Effect of unsteady natural convection on the structure of a liquid flow in a horizontal mixing chamber

Results are presented of a numerical and experimental investigation of the effect of natural convection on the structure of a liquid flow in a horizontal mixing chamber with changes in the temperature of the liquid at the inlet.Notation t_o, t_in initial temperature and temperature at the inlet to the channel - dimensionless temperature - a heat conductivity - kinematic viscosity - coefficient of cubical expansion - density - P pressure - g acceleration due to gravity - d_equ equivalent diameter of porous body - time - v_o mean velocity at the inlet - X and dimensionless vertical and radial coordinates - U and V dimensionless vertical and horizontal components of velocity - H dimensionless height of channel - R radius of inlet to channel - W velocity of liquid - t temperature drop along channel height - Re = v_oR/ Reynolds number - Pe = v_oR/a Peclet number - Fr = v _o ² /g¦t_in–t_o R Froude number - Ho = v_o/R homochroneous number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 603–610, October, 1980.     

Hydrodynamic contact between a rotating roll and a semipermeable tray

A viscous fluid flow in the gap between a side surface of a rotating roll and a rectangular cavity with a semipermeable bottom surface is considered in the Reynolds approximation.Notation x, y, z Cartesian coordinates - U peripheral velocity of the roll - W translational velocity of the tray - h gap height - h ₀ minimum gap - side gap - v _x,v _y,v _z velocity components - K coefficient of channel wall permeability - P,504-1 dimensional and dimensionless pressures - R roll radius - S channel width - fluid viscosity - angle - x₀,₁, , dimensional and dimensionless coordinates of the flow zone boundaries - dimensionless permeability - friction - ,q geometrical simplexes - dimensionless variable - Q bulk flow rate of fluid - F buoyancy force - N power - I ₁,I ₂ integral parameters of flow - ₁, ₂ angular velocities of rotor and cylinder - _c fluid density - q gravity acceleration - Re Reynolds number - R ₁,R ₂ radii of cylinder and rotor in a granulator Volgograd Technical University. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 612–618, July–August, 1995.     

Transport in fluid helium-3 under pressure

The thermal conductivity of liquid helium-3 has been measured at temperatures between 1.3° K and 4.2° K and at pressures up to 55 atm. The viscosity data for liquid helium-3, reported briefly in Ref. 1 are here presented in full for temperatures 1.20° K, 2.00° K, and 3.02° K and at pressures up to 20 atm. Thermal conductivity and viscosity data at 2.00° K are combined with estimated values ofC _vto giveMK/ C _v(whereM is molecular weight,K is thermal conductivity, is viscosity andC _vis the molar specific heat), a dimensionless parameter that is 5/2 in gases at limiting low pressures. Finally, the thermal conductivity of gaseous helium-3 at 1-cm Hg pressure has been measured between 1.3° K and 4° K and compared with available theoretical estimates.     

Stability of operation of an apparatus containing a granular bed fluidized by a gas stream

The results of numerical experiments on the investigation of the stability of the fluidization process relative to finite perturbations and its behavior upon crossing the boundary of stability are presented.Notation H bed height - H₀, H_* bed heights in motionless and steady fluidized states - g free-fall acceleration - k₁, k₂ coefficients of resistance of gas-supply system and gas-distributing device, respectively - M molecular weight of gas - m mass of bed per unit cross-sectional area - p^*, p⁰ pressure at inlet and outlet of apparatus - Q₀, Q_b minimum fluidization velocity and average velocity of gas in the bubble phase - q, q_v total mass-flow rates of gas supplied to the bed and to the free cavity - R gas constant - S cross-sectional area of bed - V volume of cavity below gas-distributing grid accessible to the gas - gas density - T absolute temperature - c,, q₀ parameters introduced into (4) - t time - z dimensionless bed height - x dimensionless time - A, B, C, D, N, n dimensionless complexes introduced into (5) - v dimensionless volume - parameter introduced into (5) - z_* dimensionless bed height in steady fluidized state - circular frequency Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 889–892, November, 1977.     

Analysis of the parameters of discrete particle motion in axisymmetric turbulent impinging jets

The parameters of discrete particle motion in axisymmetric turbulent impinging air jets are determined.Notation x, y coordinates (Fig. 1) - v_x jet velocity - V_o maximum jet velocity - r_o nozzle radius - l _i length of the initial jet section - L spacing between the nozzle and the collision plane - ¯x dimensionless coordinate referred to the nozzle radius - ¯x_i dimensionless length of the initial section referred to the nozzle radius - d particle diameter - ₁ jet density - particle density - c_x particle drag coefficient - v particle velocity - v₁ axial jet velocity - kinematic coefficient of the flow viscosity - ¯x_o dimensionless coordinate referred to the distance L - d_c cement particle diameter - d_s sand particle diameter - ¯v_i dimensionless velocity of particle insertion into the jet, referred to V_o Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 813–817, November, 1979.     

Heat transfer through subcooled He I layer from distributed heat source in a pressurized He II channel

The subcooled He I layer, in contact with a large heated surface in a channel filled with the pressurized superfluid He II (He II_p), expands the non-boiling region above the Kapitza region up to q_n, above which nucleate boiling sets in. As the bath temperature decreases, q_n is increased more rapidly than q_λ at which the superfluidity is broken at the centre of the heated surface. The value of q_n is increased as the channel gap increases, and is independent of the channel orientation as well as q_λ. Metastabilization of superconducting coils may be enhanced by taking the non-boiling limit q_n into account.     

Heat and mass transfer of a multiatomic gas in a cylindrical capillary with arbitrary Knudsen numbers

Processes of heat and mass transfer of a multiatomic gas in a cylindrical channel of circular cross section with arbitrary Knudsen numbers are considered on the basis of a model kinetic equation, taking account of the excitation of rotational and vibrational degrees of freedom of the molecules.Notation Kn Knudsen number - f, f^tr total and translational Eucken factors - R_o capillary radius - m molecular mass - k Boltzmann's constant - n, T numerical density and temperature of gas - v_i i-th component of the molecular velocity - h_ij perturbation function - E_i ^(r), e_j ^(v) energy of the i-th rotational and j-th vibrational levels - E_o ^(r), E_o ^(v) equilibrium values of the rotational and vibrational energy - P_i ^(r), P_i ^(v) probability of rotational and vibrational states of energy E _i ^r and E _j ^v - , logarithmic pressure and temperature gradients - T_o mean gas temperature - R rarefaction parameter of gas - C _V ^r , C _V ^v contributions of rotational and vibrational degrees of freedom of the molecule to the specific heat at constant volume - U macroscopic gas velocity - q^(t), q^(r), q^(v) components of the heat flux density due to translational, rotational, and vibrational degrees of freedom of the molecules - P, pressure and dynamic viscosity of the gas - l free path length of molecules - up velocity of Poiseuille flow - u_T rate of thermal creep - cross-sectional area of capillary - I_n, I_q numerical and heat fluxes averaged over the channel cross section - universal index characterizing the thermomolecular pressure difference - ^t, ^r, ^v thermal conductivities due to translational, rotational, and vibrational degrees of freedom of the molecules - mass density of the gas - D_rr, D_vv diffusion coefficients of rotationally and vibrationally excited molecules among the unexcited molecules - Z_r rotational collisional number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 71–82, July, 1984.     

Hydrodynamic focusing of a particle flux

Based on numerical integration of the equations of mechanics of multiphase media, an effect of focusing of a particle flux generated by a source located on the upper wall of a closed vessel has been revealed and investigated.Notation t time - x, y Cartesian coordinates - U₁ (u ₁, v₁),P, ₁ velocity, pressure, and density of the gas - ₂,U ₂ mean density and velocity of the dispersed phase - V _k , r _k velocity and radius vector of a macroparticle - g gravitational acceleration - e(0–1) gravity force vector - dynamic viscosity of the gas - f friction force of particles in the gas - Eu, Re Euler and Reynolds numbers - dimensionless time of the high-rate relaxation of particles Élektrogorsk Research Center, Russia; Institute of Mechanics and Biomechanics, Sofia, Bulgaria; Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 355–360, May–June, 1995.     

Quantum decoherence with the Unruh single-particle state having right and left components

We investigate the effects of quantum decoherence generated by the Unruh effect in non-inertial frames under an amplitude damping channel and a phase damping channel, respectively, when the Unruh single particle has right and left components. We not only consider the influence of acceleration on entanglement, but also consider the influence of different rates between right and left components of the Unruh single-particle state on entanglement. We find that when the Unruh single-particle state has right and left components, i.e. |1?_U?=?q _L|0?_I|1?_II?+?q _R|1?_I|0?_II, |q _R|²?+?|q _L|²?=?1, with q _L?≠?0, there appears the sudden death of entanglement, which occurs earlier under both the amplitude damping channel and the phase damping channel with the increase of acceleration than that when the Unruh single-particle state only has a right component (q _R?=?1, q _L?=?0). We also find that the initial entanglement decreases with decrease of q _R from 1 to 1/2^1/2.     

Recent advances in the numerical analysis of heat pipes

Numerical simulation of heat pipes has progressed significantly in recent years. The state-of-the-art has been advanced in steady state, continuum transient, and frozen startup simulation for high, moderate, and low temperature heat pipes of conventional cylindrical and nonconventional geometries such as wing leading edges and spacecraft nosecaps. This review summarizes these advancements and discusses the important results.List of symbols A cross-sectional area of the vapor channel, m² - c specific heat, J/(kg-K) - C _p specific heat at constant pressure, J/(kg-K) - C _v specific heat at constant volume, J/(kg-K) - D vapor space diameter, m - D _v coefficient of self-diffusion, m²/s - G vapor mass flux, kg/(m²-s) - h convective heat transfer coefficient, W/(m²-K) - h _fg latent heat of evaporation, J/kg - H latent heat due to melting or freezing, J/kg - k thermal conductivity, W/(m-K) - Kn Knudsen number, /D - L total length of the heat pipe, m - L _a length of the adiabatic section, m - L _c length of the condenser, m - M molecular weight, kg/kmol - Ma Mach number, - m _i mass flux at the liquid-vapor interface, kg/(m²-s) - P pressure, N/m² - q heat flux, W/m² - Q heat input at the active evaporator, W - Q _o heat output at the condenser, W - r radial coordinate, m - R gas constant, J/(kg-K) - R _o outer pipe wall radius, m - R _u universal gas constant, J/(kmol-K) - R _v vapor space radius, m - t time, s - T temperature, K - T _i,c interfacial temperature on the continuum vapor flow side, K - T _i,r interfacial temperature on the rarefied vapor flow side, K - T _rf reference (saturation) temperature, K - T _tr transition vapor temperature, K - v radial velocity, m/s Funding for this work was provided by a joint effort of the NASA Lewis Research Center and the Thermal Technology Center of Wright Laboratory under contract No. F33615-88-C-2820     

Characterization of deep levels in semi-insulating gallium arsenide

Two traps with activation energies ofE _c – 0·47 eV andE _v + 0·79 eV have been detected in semi-insulating GaAs:Cr through optical transient current spectroscopy (otcs) in the temperature range 300–450 K. The latter trap gives rise to rising current transients which result in a negative peak in theotcs spectrum. The theoretical expressions for current transients have been derived.     

Use of the WKB method to investigate connective heat transfer in a micropolar fluid

A general approximate solution is obtained for problems of heat transfer associated with a flow of micropolar fluid in a plane channel with boundary conditions of the first and second kind and its accuracy is determined.Notation T_o and T_w temperatures of entrance section and wall of channel, respectively - dp/dx pressure gradient - x₁, x₂ longitudinal and transverse coordinates, respectively (or x and y) - Pe=2v _m ^N h/a Peclet number - v _m ^N mean velocity of Newtonian fluid with viscosity +/2 in channel of width 2h - boundary condition parameter - 2h width of channel - v_x and v_z nonzero components of velocity and microrotation of micropolar fluid - a and thermal diffusivity and thermal conductivity of fluid - , , and viscosities of micropolar fluid - q_w heat flux density on wall - _n and Y_n(y) eigenvalues and eigenfunctions of Sturm-Liouville problem - C_n constants that can be determined by using orthogonality of eigenfunctions Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 732–738, October, 1980.     

Nonisothermal flow of anomalously viscous liquids in the channels of screw extruders

The nonisothermal flow of an anomalously viscous liquid in the channel of a screw extruder is analyzed with allowance for the influence of the side walls. A comparison with experimental data is given.Notation x, y, z, x_i, x_j Cartesian coordinates - H height of channel - W width of channel - L and S lengths of the screw and of the channel - pitch of the helical line - v₀ velocity of the upper plate; i, j=1, 2, 3 - w_x, w_y, w_z dimensionless velocities of the liquid - v_x, v_y, v_z, v_i, v_j true velocities of liquid particles - A₁ pressure gradient - Q bulk flow rate of the product - P pressure - T temperature - N power - _ij components of the stress tensor - I₂ second (quadratic) invariant of the tensor of deformation velocities - C and specific heat and thermal conductivity of the liquid - density of the liquid - ₁ and ₂ heat-exchange coefficients - C₀ and C₁ thermophysical constants - ₀, n,, T_H rheological constants - T₀ liquid temperature at the screw inlet - Re Reynolds number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 5, pp. 877–883, November, 1978.     

Hydrodynamic instability of a suspension of spherical particles through a branching network of circular tubes

A numerical method is presented for computing the unsteady flow of a monodisperse suspension of spherical particles through a branching network of circular tubes. The particle motion and interparticle spacing in each tube are computed by integrating in time a one-dimensional convection equation using a finite-difference method. The particle fraction entering a descendent tube at a divergent bifurcation is related to the local and instantaneous flow rates through a partitioning law proposed by Klitzman and Johnson involving a dimensionless exponent, q ≥ 1. When q = 1, the particle stream is divided in proportion to the flow rate; as q → ∞, the particles are channeled into the tube with the highest flow rate. The simulations reveal that when the network involves two or more generations, a supercritical Hopf bifurcation occurs at a critical value of q, yielding spontaneous, self-sustained oscillations in the segment flow rates, pressure drop across the network, and particle spacing in each tube. A phase diagram is presented to establish conditions for unsteady flow. As found recently for blood flow in a capillary network, oscillations can be induced for a given network tree order by decreasing the ratio of the tube diameter from one generation to the next or by decreasing the diameter of the terminal segments. The instability is more prominent for rigid than deformable particles, such as drops, bubbles, and cells, due to strong lubrication forces between the tightly fitting particles and tube walls. Variations in the local particle spacing, therefore, have a more significant effect on the effective viscosity of the suspension in each tube and pressure drop required to drive a specified flow rate.     

Enhancement of heat transfer of mixed convection for heated blocks using vortex shedding generated by an oblique plate in a horizontal channel

Summary The problem of heat transfer enhancement of mixed convective flow past heated blocks in a horizontal channel is investigated. The heat transfer enhancement in this paper has been accomplished by the installation of an oblique plate to generate vortex shedding, which is used in flow modulation. Results for the details of the streamlines in the channel and the Nusselt number along the blocks with and without an oblique plate have been presented.Notation C _p pressure coefficient (2f Pds/f ds) - d length of an oblique plate - ds surface area increment along an oblique plate - f_s frequency of the vortex shedding - Gr Grashof number - H channel wall-to-wall spacing - h height of the block - k thermal conductivity - L channel length - Nu Nusselt number - time-mean Nusselt number (f Nudt/f dt) - average time-mean Nusselt number - n normal vector - P dimensionless pressure (p ^*/(u ² ) - p ^* pressure - Pr Prandtl number (/) - q heat flux at the block boundary - Re Reynolds number (u w/v) - St Strouhal number (df_ssin /u ) - T^* temperature - T uniform inlet temperature - t dimensionless time (t ^* / (w/u )) - t dimensionless time increment - t ^* time - u uniform inlet velocity - u, v dimensionless velocity components (u=u ^*/u ,v=v ^*/v ) - u ^*,v ^* velocity components - w width of the block - x,y dimensionlessx ^*,y ^* coordinates (x=x ^*/w,y=y ^*/w) - x ^*,y ^* physical coordinates - thermal diffusivity - angle of inclination for a plate - dimensionless temperature ((T^*–T ^* )/(qw/k)) - v kinematic viscosity of fluid     

Reply

The row-column setting for comparing v experimental treatments is a p × q array of experimental units, with the p rows and q columns representing levels of two blocking factors. When p = q = v, the optimal design for estimating treatment contrasts is a Latin square. For a v ^t factorial treatment set in the same setting, t mutually orthogonal Latin squares are an optimal main-effects plan. Orthogonal collections of Latin squares arise when these results are generalized to b row-column layouts of size v × v, where b is greater than 1. This article studies these orthogonal collections, with special emphasis on small v and b.     

Mixed convection flow of micropolar fluid over an isothermal plate with variable spin gradient viscosity

Summary A steady two-dimensional mixed convection flow of viscous incompressible micropolar fluid past an isothermal horizotal heated plate with uniform free stream and variable spin-gradient viscosity is considered. With appropriate transformations the boundary layer equations are transformed into nonsimilar equations appropriate for three distinct regimes, namely, the forced convection regime, the free convection regime and the mixed convection regime. Solutions of the governing equations for these regimes are obtained by an implicit finite difference scheme developed for the present problem. Results are obtained for the pertinent parameters, such as the buoyancy parameter, in the range of 0 to 10 and the vortex viscosity parameters, =0.0, 1.0, 3.0, 5.0 and 10.0 for fluid with Prandtl number Pr=0.7 and are presented in terms of local shear-stress and the local rate of heat transfer. Effects of these parameters are also shown graphically on the velocity, temperature and the couple stress distributions. From the present analysis, it is observed that both the momentum boundary layer and the thermal boundary layer increase due to an increase in the vortex viscosity of the fluid.List of symbols f, F, dimensionless stream function for forced convection free convection and mixed convection, respectively - g acceleration due to gravity - Gr_x local Grashof number - j micro-inertia density - m ₂₃ distribution of couple stress - N microrotation component normal to (x, y)-plane - p pressure of the fluid - q dimensionless rate of heat transfer - Re_x local Reynolds number - T temperature of the fluid in the boundary layer - T temperature of the ambient fluid - T temperature at the surface - u, v thex andy-components of the velocity field - U free stream velocity - x, y axis in direction along and normal to the plate Greek thermal diffusivity - coefficient of volume expansion - vortex viscosity parameter - stream function - , , nondimensional similarity variables - buoyancy parameter (=Gr _x Re _x ^/5/2 ) - vortex viscosity - density of the fluid - v kinematic coefficient of viscosity - spin-gradient viscosity - stream function - dimensionless skin-friction - fluid viscosity     

Viscosities of l-Histidine/l-Glutamic Acid/l-Tryptophan/Glycylglycine?+?2 M Aqueous KCl/KNO3 Solutions at T?=?(298.15 to 323.15)?K

Viscosity values of l-histidine/l-glutamic acid/l-tryptophan/glycylglycine + 2 M aqueous KCl/KNO₃ solutions have been determined experimentally as a function of molal concentration of amino acid/peptide at different temperatures: (298.15, 303.15, 308.15, 313.15, 318.15, and 323.15) K. Using the viscosity values of the solvent and solution, the relative viscosity, specific viscosity, and viscosity B-coefficient values have been computed. The trends of the variation of experimental and computed parameters with the solute concentration and temperature have been interpreted in terms of zwitterions–ions, zwitterions–water dipoles, ions–water dipoles, and ions–ions interactions operative in the systems.     

First-order chemical reaction on flow past an impulsively started vertical plate with uniform heat and mass flux

Summary A finite-difference solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite plate with uniform heat and mass flux is presented here, taking into account the homogeneous chemical reaction of first order. The velocity profiles are compared with the available theoretical solution and are found to be in good agreement. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first order chemical reaction the velocity decreases with increasing values of the chemical reaction parameter. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically.List of symbols C concentration - C species concentration in the fluid far away from the plate - C _w species concentration near the plate - C dimensionless concentration - D mass diffusion coefficient - Gc mass Grashof number - Gr thermal Grashof number - g acceleration due to gravity - j mass flux per unit area at the plate - K dimensionless chemical reaction parameter - K _l chemical reaction parameter - k thermal conductivity - Nu_x dimensionless local Nusselt number - dimensionless average Nusselt number - Pr Prandtl number - q heat flux per unit area at the plate - Sc Schmidt number - Sh_x dimensionless local Sherwood number - dimensionless average Sherwood number - T temperature - T temperature of the fluid far away from the plate - T _w temperature of the plate - T dimensionless temperature - t time - t dimensionless time - u ₀ velocity of the plate - U, V dimensionless velocity components inX,Y-directions, respectively - u, v velocity components inx, y-directions, respectively - X dimensionless spatial coordinate along the plate - x spatial coordinate along the plate - Y dimensionless spatial coordinate normal to the plate - y spatial coordinate normal to the plate - thermal diffusivity - volumetric coefficient of thermal expansion - * volumetric coefficient of expansion with concentration - coefficient of viscosity - kinematic viscosity - _x dimensionless local skin-friction - dimensionless average skin-friction     

Non-linear diffusive flood routing

Summary A flood routing model based on a non-linear diffusion-convection equation is presented. Simplifying assumptions are made regarding the river geometry, and for the initial and boundary conditions. Solutions of the non-linear equation are discussed in terms of applicability and compared to solutions of the corresponding linearized equation. Stability aspects are investigated and two different numerical schemes are examined. Finally, results are compared to prototype observations, and the computation procedure is explained in detail.Notation A cross-sectional area - b constant river width - B variable river width - F Froude number - g gravitational acceleration - h flow depth - S _f frictional gradient - S ₀ bottom slope - K roughness coefficient - m cotangent of channel side-wall angle - p lateral inflow intensity - q discharge per unit width - q ₀ initial discharge per unit width - q ^* maximum discharge per unit width - Q non-dimensional discharge - Q ₀ non-dimensional initial discharge - Q ^* non-dimensional initial discharge surplus - Q _max non-dimensional maximum discharge - relative maximum discharge - dimensional discharge - r hydrograph shape parameter - R hydraulic radius - t time - T non-dimensional time - v average velocity - x longitudinal coordinate - X non-dimensional longitudinal coordinate - y relative flow depth - Y non-dimensional flow depth - diffusion coefficient With 11 Figures