Turbulent free convection between vertical isothermal plates with asymmetrical heating

Results of numerical investigation of the flow and heat transfer at turbulent free convection between the vertical parallel isothermal plates with different temperatures are presented. The temperature factor R _T varied within ?2 ÷ 1. The Rayleigh number changed within Ra = 10⁷ ÷ 10⁹, and the ratio of geometrical sizes of plates and distances between them was constant A = L/w = 10. Numerical studies were performed via the solution to the two-dimensional Navier—Stokes equations and energy equation in Boussinesq approximation. The considered boundary-value problem has the unknown conditions at the inlet and outlet between the plates. To describe turbulence, the modified low-Reynolds k-? model was used. The effect of the temperature factor on the flow structure at the channel inlet and outlet was analyzed. Data on distributions of velocities and temperatures between the plates, local and integral heat transfer allow deeper understanding of the mechanism of transfer processes between the parallel plates with asymmetrical heating.     

Heat transfer at a laminar free convection and separated flow past a rib in a vertical channel with isothermal walls

The results of numerical computations of a free laminar convection and heat transfer between two parallel isothermal plates in the presence of a single rib on the channel surface are presented. The investigations have been conducted for a channel with the aspect ratio AR = L/w = 10, where L is the channel height, and w is the distance between the plates. An infinitely thin adiabatic rib was located on one of the channel walls in the middle of its height. The relative rib height l/w was varied in the range 0÷0.8. The wall temperature was higher than the ambient temperature, and the Rayleigh number was varied in the range Ra = 10²÷10⁵. The main attention has been paid to the study of the influence of the rib height and the Rayleigh number on local and integral heat transfer and the Reynolds number in the channel (the convective thrust). A fundamental difference in the heat transfer over the channel height has been shown on the ribbed wall and on a smooth surface. The computational results have been compared with the case of a symmetric distribution of the ribs on the both walls with the integral height equal to a single rib.     

Laminar free convection heat transfer between vertical isothermal plates

The paper represents results on numerical investigation of flow and heat transfer between two isothermal vertical plates under laminar natural convection. A system of complete Navier–Stokes equations is solved for a two-dimensional gas flow between the plates along with additional rectangular regions (connected to inlet and outlet sections), whose characteristic sizes are much greater than the spacing between the plates. The calculations were performed over very wide ranges of Rayleigh number Ra = 10 ÷ 10⁵ and a relative channel length AR = L/w = 1 ÷ 500. The influence of the input parameters on the gas-dynamic and thermal structure of thermogravitational convection, the local and mean heat transfer, and also the gas flow rate between the plates (convective draft. We determined sizes of the regions and regime parameters when the local heat flux on the walls tends to zero due to the gas temperature approach to the surface temperature. It is shown that the mean heat transfer decreases as the relative channel length AR grows, whereas the integral gas flow rate (convective draft) and Reynolds number in the channel Re = 2wUm/ν increase. The use of a modified Rayleigh number Ra* = Ra · (w/L) (Elenbaas number) leads to generalization of calculation data on mean heat transfer. These data are in good agreement with the correlations for heat transfer [1, 2] and gas flow rate [3]. The reasons of variation of the data in the range of low Rayleigh numbers are discussed in detail.     

TURBULENT NATURAL CONVECTION IN AN ENCLOSURE WITH LOCALIZED HEATING FROM BELOW

Natural-convection heat transfer in a cylindrical enclosure, heated partially from below by a disk-shaped heating surface and cooled from the top and the side, was investigated experimentally and numerically. Heat transfer measurements are presented for the range of Rayleigh numbers from 10⁸ to 2 × 10¹⁰. The total acceleration normal to the heating surface was varied from I to 100 times the standard gravitational acceleration. The heat flux was varied from 0.19 MW / m1 to 1.5 MW / m². The test results were correlated by an equation of the form Nu_D = 0.2Ra^0.325 _D for Prandtl number 2 and aspect ratio I. The flow field was studied numerically using FLUENT code.     

Laminar free convection heat transfer and separated flow structure in a vertical channel with isothermal walls and two adiabatic opposing fins

Results of numerical study of laminar free convection and heat transfer in a vertical plane-parallel channel with two thin adiabatic fins on its walls are presented. The channel has the open inlet and outlet, and its surfaces are maintained at the same temperature. The channel height is unchanged with elongation parameter A = L/w = 10, and the fins are located in the middle of the channel toward each other. Fin height l/w = 0 ÷ 0.4 and Rayleigh number Ra = 10² ÷ 10⁵ are varied in calculations. The effect of these parameters on the flow structure, temperature field, local and integral heat transfer, and gas flow caused by gravitational forces are analyzed in detail. Numerical analysis is based on solving the full Navier–Stokes and energy equations in twodimensional statement and Boussinesq approximation. To determine the dynamic and thermal parameters at the inlet and outlet, the calculation is carried out with two large volumes attached to the inlet and outlet. The features of the flow and heat transfer at separated flow around the channel fins are studied in detail in this work.     

Superconductivity in amorphous thin films of tin–copper

The properties of the superconducting state in the amorphous Sn_1?xCu_x thin films were characterized. The concentration of copper changes in the range from 0.08 to 0.41. The calculations were conducted in the framework of the strong-coupling formalism, wherein the Eliashberg functions determined in the tunnel experiment were used. The value of the Coulomb pseudopotential equal to 0.1 was adopted. It will be shown that the critical temperature (T_C) decreases from 7 to 3.9 K. The ratio, R_Δ = 2Δ(0)/k_BT_C, differs from the BCS value: R_Δ ∈ <4.4, 3.95>, where Δ(0) represents the order parameter. Similarly behave the ratios: R_C = ΔC(T_C)/C^N(T_C) ∈ <2.2, 1.75> and R_H = T_CC^N(T_C)/H²_C(0) ∈ <0.141, 0.154>. The parameter ΔC(T_C) is the specific heat jump, C^N(T_C) denotes the specific heat of the normal state and H_C(0) is the thermodynamic critical field.     

Lattice thermal expansion of cesium plumbo chloride

The temperature variation of the lattice parameter of CsPbCl₃ in the cubic phase has been studied by x-ray method, from a determination of the precision lattice parameter at various temperatures, ranging from 50°C to 400°C. The coefficient of thermal expansion of CsPbCl₃ can be expressed by the quadratic equation,α _T = 21.6 × 10⁻⁶ + 2.44 × 10⁻⁹ T + 5.90 × 10⁻¹¹ T ².     

Elektronen-Spin-Gitter- und Spin-Spin-Relaxation von Cu(II) in Ni(II)-bis(1,1-dicyanoäthylen-2,2-dithiolat)-Einkristallen

The temperature-dependence of the electron-spin-lattice- and -spin-spin-relaxation times T₁ and T₂ of Cu(II) in (Tetrabutyl-ammonium)-Ni(II)bis(1,1-dicyanoethylene-2,2-dithiolate) single crystals are reported. In the range of the direct processes (T = 2…7°K) a dependence of the spin-lattice relaxation rate on the orientation of the Cu-nuclear spin was observed. From the temperature-dependence of the RAMAN -process the DEBYE -temperature and the averaged soundvelocity of the molecular crystal have been derived being θ = (100 ± 10)°K and 〈v〉 ≈ 0.7. 10⁵ cm/sec. In order to explain the unusual small line-width of the ^63,65Cu-hyperfine structure lines of the EP R-spectrum in the investigated large temperature-range of T = 2.0…300°K the mechanisms contributing to the line width were analyzed. The possible influence of the strong covalency of the Cu-ligand bonds to T₁ is considered.     

From fractional Chern insulators to a fractional quantum spin hall effect

Horizontal rolls, generated in convective flow above a partially heated bottom in a rectangular box are studied experimentally for a wide range of the Prandtl number (7 ≤ P _r ≤ 1020), the Rayleigh number (300 ≤ R _a ≤ 2.8 × 10⁷) and the aspect ratio (0.08 ≤ a ≤ 0.7). Experimental studies are supported by direct numerical simulations, which made possible the examination of the regimes inaccessible in the experiment, and also to investigate in detail the heat transfer in the convective flow. A variety of regimes with longitudinal helical rolls, with transverse rolls and with mixed structures has been observed. The structure of secondary flows is defined by the level of convective supercriticality in the boundary layer (Rayleigh number) and the intensity of the throughflow, defined by the Reynolds number, which depends itself on the heating and size, i.e. on the Rayleigh number. Most of the studied regimes were characterized by the appearance of longitudinal rolls. The transverse rolls appear in the flow only under the conditions of the large vertical drop in the temperature and weak large-scale flow (that is possible only at large values of the Prandtl number). Both longitudinal and transverse rolls lead to remarkable heat transfer enhancement. The formation and characteristics of horizontal rolls are described in details.     

HEAT AND MASS TRANSFER AND WALL SHEAR STRESS IN VERTICAL GAS-LIQUID FLOW

Results of an experimental investigation of heat and mass transfer and wall shear stress at gas-liquid flow in a vertical tube are presented. Local wall shear stress and mass transfer coefficients were measured by an electrochemical method. Experiments were performed in the range of Reynolds number variation with respect to liquid Rc_i, = 8.5 × 10³-5.4 × 10⁴, gas Re_g = 3 × 10³-1.4 × 10⁵, pressure 0.1-1 MPa. The relationship between heat and mass transfer and wall shear at gas-liquid flows is shown to exist. The results of measuring heat and mass transfer coefficients are generalized by formulas applied to calculate heat and mass transfer in single-phase turbulent flow.     

Fundamental optimal relation of a generalized irreversible Carnot heat pump with complex heat transfer law

The fundamental optimal relation between heating load and coefficient of performance (COP) of a generalized irreversible Carnot heat pump is derived based on a new generalized heat transfer law, which includes the generalized convective heat transfer law and generalized radiative heat transfer law, q ∝ (ΔT ⁿ ) ^m . The generalized irreversible Carnot heat pump model incorporates several internal and external irreversibilities, such as heat resistance, bypass heat leakage, friction, turbulence and other undesirable irreversibility factors. The added irreversibilities besides heat resistance are characterized by a constant parameter and a constant coefficient. The effects of heat transfer laws and various loss terms are analysed. The heating load vs. COP characteristic of a generalized irreversible Carnot heat pump is a parabolic-like curve, which is consistent with the experimental result of thermoelectric heat pump. The obtained results include those obtained in many literatures and indicated that the analysis results of the generalized irreversible Carnot heat pump were more suitable for engineering practice than those of the endoreversible Carnot heat pump.     

Lattice Boltzmann simulation of 3-dimensional natural convection heat transfer of CuO/water nanofluids

The present study investigated fluid flow and natural convection heat transfer in an enclosure embedded with isothermal cylinder. The purpose was to simulate the three-dimensional natural convection by thermal lattice Boltzmann method based on the D3Q19 model. The effects of suspended nanoparticles on the fluid flow and heat transfer analysis have been investigated for different parameters such as particle volume fraction, particle diameters, and geometry aspect ratio. It is seen that flow behaviors and the average rate of heat transfer in terms of the Nusselt number (Nu) are effectively changed with different controlling parameters such as particle volume fraction (5 % ≤ φ ≤ 10 %), particle diameter (d _p = 10 nm to 30 nm) and aspect ratio (0.5 ≤ AR ≤ 2) with fixed Rayleigh number, Ra = 10⁵. The present results give a good approximation for choosing an effective parameter to design a thermal system.     

Untersuchungen zum Existenzbereich einer BOLTZMANN-Verteilung im Argonbogenplasma

Using as plasma source a wall stabilized argon arc working within a restricted parameter range (inner tube diameter = 7 mm, pressure = 30–120 Torr, current = 5-20 A)) the existence of a Boltzmann equilibrium between spectral energy levels is checked by comparing measured occupation number densities of higher excited levels (N_{m, exp}) with the corresponding number densities calculated under the assumption of Boltzmann equilibrium (N_{m, calc}). The methods for determination of the quantities N_{m, exp'} T_g (2300–5405°K), T_e (7170–9950°K) and N_e (0.33 – 2.4 × 10¹⁵ cm^?3) needed for this comparison are described. It can be shown within the limit of experimental error that a Boltzmann equilibrium exists at least for electron densities of N_e > 3 · 10¹⁴ cm^?3. The problem of energy balance of that type of arcs used in these experiments is discussed.     

Thermal conductivity of nitrogen in the temperature range 350–2500 K

The thermal conductivity of nitrogen is determined in a conductivity column instrument in the temperature range of 338 to 2518 K with an estimated uncertainty of about ± 1·5 per cent. The experimental data points are correlated by a cubic polynomial in temperature, viz. k(T)/(mW m^-1 K^-1) = 12·18 + 0·05224(T/K) - 0·6482 × 10^-6(T/K)² - 0·2765 × 10^-9(T/K)³. These conductivity values determined from heat transfer data taken in the continuum regime are found to be in fair agreement with the values obtained from similar data referring to low pressure range.

The present results are compared with the conductivity determinations of other workers and with the predictions of various theories developed for polyatomic gases. It is pointed out that a reliable calculation of thermal conductivity over an extended temperature range is impossible at the present time due to the absence of a large variety of experimental molecular data needed for such an effort. Average values of the vibrational energy diffusion coefficient, D _vib, are computed from the present k(T) data.     

Negative Ions,Ozone, and Metastable Components in dc Oxygen Glow Discharge

In a dc glow discharge in oxygen, the concentrations of minor components of O₂(a¹Δ_g), O₂(b¹ Σ_g), O₃, O(¹D), as well as nagative ions and electrons have been measured. Balance equations have been derived which describe satisfactorily the stationary concentrations of these components as functions of gas pressure and discharge current. For the first time, the rate constants of important aeronomical reactions (a) O^? + O₂(a¹Δ_g) → O₃ + e, (b) O₂^? + O₂(a¹Δ_g) → 2O₂ + e and (c) e + O₃ → O₂^? +O have been measured as functions of gas temperature T and mean energies of ions E_i and electron E₆: K_a = (2.5 ± 0.5) · 10^?9 · (T/300)^{4 ± 0.4}· (E_i/0.04)^{?2.6 ± 0.4} cm³/s for T = 385?605 K and E_i = 0.10 ? 0.66 eV; K_b = (1.0 ± 0.3) · 10^?10 · (T/300)^{?2 ± 0.5} · (E_i/0.04)^{0.23 ± 0.05} cm³/s for T = 330?605 K and E_i = 0.09 + 1.5 eV; K_c for E_e = 0.8÷5 eV.     

Critical point phenomena in the electrical resistivity of binary liquid systems: CS2 + CH3CN and CS2 + CH3NO2

Electrical resistance measurements are reported on the binary liquid mixtures CS₂ + CH₃CN and CS₂ + CH₃NO₂ with special reference to the critical region. Impurity conduction seems to be the dominant mechanism for charge transport. For the liquid mixture filled at the critical composition, the resistance of the system aboveT _c follows the relationR=R _c−A(T−T _c) ^b withb=0·6±0·1. BelowT _c the conductivities of the two phases obey a relation σ₂−σ₁=B(T _c−T)^β with β=0·34±0·02, the exponent of the transport coefficient being the same as the exponent of the order parameter, an equilibrium property.     

Peculiarities of deformation of compliant coatings with increased strength

Influence of elasticity module of coating material on the parameters of hard compliant coatings deformation has been analysed. Calculation using two-dimensional model has shown that maximum coating deformation is achieved at the ratio of flow rate U to the parameter C _t ⁰ = (E/3ρ)^0.5 approximately equal to 2.5, however, velocity of wall surface motion has first local maximum at U/C _t ⁰≈1. The range of coating parameters’ values at which compromise between its hardness and intensity of interaction with turbulent flow is provided has been determined. For rubbery materials with Poisson coefficient of about 0.5, correlations of the flow velocity and parameter C _t ⁰ shall be in the range 1÷1.5. It is shown that at such parameters, the mean square value of the coating surface deflection/inflection is less than the viscous sublayer thickness, its correlation with the wavelength is very small and equals (1÷5)·10⁻⁴. Such form of deformed surface fundamentally differs from the parameters of the wave wall in Kendall’s experiments which results are used for calculation of inverse influence of wall deformation on the flow. It was assumed that solid compliant coatings do not cause instability of interaction with the ambient flow.     

GaSb layers with low defect density deposited on (001) GaAs substrate in two-dimensional growth mode using molecular beam epitaxy

We report on the growth of fully relaxed and smooth GaSb layers with reduced density of threading dislocations, deposited on GaAs substrate. We prove that three parameters have to be controlled in order to obtain applicable GaSb buffers with atomically smooth surface: interfacial misfit (IMF), the etch pit density (EPD) and the growth mode.The GaSb/GaAs interfacial misfit array and reduced EPD ≤1.0 × 10⁷ cm^?2 were easily obtained using As-flux reduction for 3 min and Sb-soaking surface for 10 s before the GaSb growth initiation. The successive growth of GaSb layer proceeded under the technological conditions described by the wide range of the following parameters: r_G ∈ (1.5 ÷ 1.9) Å/s, T_G ∈ (400 ÷ 520)°C, V/III ∈ (2.3 ÷ 3.5). Unfortunately, a spiral or 3D growth modes were observed for this material resulting in the surface roughness of 1.1 ÷ 3.0 nm. Two-dimensional growth mode (layer by layer) can only be achieved under the strictly defined conditions. In our case, the best quality 1-μm-thick GaSb buffer layer with atomically smooth surface was obtained for the following set of parameters: r_G = 1.5 Å/s, T_G = 530 °C, V/III = 2.9. The layer was characterized by the strain relaxation over 99.6%, 90° dislocations array with the average distance of 5.56 nm, EPD ～8.0 × 10⁶ cm^?2 and 2D undulated terraces on the surface with roughness of about 1 ML. No mounds were observed. We belive that only thin and smooth GaSb layer with reduced EPD may be applied as the buffer layer in complex device heterostructures. Otherwise, it may cause the device parameters deterioration.     

Analytical solution of non-Fourier temperature response in a finite medium symmetrically heated on both sides

This paper presents an analytical solution of transient heat conduction in a thin film subjected to symmetrical laser heating, employing the dual-phase lag model. Laser heating is modeled as an internal heat source. The analytical solution is derived using the finite integral transforms and the method of variation of parameters. The solutions for different time characteristics of heat sources capacity (instantaneous, rectangular, light, and Gaussian) are discussed. The effect of the control parameter B =τ _T /2r _q on the temperature profiles is examined in details.     

Effect of Discharge Plasma Potential on Diffusion Plasma Parameters Controlled by a Mesh Grid in a Double Plasma Device

The plasma region under investigation is separated from the discharge region by a mesh grid. Plasma potential and electron number densities and electron temperatures under bi‐Maxwellian approximation for electron distribution function of the multi‐dipole argon plasma are measured. The cold electrons in the diffusion region are produced by local ionization. The hot electrons are the ionizing electrons behaving as Maxwellian. The electron trapping process in the discharge region is produced by potential well due to positive plasma potential with respect to the anode and by a repulsive grid. The dependence of ratios of the density of the hot to the cold electrons N_E (=N_eh/N_ec) and hot to cold electron temperature T(=T_eh/T_ec) in the diffusion region on the depth of the potential well has been investigated. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)