivity of cellular materials

Diverse expressions for the thermal conductivity of cellular materials are reviewed. Most expressions address only the conductive contribution to heat transfer; some expressions also consider the radiative contribution. Convection is considered to be negligible for cell diameters less than 4 mm. The predicted results are compared with measured conductivities for materials ranging from fine-pore foams to coarse packaging materials. The dependencies of the predicted conductivities on the material parameters which are most open to intervention are presented graphically for the various models.Nomenclature a Absorption coefficient - C _v (Jmol^–1 K^–1) Specific heat - E Emissivity - E _L Emissivity of hypothetical thin parallel layer - E ₀ Boundary surfaces emissivity - f Fraction of solid normal to heat flow - fics Fraction of total solid in struts of cell - K(m^–1) Mean extinction coefficient - k(W m^–1 K^–1) Effective thermal conductivity of foam - k _cd(W m^–1 K^–1) Conductive contribution - k _cr(W m^–1 K^–1) Convective contribution - k _g(W m^–1 K^–1) Thermal conductivity of cell gas - k _r(W m^–1 K^–1) Radiative contribution - k _s(W m^–1 K^–1) Thermal conductivity of solid - L(m) Thickness of sample - L _g(m) Diameter of cell - L _s(m) Cell-wall thickness - n Number of cell layers - r Reflection coefficient - t Transmission coefficient - T(K) Absolute temperature - T _m(K) Mean temperature - T _N Fraction of energy passing through cell wall - T ₁(K) Temperature of hot plate - T ₂(K) Temperature of cold plate - V _g Volume fraction of gas - V _w Volume fraction of total solid in the windows - w Refractive index - (m) Effective molecular diameter - (Pa s) Gas viscosity - Structural angle with respect to rise direction - (W m^–2 K^–4) Stefan constant     

Pore formation in cast metals and alloys

Porosity occurs in cast solidifying metals and alloys due to negative pressures generated during solidification contraction, and pressure developed by gases dissolved in the motten metal. Both the above processes may act either together or separately to produce such shrinkage or gas defects (collectively termed pores). They are generally unwanted and constitute a major industrial problem. This paper is an attempt to review up-to-date knowledge of the conditions of pore formation in cast metals and alloys. Various mechanisms responsible for pore nucleation and growth are summarized, and experimentally evaluated using an unfed type of mould with aluminium alloy castings. The observations are in support of a non-nucleation mechanism of pore formation playing a major role in the occurrence of such defects in cast metals. Further, in gas-containing alloy melts the critical amounts of gas required for single and multiple pore nucleation have been determined quantitatively and are listed in the text. The gas contents of the melts were measured using an apparatus based on the first bubble technique. It is also experimentally observed that under poor feeding conditions more than one of the non-classical nucleation mechanisms may be functional at the same time for the formation of such defects.Nomenclature P _e Sum of external forces which tend to collapse a pore - P _h Hydrostatic pressure - P _g Internat gas pressure in liquid metal - P _a Atmospheric pressure applied during solidification - P _s Shrinkage pressure - Surface tension at gas-metal interface - P _f Fracture pressure of liquid metal - 2_/r Surface tension resistance - V _i Volume of initial gas content of liquid Metal - P _i Total internal pressure due to gas and/or shrinkage - K _s,K _L Gas solubility constants of solid and liquid metal, respectively - K K_s/K_L - r Radius of liquid channel - R Radius of cylindrical casting - L Length of liquid channel - L _c Length of cylindrical casting - f ₁ Fraction of liquid left in the casting of pure and short freezing-range alloy, r ² L/R ² L _c - V _i ^* Critical gas content - t Tortuosity of channel - n Number of channels (approximately number of dendrite arms per unit area) - f _L Fraction of liquid left in the casting of mushy freezing alloys, r ² nt/R ² - B K _Lnt(1 -K) - nb _i ² B² (approximately) - r* Critical radius for pore nucleation (pore belowr* size cannot exist) - Surface tension of liquid - N Avogadro's number - k Boltzmann constant - h Planck's constant - T Temperature (K) - a,b Inner and outer radii of solidified shell - Y Uniaxial yield stress - , _s Energy per unit area of solid-liquid and solid-vapour interface, respectively - h Thermal diffusivity of solid metal - C_p Specific heat of solid metal - m,K ₁,K ₂ Constants - Fractional contraction of liquid phase on solidification [(solid density — liquid density)/solid density] - /(1 –) - Vortex circulation factor - d Density of liquid - Metal viscosity - h ₁ Thermal conductivity of mould - H Heat of fusion of metal     

Prediction of friction and heat transfer for viscoelastic fluids in turbulent pipe flow

Experimental measurements of the friction factor and the dimensionless heat-transfer j-factor were carried out for the turbulent pipe flow of viscoelastic aqueous solutions of polyacrylamide. The studies covered a wide range of variables including polymer concentration, polymer and solvent chemistry, pipe diameter, and flow rate. Degradation effects were also studied. It is concluded that the friction factor and the dimensionless heat transfer are functions only of the Reynolds number, the Weissenberg number, and the dimensionless distance, provided that the rheology of the flowing fluid is used.Nomenclature cp Specific heat of fluid, J · kg^–1 · K^–1 - d Diameter of tube, m - f Fanning friction factor, _w/(V²/2) - h Convective heat-transfer coefficient, q _w(T _w{T _b), W · m^–2 · K^–1 - k Thermal conductivity of fluid, W · m^–1 · K^–1 - j _H Heat-transfer j-factor, StPr _a ^2/3 - L _e Entrance length, m - Nu Nusselt number, hd/k - Pr _a Prandtl number based on apparent viscosity at the wall, c _p/k - q _w Heat flux at the wall, W · m^–2 - Re _a Reynolds number based on apparent viscosity at the wall, Vd/ - St Stanton number, Nu/(Re _a Pr _a) - T Temperature, K - T _b Bulk temperature of fluid, K - T _w Inside-wall temperature, K - V Average velocity, m · s^–1 - Ws Weissenberg number, V/d - x Axial coordinate, m Greek symbols g Shear rate, s^–1 - Apparent viscosity evaluated at the wall, P⁵ - ₀ Zero shear-rate viscosity, P⁵ - Apparent viscosity at infinite shear rate, P⁵ - Characteristic time of fluid, s - Density of fluid, kg · m^–3 - _w Wall shear stress, N · m^–2 Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

An assessment of expressions for the apparent thermal conductivity of cellular materials

Diverse expressions for the thermal conductivity of cellular materials are reviewed. Most expressions address only the conductive contribution to heat transfer; some expressions also consider the radiative contribution. Convection is considered to be negligible for cell diameters less than 4 mm. The predicted results are compared with measured conductivities for materials ranging from fine-pore foams to coarse packaging materials. The dependencies of the predicted conductivities on the material parameters which are most open to intervention are presented graphically for the various models.Nomenclature a Absorption coefficient - C _itv(J mol^–1 K^–1) Specinc heat - E Emissivity - E _L Emissivity of hypothetical thin parallel layer - E _o Boundary surfaces emissivity - f Fraction of solid normal to heat flow - f _s Fraction of total solid in struts of cell - K(m^–1) Mean extinction coefficient - k(Wm^–1 K^–1) Effective thermal conductivity of foam - k _cd(Wm^–1 K^–1) Conductive contribution - k _cr(Wm^–1 K^–1) Convertive contribution - k _g(Wm^–1K^–1) Thermal conductivity of cell gas - k _r(Wm^–1 K^–1) Radiative contribution - k _s(Wm^–1 K^–1) Thermal conductivity of solid - L(m) Thickness of sample - L _g(m) Diameter of cell - L _s(m) Cell-wall thickness - n Number of cell layers - r Reflection coefficient - t Transmission coefficient - T(K) Absolute temperature - T _m(K) Mean temperature - T _N Fraction of energy passing through cell wall - T ₁(K) Temperature of hot plate - T ₂(K) Temperature of cold plate - V _g Volume fraction of gas - V _w Volume fraction of total solid in the windows - w Refractive index - (m) Effective molecular diameter - (Pa s) Gas viscosity - Structural angle with respect to rise direction - (Wm^–2 K^–4) Stefan constant     

Tunneling Conductance of Ba1−x K x Fe2As2–GaAs Junction

We carried out point contact tunneling measurements by simply contacting degenerate GaAs semiconductor to polycrystalline Ba_1−x K _x Fe₂As₂ with T _c=31.1±1.0 K. The gap related structure was easily obtained. The gap value 2Δ determined from peak-to-peak voltage was 18.0 meV, and 2Δ/k _B T _c was 6.8. Small structures were observed at V∼±23 mV in the conductance curve separately from the gap edge structure. These values are included in phonon energy region and correspond to a peak of phonon density of states. Thus, the structures are attributed to phonon structure. We calculated d² I/dV ² and T _c, Δ in using Eliashberg equations by assuming α ² F(ω) from neutron phonon spectrum. The first phonon structure in calculated d² I/dV ² is comparable to experimental one.     

Crack propagation studies in brittle materials

An analysis was made of cantilever beam specimens used for crack propagation studies, Included in this analysis were the effects of a plastic zone at the crack tip, beam rotation, and the viscoelastic response of the material. This analysis showed that application of a constant bending moment to the specimen rather than a constant load provides a test in which the strain energy release rate,G, is independent of crack length. Other advantages of this test configuration are that corrections for shear or beam rotation effects are not necessary. Results of this test on both glass and ceramics are reported.List of symbols a crack length - A cross-sectional area of beam - b total thickness of specimen - d deflection of loading arm - E elastic modulus of material - E ₁ dynamic modulus - E ₂ transient response modulus - G shear modulus of material - G strain energy release rate - G _vE strain energy release rate of viscoelastic material - h half height of specimen - I moment of inertia of cantilever beam =bh ^/12 - k modulus of elastic foundation - K stress intensity factor - L distance from point of load application to fulcrum of loading arm - L distance from point at which arm deflection is measured to fulcrum - M applied bending moment - P force applied to beam - r length of plastic zone - t thickness of specimen at groove - T force applied to loading arm - u displacement of beam - V crack velocity - w half height of groove - W stored elastic energy - characteristic length of beam on elastic foundation - reciprocal of the characteristic length of beam - rotation of beam - X viscoelastic creep compliance function - time - inherent opening distance as defined by Wnuk [10] - _y yield strength of material - Poisson's ratio     

Designing and upgrading model of pre-denitrification systems

This paper reports a three-substrate steady-state integrated model, whose unknowns are expressed in explicit terms once concentrations of nitrogen compounds in the effluent flow are fixed. The model can be applied both to design and to upgrade wastewater treatment plants. The model is also able to evaluate the flexibility of existing wastewater treatment plants, which represents the capacity of the system to operate under different working conditions caused by increases in influent load or reductions in effluent quality standards. In this case the admissible variation of influent load or effluent concentration can be measured using suitable dimensionless flexibility indexes.List of symbols Q influent flow [L³ T^–1] - R₁ sludge recycle flow ratio - R₂ aerated mixed liquor recycle flow ratio - V_D denitrification reactor volume [L³] - V_N nitrification reactor volume [L³] - S biodegradable organic substrate concentration [M L^–3] - N-NH₄ ammonia nitrogen concentration [M L^–3] - N-NO₃ nitrate nitrogen concentration [M L^–3] - N_tot total nitrogen concentration [M L^–3] - O₂ oxygen concentration in the nitrification reactor [M L^–3] - X_H heterotrophic biomass concentration [M L^–3] - X_AUT autotrophic biomass concentration [M L^–3] - maximum removal rate of biodegradable organic substrate for an assigned value of temperature [T^–1] - maximum removal rate of nitrate for an assigned value of temperature [T^–1] - maximum removal rate of ammonia nitrogen for assigned values of pH and temperature [T^–1] - _S removal rate of biodegradable organic substrate [T^–1] - _D removal rate of nitrate [T^–1] - _N removal rate of ammonia nitrogen [T^–1] - K_S saturation coefficient for biodegradable organic substrate [M L^–3] - K_D saturation coefficient for nitrate [M L^–3] - K_SD saturation coefficient for organic substrate in the denitrification kinetic [M L^–3] - K_N saturation coefficient for ammonia nitrogen [M L^–3] - saturation coefficient for oxygen [M L^–3] - Y_H yield coefficient for heterotrophic microorganisms in the biodegradable organic substrate removal process - Y_D yield coefficient for heterotrophic microorganisms in the nitrate nitrogen removal process - Y_AUT yield coefficient for autotrophic microorganisms in the ammonia nitrogen removal process - (X_H)_r heterotrophic biomass concentration in the recycle sludge [M L^–3] - (X_AUT)_r autotrophic biomass concentration in the recycle sludge [M L^–3] - biodegradable organic mass consumption for unitary nitrate nitrogen mass reduction in the denitrification reactor - nitrogen consumption in the biodegradable organic oxidation process by mean of heterotrophic biomass     

A numerical study of the similarity of fully developed laminar flows in orthogonally rotating rectangular ducts and stationary curved rectangular ducts of arbitrary aspect ratio

 The present study showed that a quantitative analogy of fully developed laminar flow in orthogonally rotating rectangular ducts and stationary curved rectangular ducts of arbitrary aspect ratio could be established. In order to clarify the similarity of the two flows, the dimensionless parameters K _LR=Re/(Ro)^1/2 and the Rossby number, Ro=w _m /Ωd _h , in a rotating straight duct were used as a set corresponding to the Dean number, K _LC=Re/λ^1/2, and curvature ratio, λ=R/d _h , in a stationary curved duct. Under the condition that the value of the Rossby number and the curvature ratio was large enough, the flow field satisfied the `asymptotic invariance property'; there were strong quantitative similarities between the two flows such as in the friction factors, flow patterns, and maximum axial velocity magnitudes for the same values of K _LR and K _LC. Based on these similarities, it is possible to predict the flow characteristics in rotating ducts by considering the flow in stationary curved ducts, and vice versa. Received: 10 September 2001 / Accepted: 13 May 2002     

On the directional stability of wedging

The directional stability of the crack path during wedging of a strip is investigated, using finite element methods. Linearly elastic material and plane conditions are considered. No dynamic effects are included. Stable crack growth in the direction of maximum mode I stress intensity factor at the tip of the crack is assumed. It is found that directional stability seems to prevail if the thickness of the wedge at the foremost point of contact between the wedge and the crack surfaces is less than about 1.69 K _Ic% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaaca% WG3bGaai4laiaadweaaSqabaaaaa!3A93!\[\sqrt {w/E}\], where K _Ic is the fracture toughness, w half the width of the strip and E the modulus of elasticity.     

Stress-strain behaviour of nitrogen bearing austenitic stainless steels in the temperature range 298–473 K

The stress-strain behaviour of three nitrogen-bearing low-nickel austenitic stainless steels has been investigated via a series of tensile tests in the temperature range 298–473 K at an initial strain rate of 1.6×10^–5s^–1. Experimental stress-strain data were analysed employing Rosenbrock's minimization technique in terms of constitutive equations proposed by Hollomon, Ludwik, Voce and Ludwigson. Ludwigson's equation has been found to describe the flow behaviour accurately, followed by Voce's equation. The resultant strain-hardening parameters were analysed in terms of variations in temperature. A linear relationship between ultimate tensile stress and the Ludwigson parameters has been established. The influence of nitrogen on the Ludwigson modelling parameters has also been explained.Nomenclature True stress - _t True strain - _f True fracture strain - Strain rate - T Temperature - K _H, n _H Hollomon parameters - K _L, n _L Ludwik parameters - K _1L, k _2L, n _1L, n _2L Ludwigson parameters - _s, K _V, n _V Voce parameters - _{u relation} Uniform strain computed from a particular relation - _L Transient strain - ₀ Flow stress at zero plastic strain (Ludwik) - _L Transient stress - _y Yield stress - _u Ultimate tensile stress     

Kinetics of zero-valent iron reductive transformation of the anthraquinone dye Reactive Blue 4

The effect of operational conditions and initial dye concentration on the reductive transformation (decolorization) of the textile dye Reactive Blue 4 (RB4) using zero-valent iron (ZVI) filings was evaluated in batch assays. The decolorization rate increased with decreasing pH and increasing temperature, mixing intensity, and addition of salt (100 g L⁻¹ NaCl) and base (3 g L⁻¹ Na₂CO₃ and 1 g L⁻¹ NaOH), conditions typical of textile reactive dyebaths. ZVI RB4 decolorization kinetics at a single initial dye concentration were evaluated using a pseudo first-order model. Under dyebath conditions and at an initial RB4 concentration of 1000 mg L⁻¹, the pseudo first-order rate constant (k_obs) was 0.029 ± 0.006 h⁻¹, corresponding to a half-life of 24.2 h and a ZVI surface area-normalized rate constant (k_SA) of 2.9 × 10⁻⁴ L m⁻² h⁻¹. However, as the initial dye concentration increased, the k_obs decreased, suggesting saturation of ZVI surface reactive sites. Non-linear regression of initial decolorization rate values as a function of initial dye concentration, based on a reactive sites saturation model, resulted in a maximum decolorization rate (V_m) of 720 ± 88 mg L⁻¹ h⁻¹ and a half-saturation constant (K) of 1299 ± 273 mg L⁻¹. Decolorization of RB4 via a reductive transformation, which was essentially irreversible (2–5% re-oxidation), is believed to be the dominant decolorization mechanism. However, some degree of RB4 irreversible sorption cannot be completely discounted. The results of this study show that ZVI treatment is a promising technology for the decolorization of commercial, anthraquinone-bearing, spent reactive dyebaths.     

The mechanism of adhesion of moist powders to solid surfaces in the presence of a temperature field

An examination is made of the basic factors which influence the creation of forces causing powders to adhere to solid surfaces in the presence of a temperature field. An experimental investigation has been conducted on an apatite concentrate.Notation p_c capillary pressure - density of fluid - g acceleration due to gravity - h_cap, h limiting and actual height of capillary rise - surface tension - r radius of equivalent capillary - q specific suction force - k_w water saturation coefficient - V_w volume of water in pores - V_pore volume of pores - Wg humidity by weight - R particle radius - polar angle - _c area of contact - N total adhesive force - _m, _w specific weight of powder and water     

Space charge limited conduction and determination of density of localised states in semiconductor cobalt doped TiO2

Abstract

The space charge limited conduction (SCLC) mechanism in Co doped TiO₂ has been investigated at different temperatures. At lower electric fields, ohmic behaviour is observed while at higher electric fields nonohmic behaviour is observed. The results obtained confirm the presence of SCLC in Co doped TiO₂. The electronic parameters such as the position of the Fermi level above the valence band edge E _F, the density of states in valence band N _V and effective mass of holes m _h were found as 12·32 meV, 1·26 × 10¹⁵ m^?3 and 1·33 × 10^?7 m_e, respectively. The distribution of localised states in the forbidden band gap of the Co doped TiO₂ was characterised by current–voltage measurements and the density of localised states near the Fermi level N(E_F) was found to be 2·11 × 10¹⁷ eV^?1 m^?3.     

Interaction between the Ferromagnetic Dots and Vortices: Numerical Calculation and Experimental Results

Enhancing the pinning force in high-T _c superconductors can be achieved by externally introduced periodic magnetic dots. We numerically calculate the interaction between ferromagnetic dots and vortices in high-T _c superconductors. The London equation is used to generate two-dimensional vortex lattice. In the matching condition, we calculate the attraction force between magnetic dots and vortices. It is found that in an ideal condition, the pinning force of the magnetic dot reaches 2.5×10⁻¹¹ N that is more than one order magnitude stronger than the intrinsic pinning force in YBa₂Cu₃O₇ thin films. In the experimental side, we use a novel nano-technique to deposit periodic submicron Ni dots on YBa₂Cu₃O₇ thin films. The current versus voltage characteristics of an YBa₂Cu₃O₇ thin film strip with uniform Ni dots are measured at various temperatures and magnetic fields. They are compared with the current versus voltage characteristics of a bare YBa₂Cu₃O₇ thin film strip without magnetic dots. It is found the critical current value of the strip with Ni dots reduces with a much slower pace as the magnetic field strength increases in comparison with the value of the bare sample.