Combined Effects Of Convection Research Articles

Convection Theory and Related Problems in Stellar Structure, Evolution, and Pulsational Stability II. Turbulent Convection and Pulsational Stability of Stars

Using our non-local and time-dependent theory of convection and a fixed set of convective parameters (C1, C2/C1 , C3)= (0.70, 0.50, 3.0) calibrated against the Sun, the linear non-adiabatic oscillations for evolutionary models with masses 1–20 M⊙ are calculated. The results show that almost all the classical instability strips can be reproduced. The theoretical instability strips of δ Scuti and γ Doradusvariables agree well with Kepler spacecraft observations. There is no essential difference in the excitation mechanism for δ Scuti and γ Doradus stars. They are excited by the combined effects of the radiative κ-mechanism and coupling between convection and oscillations. They represent two subgroups of a broader type of δ Scuti and γ Doradus stars, located in the lower part of the Cepheid instability strip. δ Scuti is the p-mode subgroup and γ Doradus is the g-mode subgroup. The luminous variable red giants observed by MACHO and OGLE are low-order radial pulsators among low-mass red giant and asymptotic giant branch stars. The excitation and damping mechanism of oscillations for low-temperature stars is studied in detail. Convective flux and turbulent viscosity are consistent damping mechanisms. The damping effect of the convective enthalpy flux is inversely proportional to the frequency of the modes, so it plays an important role in stabilizing the low-order modes and defining the red edge of the Cepheid instability strip. The damping effect of turbulent viscosity reaches its maximum at 3ωτc/16∼1, where τc is the dynamic time scale of turbulent convection and ω is the angular frequency of the modes. Turbulent viscosity is the main damping mechanism for stabilizing the high-order modes of low-temperature variables. The turbulent pressure is, in general, an excitation mechanism; it reaches maximum at 3ωτc/4∼1, and it plays an important role for the excitation of red variables. Convection is not, in fact, a pure damping effect for stellar oscillations. The relative contributions of turbulent pressure, turbulent viscosity, and convective enthalpy flux for excitation and damping effects change with stellar parameters (mass, luminosity, effective temperature) and with the radial order and spherical harmonic degree of the oscillation mode; therefore, the combined effect of convection is sometimes damping, and sometimes the excitation of oscillations. Our research shows that, for low-luminosity red giants, the low-order modes are pulsationally stable, while the intermediate- and high-order modes are unstable. Toward higher luminosity, the range of unstable modes shifts gradually toward the lower order. All of the intermediate- and high-order modes become stable, and a few low-order modes become unstable for high-luminosity red giants. They show the typical pulsational characteristics of Mira-like variables. The variable red giants are, at least for the high-luminosity RGs, self-excited. For red giants, the frequency of the maximally unstable modes predicted by our theory is similar to that given by the semi-empirical scaling relation.

Combined Effect of Thermal Anisotropy and Forced Convection on the Growth of Binary Alloy Equiaxed Dendrites

A numerical model has been developed to simulate the growth of an equaixed binary alloy dendrite under the combined effect of thermal anisotropy and forced convection. A semi implicit–explicit approach is used where the velocity and pressure fields are solved implicitly using the SIMPLER algorithm, while energy and species conservation equations are treated explicitly. The effect of thermal anisotropy present in the solid crystal is implemented by the addition of a departure source term in the conventional isotropic heat transfer based energy equation. The departure source represents the anisotropic part of the diffusive term in the isotropic heat transfer based energy equation. Simulations were performed to find the relative effect of convection strength and thermal anisotropy on the growth rate and morphology of a dendrite. Subsequently, parametric studies were conducted to investigate the effect of thermal anisotropy ratio, inlet flow velocity, undercooling temperature, and the relative strength of the thermal to mass diffusivity ratio by analyzing the variation of the equilibrium tip velocity of the top and left arms, the arm length ratio (ALR), and the equivalent grain radius. Based on simulations, a chart has been developed, which demarcates different regimes in which convection or thermal anisotropy is the most dominant factor influencing the dendrite growth rate. The model has also been extended to study the growth of multiple dendrites with random distribution and orientation. This can be useful for the simulation of microstructure evolution under the combined effect of convection and thermal anisotropy.

Solution of general dynamic equation for nanoparticles in turbulent flow considering fluctuating coagulation

A new averaged general dynamic equation (GDE) for nanoparticles in the turbulent flow is derived by considering the combined effect of convection, Brownian diffusion, turbulent diffusion, turbulent coagulation, and fluctuating coagulation. The equation is solved with the Taylor-series expansion moment method in a turbulent pipe flow. The experiments are performed. The numerical results of particle size distribution correlate well with the experimental data. The results show that, for a turbulent nanoparticulate flow, a fluctuating coagulation term should be included in the averaged particle GDE. The larger the Schmidt number is and the lower the Reynolds number is, the smaller the value of ratio of particle diameter at the outlet to that at the inlet is. At the outlet, the particle number concentration increases from the near-wall region to the near-center region. The larger the Schmidt number is and the higher the Reynolds number is, the larger the difference in particle number concentration between the near-wall region and near-center region is. Particle polydispersity increases from the near-center region to the near-wall region. The particles with a smaller Schmidt number and the flow with a higher Reynolds number show a higher polydispersity. The degree of particle polydispersity is higher considering fluctuating coagulation than that without considering fluctuating coagulation.

THE COMBINED EFFECT OF PRECESSION AND CONVECTION ON THE DYNAMO ACTION

ABSTRACT To understand the generation of the Earth’s magnetic field and those of other planets, we numerically investigate the combined effect of precession and convection on dynamo action in a spherical shell. Convection alone, precession alone, and the combined effect of convection and precession are studied at the low Ekman number at which the precessing flow is already unstable. The key result is that although precession or convection alone are not strong enough to support the dynamo action, the combined effect of precession and convection can support the dynamo action because of the resonance of precessional and convective instabilities. This result may explain why the geodynamo has been maintained for such a long time compared to the Martian dynamo.

Radiative heating of supercritical carbon dioxide flowing through tubes

Brayton power cycles using high temperature, high pressure supercritical carbon dioxide (s-CO2) as the working fluid have been increasingly considered as attractive candidates for solar-thermal power plants. Several configurations of heat exchangers and solar receivers are under investigation, with predicted tube temperatures ∼1000K. The inclusion of radiation modeling to capture the effect of absorption bands of s-CO2 and the radiative heat transfer among the equipment surfaces makes the computation costly and time consuming, and is often neglected on the basis of convection being the dominant transport mechanism.In this work, a numerical study has been performed to characterize the heat transfer in simultaneously developing laminar flow of s-CO2 through a circular pipe. The combined effects of convection and radiation are presented by varying the Reynolds number, pipe diameter, length to diameter ratio, wall emissivity and the total wall heat flux. It is shown that neglecting the effects of radiative heat transfer, and in particular the participation of s-CO2 in thermal transport can lead to large errors in predicting wall temperature, and by extension, the component lifetime. The error in wall temperature also leads to erroneous predictions on losses to the environment. The calculations indicate that there is a range of flow conditions over which the design process needs to incorporate radiation modeling.

A numerical study on natural convection in an inclined square enclosure with a circular cylinder

This study examined numerically the natural convection induced by a temperature difference between a cold outer inclined square enclosure and a hot inner circular cylinder. A two-dimensional solution for natural convection was obtained using the finite volume method with second-order accuracy and the immersed boundary method to handle efficiently the inner circular cylinder within an inclined square enclosure. The present study considered the effects of the following parameters on fluid flow and heat transfer in an enclosure: Rayleigh number from 103 to 106, the dimensionless cylinder radii from 0.1 to 0.3 and tilted angle of the enclosure from 0° to 45°. The results showed that the distribution of isotherms, streamlines, local and surface-averaged Nusselt numbers are determined by the combined effects of convection and the distance between the cylinder and walls of the enclosure, which are a function of the Rayleigh number, dimensionless cylinder radius and tilted angle of the enclosure.

Generalized dispersion of unsteady convective diffusion in couple stress poorly conducting fluid bounded by porous layer in the presence of an electric field

We investigate in this paper the simultaneous effects of electric field, couple stress, porous parameter and slip at the permeable surface on the generalized dispersion of an unsteady convective diffusion in a poorly conducting fluid in a channel bounded by porous layers. A two dimensional flow has been considered and the resulting partial differential equations have been solved analytically. The solutions are computed and the results show that the solute is dispersed relative to a plane moving with the mean speed of couple stress poorly conducting fluid with a relative unsteady dispersion coefficient. These relative unsteady dispersion coefficients are numerically computed and found that they increase with the increase in porous parameter and decrease with an increase in couple stress parameters. We have also estimated the contribution of diffusion and pure convection on the generalized dispersion coefficient. The effect of pure convection, neglecting diffusion terms on mean concentration is computed and the results show that the effect of pure convection decreases mean concentration compared to combined effect of convection and diffusion.

Piecewise linear approximation of nonlinear ordinary differential equations

The study of linear ordinary differential equations (ODEs) is an important component of the undergraduate engineering curriculum. However, most of the interesting behaviour of nature is described by nonlinear ODEs whose solutions are analytically intractable. We present a simple method based on the idea that the curve of the nonlinear terms of the dependent variable can be replaced by an approximate curve consisting of a set of line segments tangent to the original curve. This enables us to replace a nonlinear ODE with a finite set of linear inhomogeneous ODEs for which analytic solutions are possible. We apply this method to the cooling of a body under the combined effects of convection and radiation and demonstrate very accurate solutions with a relatively few number of line segments. Furthermore, we discuss how a number of key and usually disparate concepts of calculus are needed to apply this method, including continuity and differentiability, Taylor polynomials and optimisation. References S. Theodorakis and E. Svoukis. Piecewise linear emulation of propagating fronts as a method for determining their speeds. Physical Review E 68, 2003, 027201. doi:10.1103/PhysRevE.68.027201 D. D. Ganji, M. J. Hosseini and J. Shayegh. Some nonlinear heat transfer equations solved by three approximate methods. International Communications in Heat and Mass Transfer 34, 2007, 1003--1016. doi:10.1016/j.icheatmasstransfer.2007.05.010 H. D. Young. University Physics. 8th edition, Addison-Wesley Publishing Company, Massachusetts, 1992. F. P. Incropera, D. P. Dewitt, T. L. Bergman and A. S. Lavine. Fundamentals of Heat and Mass Transfer. 6th edition, John Wiley and Sons, New Jersey, 2007.

Two-Phase Multicomponent Diffusion and Convection for Reservoir Initialization

Summary We present formulation and numerical solution of two-phase multicomponent diffusion and natural convection in porous media. Thermal diffusion, pressure diffusion, and molecular diffusion are included in the diffusion expression from thermodynamics of irreversible processes. The formulation and the numerical solution are used to perform initialization in a 2D cross section. We use both homogeneous and layered media without and with anisotropy in our calculations. Numerical examples for a binary mixture of C1/C3 and a multicomponent reservoir fluid are presented. Results show a strong effect of natural convection in species distribution. Results also show that there are at least two main rotating cells at steady state: one in the gas cap, and one in the oil column. Introduction Proper initialization is an important aspect of reliable reservoir simulations. The use of the Gibbs segregation condition generally cannot provide reliable initialization in hydrocarbon reservoirs. This is caused, in part, by the effect of thermal diffusion (caused by the geothermal temperature gradient), which cannot be neglected in some cases; thermal diffusion might be the main phenomenon affecting compositional variation in hydrocarbon reservoirs, especially for near-critical gas/condensate reservoirs (Ghorayeb et al. 2003). Generally, temperature increases with increasing burial depth because heat flows from the Earth's interior toward the surface. The temperature profile, or geothermal gradient, is related to the thermal conductivity of a body of rock and the heat flux. Thermal conductivity is not necessarily uniform because it depends on the mineralogical composition of the rock, the porosity, and the presence of water or gas. Therefore, differences in thermal conductivity between adjacent lithologies can result in a horizontal temperature gradient. Horizontal temperature gradients in some offshore fields can be observed because of a constant water temperature (approximately 4°C) in different depths in the seabed floor. The horizontal temperature gradient causes natural convection that might have a significant effect on species distribution (Firoozabadi 1999). The combined effects of diffusion (pressure, thermal, and molecular) and natural convection on compositional variation in multicomponent mixtures in porous media have been investigated for single-phase systems (Riley and Firoozabadi 1998; Ghorayeb and Firoozabadi 2000a).The results from these references show the importance of natural convection, which, in some cases, overrides diffusion and results in a uniform composition. Natural convection also can result in increased horizontal compositional variation, an effect similar to that in a thermogravitational column (Ghorayeb and Firoozabadi 2001; Nasrabadi et al. 2006). The combined effect of convection and diffusion on species separation has been the subject of many experimental studies. Separation in a thermogravitational column with both effects has been measured widely (Schott 1973; Costeseque 1982; El Mataaoui 1986). The thermogravitational column consists of two isothermal vertical plates with different temperatures separated by a narrow space. The space can be either without a porous medium or filled with a porous medium. The thermal diffusion, in a binary mixture, causes one component to segregate to the hot plate and the other to the cold plate. Because of the density gradient caused by temperature and concentration gradients, convection flow occurs and creates a concentration difference between the top and bottom of the column. Analytical and numerical models have been presented to analyze the experimental results (Lorenz and Emery 1959; Jamet et al. 1992; Nasrabadi et al. 2006). The experimental and theoretical studies show that the composition difference between the top and bottom of the column increases with permeability until an optimum permeability is reached. Then, the composition difference declines as permeability increases. The process in a thermogravitational column shows the significance of the convection from a horizontal temperature gradient.

Flame Holding Characteristics in Flame-Base of Lean-Rich Combustion. Numerical Unsteady-State Analysis of Laminor Lean-Rich Combustion Flames.

Recently much attention has been paid on lean-rich combustion as one of the methods to reduce NOx emission level. In this investigation NOx emission characteristics of the lean-rich combustion were numerically analyzed by taking a set of elementary reactions into consideration. It was found that decreasing the equivalence ratio of the rich flame effectively reduces the NOx level, while it makes the rich flame slightly unstable. In this paper, therefore, unsteady structure and stability characteristics of the attached flames after ignition are examined by using the numerical analysis with a set of elementary reactions installed. According to the results, the combined effects of convection and diffusion of fuel, active species and heat from the rich-side flame to the lean-side flame in the attached regions near the rim are found to control the structure and stability of the leanrich combustion. It is considered that the vortex region formed behind the rim performs an important part in the flame stabilization of the lean-rich combustion.

Effects of thermal radiation on airflow with displacement ventilation: an experimental investigation

Various wall surface emissivities are used to examine the radiative effects on the vertical air temperature profile and gravity current in a full-scale model of a room ventilated by displacement. The vertical temperature stratification is a combined effect of convection, conduction and radiation. The radiative effects are to heat the floor surface and alter the flow rate in the thermal plumes, which weakens the gravity current and lowers the stratification level. The intermittance at the upper edge of the gravity current is illustrated by studying its turbelent structure. The data gathered in this work are suitable for validating flow and radiation models.

Emergence of solar magnetic flux from the convection zone into the photosphere and chromosphere

A two-dimensional MHD code is used to study the nonlinear dynamics of solar magnetic flux emerging from the convection zone into the photosphere and chromosphere. An isolated horizontal magnetic flux with beta of about 4 is initially located in a convectively unstable layer (solar convection zone) beneath a two-temperature layered atmosphere (solar corona-chromosphere/photosphere). The combined effects of convection and magnetic buoyancy carry the magnetic flux from the convection zone into the photosphere, where it then expands through the photosphere and chromosphere. Gas slides down the expanding loop, resulting in its evacuation and subsequent rise due to enhanced magnetic buoyancy. Initially, weak convection zone magnetic flux (B of about 600 G) is amplified up to 1000 G or more after emerging into the photosphere. The resulting velocity fields are similar to those observed in arch filament systems. 19 refs.

Dynamo waves and palaeomagnetic secular variation

Summary. A dynamic model is proposed for large amplitude geomagnetic secular variation with periodicity in the range of 1000-3000yr. Thermal convection in the lower mantle imposes a spatially variable heat flux at the core-mantle boundary. If the total heat loss from the core exceeds approximately 3 x 10'2W, then both (i) a convective layer and (ii) large scale, quasigeostrophic shear flows are likely to exist beneath the core-mantle boundary. The combined effects of convection and shear at the top of the outer core can generate three-dimensionally propagating magnetic field disturbances called cuw-dynamo waves. An analysis is made of the surface magnetic field disturbances due to dynamo wave propagation in the outer core in the presence of turbulent convection and an east-west shear flow. Nonaxisymmetric disturbances exhibit the following characteristics: (i) dynamo waves propagate in each hemisphere with a poleward or equatorward component, depending on the sign of the a-effect; (ii) both eastward and westward propagation is allowed althcugh westward propagation is preferred. The apparent velocity at the earth's surface is the sum of propagation and drift velocities in the core; (iii) dynamo wave disturbances are transient, with exponential growth and decay phases; (iv) traces of inclination versus declination of individual Fourier components obey Runcorn's circularity rule. A comparison is made with lake sediment secular variation records from central North America measured by Lund & Banerjee. The band-passed time series and the major inclination/declination loops can be modelled from 2600 to 10 000 yr BP by a single dynamo wave, periodic in 2400 yr, propagating under the site along an azimuth of 345. Between 0 and 2600 yr BP, the record can be modelled by addition of a wave with 1200yr period, propagating along an azimuth of 30. This indicates that the palaeomagnetic secular variation record in North America to 10 000 yr may be dominated by poleward propagating wave-like disturbances.

A simultaneous concentration of a vortex and a magnetic field in magnetohydrodynamic flows

A three-dimensional magnetodydrodynamic flow with a combined effect of convection and diffusion is reduced to a two-dimensional problem by a variable transformation. The original field is composed of a unidirectional vorticity and an aligned magnetic field superimposed on an axisymmetric straining flow in an incompressible, viscous, electrically conducting fluid. By restricting consideration to the axisymmetric vorticity and magnetic fields, an exact solution is presented, which shows time evolution from general initial profiles. In a particular case of constant straining, the solution simultaneously approaches the state of a concentrated cylindrical vortex and a magnetic tube of Gaussian profile sharing a common symmetry axis.

Mechanisms affecting gas transport during high-frequency oscillation

Traditional concepts of gas transport in the lung cannot explain the adequate alveolar ventilation observed during high-frequency ventilation (HFV) with tidal volumes (VT) less than the anatomic dead space (VD). Different physical mechanisms enhance and limit gas exchange during HFV. Mechanisms enhancing transport include: diffusion, the spontaneous intermingling of the molecules of 2 gases due to Brownian motion; convective mechanisms which depend on bulk flow, such as direct alveolar ventilation, pendelluft, and streaming; and the combined effects of convection and diffusion, often termed augmented transport. Equations describing some of these mechanisms have been incorporated into theorectical models of gas transport which predict that the efficiency of HFV is proportional to faVTb, where f is frequency and b is greater than a. These predictions generally agree with experimental results obtained in healthy animals and humans. However, experimental results in subjects with lung disease show that, at a fixed VT, gas transport efficiency plateaus as f increases. One explanation for this plateau is that in subjects with increased peripheral airway resistance, the upper airways act as a shunt compliance, absorbing a fraction of the delivered VT. Experimental results to date have not confirmed or refuted any specific theory, but it seems likely that gas mixing during HFV is enhanced by a number of the mechanisms mentioned above and that the mechanical properties of the lungs might limit gas transport, especially in patients with peripheral airway obstruction.

Granulation and Supergranulation as a Diagnostic Test of Solar Structure

One of the most difficult tasks facing theoretical astrophysics today is to find a satisfactory model for the convective transport of energy in regions where the temperature gradient is superadiabatic. A number of such models have been proposed, such as the mixing-length theory and its extensions (Vitense 1953, Böhm-Vitense 1958, Spiegel 1963, Travis and Matsushima 1973 a, b, Parson 1969), to take into account the combined effects of convection and turbulence but it is generally agreed that, to-date, no satisfactory theory has been put forward.

An Approximate Analysis of Laminar Dispersion in Circular Tubes

The combined effects of convection and diffusion for dispersion on mass transport in fully developed laminar flow through circular tubes are investigated. The present method, which in general may be used to yield solutions at any arbitrary dimensionless time, in its zeroth-order approximation is identical to Taylor’s analysis for the average concentration. Solutions to the basic differential equation for an initial input of solute either concentrated at a section of the tube or uniformly distributed in the form of a slug of finite axial extension are developed. Numerical results for the former input are presented over a large range of dimensionless time and Peclet numbers. The time limitations of Taylor’s solution and Lighthill’s small time approximation [15] are placed on more reliable quantitative bases by comparison with the present calculations.

Effects of unstirred layers or transport number discontinuities on the transient and steady-state current-voltage relationships of membranes

The effects of current-induced electrolyte accumulation and depletion on the electrical properties of a two-layered membrane system have been examined. The membrane consisted of a charged, ion permselective layer and an uncharged, non-selective layer. The model was designed to reveal the properties of membranes possessing long pores with ionic charges at one end or of ion-selective membranes bounded by highly unstirred aqueous layers. Electrolyte concentration profiles in the inert layer and their time-dependent changes were obtained from solutions of the diffusion equation under the condition of constant current. The profiles were then used to calculate the voltage developed across the membrane at various times after the current is switched on. The theoretical results are presented in the form of i-V curves with reduced coordinates that can be used to obtain time-current-voltage relationships for membranes of the type considered having any thickness of the non-selective layer and bathed in any concentration of any 1:1 electrolyte. Experimental results on a model composite membrane were in good agreement with calculations that assume that ion transport occurs only under the influence of electrical potential and concentration gradients, suggesting that in such systems, the combined effects of convection, osmosis, electro-osmosis, and concentration-dependence of diffusion coefficients, activity coefficients, and transference numbers are small. Voltage fluctuations in the form of periodic spikes were observed experimentally at the limiting current density (the current density at which the electrolyte concentration at one surface of the selective layer goes to 0). These phenomena were not seen when the current was in the direction leading to accumulation of electrolyte in the non-selective (unstirred) layer. Such composite membranes can exhibit S-shaped and N-shaped i-V curves under ramp-voltage and ramp-current clamps, respectively.