Entropy Flow of Chemical Oscillating Reactions Involving Amino Acids

Variations of H⁺, Mn²⁺, and BrO₃^-{{\rm BrO}_3^-} during chemical oscillating reactions involving amino acids were investigated using H₂SO₄–BrO₃^-{{\rm BrO}_3^{-}} –Mn²⁺–acetone as an oscillator, and the thermodynamic functions (ΔS, ΔH, and ΔG) were calculated. The results indicated that the oscillating reaction is a process from disorder to order. In the oscillating system, the heat provided by the environment is used to increase the internal energy and entropy. When external positive entropy flow could make the system reach negative entropy flow, the system starts to oscillate and to maintain oscillations by a stable entropy.     

Thermodynamic analysis of free convection film condensation on an elliptical cylinder

Abstract

This paper aims to perform thermodynamic analysis of saturated vapor flowing slowly onto and condensing on an elliptical cylinder. This is the first approach to investigate how the geometric parameter‐ellipticity and surface tension affect local entropy‐generation rate during film‐wise condensation heat transfer process. The results observe that entropy generation decreases with decreasing ellipticity. It indicates that the entropy generation number is nearly unaffected by surface tension forces at small ellipticity like e ≤ 0.7, but somewhat influenced at large ellipticity for the whole perimeter. From the second law point of view, local entropy generation increases with ellipticity as local heat transfer coefficient does. Furthermore, the entropy‐generation rate due to gravity‐driven film flow friction is proportional to Brinkman group parameter. The irreversibility ratio indicates that film flow friction irreversibility starts to dominate over heat transfer irreversibility in the lower half of streamwise length for higher values of Brinkman group parameter (Br/T = 1).     

Self-Organized Heat Transport Near the Superfluid Transition in 4He

Heat transport through a column of superfluid ⁴ He has been observed experimentally to self-organize, resulting in a thermal gradient that exactly matches the gradient in the superfluid transition temperature across the column, leaving the entire sample at a constant distance from the superfluid critical point¹. We describe a new experiment that is designed to accomplish three objectives: 1) search for the upper critical heat flux above which self-organized heat transport can no longer occur, 2) measure the heat capacity of the self-organized heat transport state, and 3) test recent theoretical predictions^2,3 of the microscopic mechanism that is responsible for this self-organization.     

Measurement of fountain pressure and other thermal properties in superfluid3He

The fountain pressure, heat capacity, and thermal conductivity of superfluid ³ He have been measured simultaneously at pressures of 29, 23.2, 10, and 2.5 atm and at the saturated vapor pressure. If the fountain equation, based on the two-fluid model, is used to compute the entropy from the observed fountain pressure, it is consistent with the entropy obtained by integrating the specific heat. The measured thermal conductivities are dominated by a diffusive conductivity which is inversely proportional to the temperatureT _c .Work supported by NSF, DMR-72-02926.     

Investigations on the heat transfer of boiling binary refrigerant mixtures

Heat transfer during nucleate pool boiling was experimentally determined for the mixtures R-12/R-113, R-22/R-12, R-13/R-12, R-13/R-22 and R-23/R-13. For purposes of comparison, the respective five pure refrigerants were also investigated. Dependent upon the mixture, the measurements were made at boiling pressures of p = 0.1 to 2 MPa within the temperature region of t = 198 to 333 (−75° + 60°C) and at heat fluxes of Q = 4 × 10³ to 10⁵ W m⁻². A horizontal, electronically heated copper plate with A = 3 cm² was used. The following quantities were measured: pressure; temperature difference between the heating surface and the boiling liquid; composition and temperature in the liquid and vapour phases; and heat flow rate. The mean error of the heat transfer coefficients found was ± 5%.The results clearly show that the heat transfer for an evaporating mixture deteriorates as compared to the pure components. Essential parameters influencing this reduction are pressure, difference between vapour and liquid composition and heat flux. The fundamental relations and characteristic differences between the individual mixtures are illustrated by figures. The heat transfer coefficients measured can be represented within the whole region studied by a modified relation according to Körner.Observation of the process of evaporation has shown that by agitation (increase of convection) the heat transfer in mixtures can be improved. Additional experiments with evaporation during fluid flow in a pipe are presently in progress.     

Investigation of entropy generation in a helically coiled tube in flow boiling condition under a constant heat flux

There are many methods to augment the heat transfer rate in flow boiling in industrial applications. The helically coiled tubes are one of the best geometries to enhance the heat transfer rate. The entropy generation analysis is an appropriate tool to evaluate the contribution of heat transfer and pressure drop mechanisms. In the present paper, the entropy generation in the helically coiled tube under flow boiling is studied. The optimum tube and coil diameters under specified conditions are found. The effect of different flow conditions such as mass velocity, inlet vapor quality, saturation temperature, and heat flux on contributions of pressure drop and heat transfer in entropy generation is discussed. The Bejan number (Be) and irreversibility distribution ratio (IDR) at different saturation temperatures versus mass velocity are plotted. The comparison between entropy generation and contributions of pressure drop and heat transfer for the helically coiled tube and the straight one is presented. The entropy generation number (N_s) for different flow conditions is plotted. The entropy generation analysis shows that there is a favorable region to use the helically coiled tube with respect to the straight one.     

The importance of water migration in the measurement of the thermal conductivity of unsaturated frozen soils

The transport of heat in frozen soil may occur by conduction and by the convective transport of sensible and latent heat arising from the flow of water in the vapor, liquid and solid states. Theory describing the coupled flow of heat and of water in the liquid and vapor states is used to derive a definition of apparent thermal conductivity (the convective transport of heat in the movement of ice in unstaturated soils is assumed to be negligible). Calculations suggest that, at temperatures close to 0°C, the transport of latent heat may exceed the contribution of heat flow by conduction. Under these conditions, the apparent thermal conductivity will be much greater than the thermal conductivity calculated from the thermal conductivities and volume fractions of the components.Insufficient published data prevent a rigorous evaluation of the theory. However the functional dependence on temperature of both thermal conductivity and the apparent thermal conductivity are calculated for a Tomakomai soil at different subzero temperatures. These values are compared to the apparent thermal conductivities of this soil which were measured at a water content in the unfrozen state of 0.48 cm³ cm^?3 and at temperatures ranging from ?0.7°C to ?10°C using the line heat source technique. The dependence of apparent thermal conductivity on subzero temperature, as calculated from theory, compares favourably to the dependence which was observed for this soil.     

Heat Transfer in a Packed Bed at Moderate Values of the Reynolds Number

Results are given of an experimental investigation of the coefficient of wall heat transfer of a round tube filled with a packed medium formed by monodisperse glass spheres of different diameters (d _p = 0.9, 3.2, 8.9 mm) in a stabilized region of heat transfer under conditions of filtering of water and aqueous solution of glycerin. A two-layer model of heat transfer is used to calculate the contribution made by the heat resistance of the flow core and of the wall zone using the measured coefficients of heat transfer and temperature profiles across the packed bed. The form of dependence for the effective coefficient of thermal conductivity is determined. Data are given of the measurement of the coefficient of wall heat transfer of annular channel filled both with a single layer of spheres with packing of two types (cubic and rhombohedral) and with several layers of spheres with random packing in a stabilized region of heat transfer under conditions of filtering of water. It is demonstrated that, in the case of inertial mode of filtering of liquid through the packed bed, the values of the Nusselt number both in the tube and in the annular channel correspond to the relation Nu _e (d _e/D)Pe^1/2 _e . A semi-empirical correlation is suggested, which generalizes well our experimental data (and the data of other authors) on heat transfer in the tube and in the annular channel. A theoretical model is suggested, according to which the variation of heat transfer is defined by the behavior of the effective coefficient of thermal conductivity _ef/ _f Pe^1/2 _d associated with the predominant contribution made to convective heat transfer by the transport processes in vortex cells with closed lines of flow.     

Gravitational Effects on Nonlinear Heat Transport Near the Superfluid Transition in 4He

We have recently observed nonlinear heat transport within 30 nK of the superfluid transition temperature using heat flux, Q, in the range 0.1 < Q < 2 erg/(s cm ² ). While Haussmann and Dohm (HD) accurately predict the initial departure of the thermal conductivity, , from the linear response region, is greater than expected very close to T . We anticipate that the nature of the thermal conductivity's nonlinearity may depend upon Earth's gravity in the low heat flux limit (Q < 0.5 erg/(s cm ² )). Comparison of our data to similar data to be taken in a microgravity laboratory will provide an experimental determination of the effect of gravity on nonlinear heat transport near the superfluid transition. The microgravity measurements will also permit the first experimental test of theories that do not consider gravitational effects, such as those by HD.     

Thermal and magnetic properties of copper potassium tutton salt below 0.15 K

The specific heat and the ac susceptibility of copper potassium tutton salt have been measured between 0.01 and 0.15 K. The magnetic phase transition from the paramagnetic to the canted ferromagnetic state was observed at 29.5 mK in zero field. From the obtained electronic entropy curve this salt is considered to be a Heisenberg-type ferromagnet. The copper nuclear specific heat of the hyperfine splitting is estimated to beC _N =1.1×10^–5 R/ (T ²/[K²]), which is one order smaller than the value calculated from previous results of the paramagnetic resonance.     

Contributions to the heat capacity of solid molybdenum in the range 300–2890 K

An analysis has been made of contributions to the heat capacity of Mo, with a special examination of the effect of the formation of vacancies near the melting point. Literature values of the heat capacity at constant pressure C _P were fitted to a polynomial. Using recent measurements of the velocity of sound at high temperature and literature data of the coefficient of expansion, the dilation correction was made to C _P to obtain the heat capacity at constant volume C _V . This heat capacity was taken to consist only of independent contributions from electron excitations (C _VE), harmonic lattice vibrations (C _VH), anharmonic lattice vibrations (C _VA), and the formation of vacancies (C _VV). Three models of C _VE (free electron, band theory, and electron-photon) have been used to calculate the electronic contribution, and an examination of the results indicates that the electron-phonon model is the best. C _VH is assumed to be given by the Debye model, with a single Debye temperature. Thus, the excess heat capacity C _VEX= C _V -C _VE -C _VH is taken as equal to (C _VA +C _VV ), where C _VA is linear with temperature (C _VA=A T), and we have fitted the values of C _VEX to determine the values of A and the energy and entropy of formation of vacancies which give the best fit. The anharmonic contribution is positive. The energy of vacancy formation is 100,000 J · mol^–1, in agreement with estimates by Kraftmakher from C _P data. The entropy of formation is 11.6 J · mol^–1 · K^–1. The concentration of vacancies at the melting point (2890 K) is calculated to be 6.3%.     

Free-convective heat transfer within a differentially heated vertical plane during additional heat supply through a bottom wall

This work presents results of a numerical investigation of the structure of flow and heat exchange in a vertically closed interlayer with various relative heights A = H/L = 4–16 during variation in heat supply to its bottom. The vertical walls were isothermic; top wall, bottom wall, heat flow was supplied uniformly. The nonstationary Navier-Stokes equations were solved numerically in the two-dimensional formulation for the laminar flow. At small Rayleigh numbers (Ra ≈ 10³), when conductive heat transfer prevails within the interlayer, the effect of heat supply from below results in a change of heat transfer only in an immediate vicinity of the bottom. As the Rayleigh number and supplied heat increase, flow destabilization is observed, which results in strong heterogeneity of the density of heat flow along the wall height. At the same time, the heat flow at the hot vertical wall at defined Rayleigh numbers and heating from below may change the sign to the opposite one.     

Development of a flow field structure in the vicinity of a circular cylinder in the presence of a laminar-turbulent transition

The Reynolds equations and the two-parameter differentialq-Ω model of turbulence are used to investigate a flow past a circular cylinder with an isothermal surface (temperature factorT _w0 = 0.5) at the Mach numberM _∞ = 5 in the range of Reynolds numbers Re = 10⁴-10⁸. It is demonstrated that the turbulization of flow leads to a shift of the separation point downstream, a reduction and stabilization of the separation zone length, a decrease in the maximum velocity in the separation zone, and an increase in the heat flux at the rear stagnation point compared with its value at the forward stagnation point.     

Heat transfer and hydrodynamics of channelled cryogenic liquids in fields of centrifugal forces

This Paper reports experimental results on the hydrodynamics and heat transfer during a free-convective and forced motion of cryogenic liquids within a channel in the field of centrifugal forces. Investigations were carried out on the hydrodynamics and heat transfer of a two-phase flow of nitrogen and helium in the heated axial part of the ⊓-shaped duct in the 50–300 range of relative accelerations. It was found that during the free-convective motion the volume flow of liquid nitrogen, with heat fluxes varying from 3 × 10³ to 1 × 10⁴Wm⁻², increased more than 30 times. The volume flow is accompanied by large oscillations and increases with growing relative accelerations. The heat transfer coefficients also are shown to grow with the relative acceleration, which is due to an increase in the hydrostatic pressure at the radial inlet of the duct. Experimental results are presented concerning the heat transfer intensity during forced motion of two-phase helium along a heated axial channel of a rotating □-shaped duct at flow rates <- 7.5 × 10⁻⁵kgs⁻¹. At the relative acceleration of ≈ 100 the heat transfer and critical heat flux are observed to increase with the flow rate. At flow rates <- 10⁻⁴ kg s⁻¹the heat transfer to helium is the same as during pool boiling.     

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     

The study of entropy generation during flow boiling in a micro-fin tube

Increasing in the heat transfer rate in flow boiling is a common and key issue for engineers. Generally, the heat transfer coefficient augmentation methods are divided into two main categories (active and passive methods). In passive methods the increase in heat transfer rate causes the increase in pressure drop. In order to evaluate the contribution of heat transfer and pressure drop mechanisms, the entropy generation analysis is used. In this paper, the entropy generation in micro-fin tube is investigated under flow boiling condition. The effect of different geometrical parameters and flow conditions is discussed on pressure drop contribution and heat transfer one in entropy generation, irreversibility distribution ratio (IDR) and Bejan number (Be). The frictional pressure drop and heat transfer coefficient in the micro-fin tube and the helically coiled one are compared as two enhancements passive heat transfer methods with the smooth straight tube in the literatures. Therefore, by introducing entropy generation number (N_s), the favorable geometry between the micro-fin tube and the helically coiled one with respect to the smooth straight tube is recognizable at equivalent boundary conditions.     

Two-phase lattice Boltzmann simulation of natural convection in a Cu-water nanofluid-filled porous cavity: Effects of thermal boundary conditions on heat transfer and entropy generation

The present work investigates the effect of four different thermal boundary conditions on natural convection in a fluid-saturated square porous cavity to make a judicious choice of optimal boundary condition on the basis of entropy generation, heat transfer and degree of temperature uniformity. Four different heating conditions- uniform, sinusoidal and two different linear temperature distributions are applied on the left vertical wall of the cavity respectively, while maintaining the right vertical wall uniformly cooled and the horizontal walls thermally insulated. The two-phase thermal lattice Boltzmann (TLBM) model for nanofluid is extended to simulate nanofluid flow through a porous medium by incorporating the Brinkman–Forchheimer-extended Darcy model. The close agreement between present LBM solutions with the existing published results lends validity to the present findings. The current results indicate that the uniform and bottom to top linear heating are found to be efficient heating strategies depending on Rayleigh number (10³?≤?Ra?≤?10⁵) and Darcy number (10^?1?≤?Da?≤?10^?6). It is observed that the nanofluid improves the energy efficiency by reducing the total entropy generation and enhancing the heat transfer rate although its augmentation depends on the optimal volume fraction of nanoparticles.     

Critical Transport Properties Near the Superfluid Transition in 3He-4He Mixtures

The renormalization group(RG) functions for the critical dynamics at the λ-transition in ³He–⁴He mixtures (model F^′) have been calculated in two loop order. Comparison is made with the hydrodynamic transport coefficients as functions of the concentration of ³He. Improvement is achieved with respect to an earlier calculation based on a combination of one loop and two loop terms in the field theoretic functions, The non-universal initial values of the flow parameters take values more compatible with the physical expectation. As a corollary we obtain the field theoretic functions of model F describing the critical dynamics of the superfluid transition in pure ⁴He. Comparing with experiments in pure ⁴He improves the background value of the imaginary part of the time scale ratio between the order parameter and the entropy density.     

Heat transfer in the flow of low-density air in narrow channels

Results are given from measurements on air flow in narrow channels; relationships in dimensionless terms are derived for the heat transfer over a wide range in speed (1–120 m/sec) and in pressure (1 · 10⁵ > P > 1.33 · 10³) N/m².Notation V volume flow rate of air - N total number of buret divisions - P₀ pressure in measuring tank - l length of measuring section of buret - t time of oil column rise to the height h_i - n number of buret division corresponding to_i - _o, _m specific weights of oil and mercury - c scale division of buret - h₂ height of oil drop in measuring cylinder - v₀ total volume of system from needle throttle to heat exchanger inlet - P_p pressure at heat exchanger inlet - T_p, T₀ temperature at heat exchanger inlet and of surrounding air - G flow rate in mass terms - c_p mean specific heat of air - t temperature variation over measuring section - Nu, Re Nusselt and Reynolds numbers - l, d length and diameter of channel Translated from Inzhenerno-Fizicheskii Zhurnal, vol. 20, No. 5, pp. 879–883, May, 1971.     

Three-dimensional laminar convection in a parallelepiped with heating of two side walls

Three-dimensional laminar free convection in a parallelepiped with heating of two side walls with variation of the height-to-width aspect ratio over a wide range A _x = L/H = 0.1–5 is investigated numerically. The Rayleigh number changed over the range Ra = 10³−10⁶. The influence of the volume geometry on the three-dimensional flow structure and heat transfer is studied. It is shown that the three-dimensional character of the flow has a profound effect on heat transmission at a small aspect ratio parameter (A _x < 1). For longer length volumes, the whole coefficient of heat emission does not depend on the height-to-width aspect ratio of the enclosure and can be determined from a 2D-approach.