Mass Flux Model Research Articles

Cattaneo-Christov heat and mass flux model for 3D hydrodynamic flow of chemically reactive Maxwell liquid

This research focuses on the Cattaneo-Christov theory of heat and mass flux for a three-dimensional Maxwell liquid towards a moving surface. An incompressible laminar flow with variable thermal conductivity is considered. The flow generation is due to the bidirectional stretching of sheet. The combined phenomenon of heat and mass transport is accounted. The Cattaneo-Christov model of heat and mass diffusion is used to develop the expressions of energy and mass species. The first-order chemical reaction term in the mass species equation is considered. The boundary layer assumptions lead to the governing mathematical model. The homotopic simulation is adopted to visualize the results of the dimensionless flow equations. The graphs of velocities, temperature, and concentration show the effects of different arising parameters. A numerical benchmark is presented to visualize the convergent values of the computed results. The results show that the concentration and temperature fields are decayed for the Cattaneo-Christov theory of heat and mass diffusion.

Homotopic solutions for unsteady second grade liquid utilizing non-Fourier double diffusion concept

Main purpose of the current work is to investigate the features of unsteady Cattaneo–Christov heat and mass flux models on the second grade fluid over a stretching surface. The characteristics of unsteady Cattaneo–Christov heat and mass flux models are incorporated in the energy and concentration equations. The unsteady Cattaneo–Christov heat and mass flux models are the generalization of Fourier’s and Fick’s laws in which the time space upper-convected derivative are utilized to describe the heat conduction and mass diffusion phenomena. The suitable transformations are used to alter the governing partial differential equations into the ordinary differential equations. The resulting problem under consideration is solved analytically by using the homotopy analysis method (HAM). The effect of non-dimensional pertinent parameters on the temperature and concentration distribution are deliberated by using graphs and tables. Results show that the temperature and concentration profiles diminish for augmented values of the thermal and concentration relaxation parameters. Additionally, it is perceived that the temperature and concentration profiles are higher in case of classical Fourier’s and Fick’s laws as compared to non-Fourier’s and non-Fick’s laws.

An improved heat conduction and mass diffusion models for rotating flow of an Oldroyd-B fluid

An analysis is presented to inspect the steady three-dimensional boundary layer flow of an Oldroyd-B fluid over a stretching surface. Heat and mass transfer analysis are scrutinized by utilizing the non-Fourier’s and non-Fick’s models in rotating frame. The expressions of heat and mass fluxes are based upon the Cattaneo-Christov theory. The Cattaneo-Christov heat and mass flux models are used for the development of energy and concentration equations which account the contribution of thermal and concentration relaxation times. Additionally, temperature dependent thermal conductivity is also considered here. Apposite transformations are betrothed to obtain the ordinary differential equations with high nonlinearity. The analytical solutions are established for the resulting ordinary differential system by utilizing the homotopy analysis method (HAM). Our observations reveal that the rotation parameter serves to diminish the primary velocity f′(η) and associated momentum boundary layer thickness and similar trend is observed for the secondary velocity g(η). It is also observed that the thermal and concentration relaxation time parameters reduce the temperature and concentration profiles. For endorsement of the current relation, the attained consequences are eminent with former exploration in precise cases and splendid agreement has been distinguished.

Aspects of developed heat and mass flux models on 3D flow of Eyring-Powell fluid

The variable thermal conductivity impacts and generalized Fourier’s and Fick’s laws over an exponentially stretching surface are reported in this paper. Another heat flux idea involving mystery of heat conduction is exploited which is not quite the same as the usual literature. Such idea has been utilized as a part of perspective of Cattaneo-Christov heat flux theory. The characteristic of temperature and concentration relaxation features are described. Other than this, chemical reactions are additionally considered.To solve the system of six highly non-linear coupled differential equations, a numerical technique bvp4c is adopted. The skin friction coefficient for three dimensional Eyring-Powell fluid model is calculated. From the present analysis we observe that the temperature and concentration profiles declines for higher values of thermal and concentration relaxation parameters. Also, for higher values of strength of reaction parameters, the concentration profile decreases. Current effort for three dimensional Cattaneo-Christov double diffusion and homogeneous-heterogeneous reactions over an exponentially stretching surface does not yet exist in the literature.

Research on shale gas transportation and apparent permeability in nanopores

Shale gas transport mechanisms in matrix nanopores include the Knudsen diffusion, transition diffusion, slip flow of free gas and surface diffusion of adsorbed gas. Previous research focused on shale gas Knudsen diffusion, slip flow and surface diffusion. In this paper, we present a shale gas mass flux model for the shale formation matrix that incorporates transition diffusion, slip flow and surface diffusion. A set of shale formation data was used to analyse the sensitivity of the gas mass flux to the pore radius and pressure for each gas transport mechanism. The results show that each gas transport mechanism mass flux contribution varies with the pore radius and pressure. The results of the gas mass flux sensitivity analysis are as follows: (1) the slip flow mass flux increases with increasing pore radius and pore pressure, (2) the surface diffusion mass flux decreases with increasing pore pressure and pore radius, and (3) the transition diffusion mass flux decreases with increasing pore pressure and has only a slight dependence on the pore radius. Furthermore, the gas type notably influences the apparent permeability. We recommend this model for the description of the shale gas mass flux in matrix nanopores. It provides insights into the effects of transition diffusion, slip flow and surface diffusion on the shale gas transportation in nanopores.

Numerical investigation of generalized Fourier's and Fick's laws for Sisko fluid flow

The principal emphasis of this article is to investigate the characteristics of Cattaneo-Christov heat and mass flux models on steady 2D flow of Sisko fluid over a nonlinear stretching surface. The Cattaneo-Christov heat and mass flux models are the generalization of classical Fourier's and Fick's laws through thermal and concentration relaxation times, respectively. The heat transfer analysis is carried out in the presence of temperature dependent thermal conductivity. The nonlinear ordinary differential equations are first established through the transformation procedure which are then solved numerically by using the bvp4c function in MatLab. The influences of involved parameters on the temperature and concentration distributions are deliberated and physical characteristics of these parameters are examined through graphs and discussed in detail. Results reveal that the temperature and concentration profiles have converse relationship with the nondimensional thermal and concentration relaxation time parameters. Moreover, it is also fascinating to observe that the concentration profile is significantly affected by the power-law index when it escalates from n<1 to n>1

Impact of chemical processes on 3D Burgers fluid utilizing Cattaneo-Christov double-diffusion: Applications of non-Fourier's heat and non-Fick's mass flux models

This article communicates the characteristics of Cattaneo-Christov heat and mass flux models on steady three-dimensional flow of Burgers fluid over a bidirectional stretching surface. These models are the modifications of classical Fourier's and Fick's laws through thermal and concentration relaxation times, respectively. Additionally, characteristics of heterogeneous and homogeneous reactions are further investigated. Transformation procedure is adopted to obtain the highly coupled nonlinear ordinary differential equations. The developed nonlinear problem is then solved analytically by utilizing the homotopy analysis method (HAM). The impact of various physical parameters on the temperature and concentration distributions are deliberated and physical characteristics of these parameters are exhibited through graphs and discussed through the reasonable judgment. Our investigation conveys that the temperature and concentration profiles decay as the nondimensional thermal and concentration relaxation time parameters enhances. On the other hand, it is perceived that concentration boundary layer thickness moderates with the growth of Deborah numbers β1 and β2. Additionally, it is fascinating to find that the concentration profiles decline as the Schmidt number escalates. To sum up, the verdict of the present investigation is that the proficiency of thermal and concentration systems can be enriched by introducing the Cattaneo-Christov heat and mass flux models.

Quantification of wind erosion from some arid soils in Jordan under two different management practices

Jordan’s national food security is challenged by many threats such as soil erosion and desertification. Unfortunately, Jordan lacks field data that can strengthen efforts in reducing erosion and therefore combating desertification necessary to enable sustainable decision making. This study aimed to investigate the effect of passing sheep on soil wind erosion and to quantify windblown soil mass in arid soils. The field was divided into two sites; the first site was subject to disturbance through passage of about 40 sheep biweekly, while the other site was kept undisturbed. Two Big Spring Number Eight (BSNE) sediment catcher traps were installed on each site. Two mass flux models were tested for calculating mass transport rates. The total horizontal flux is obtained by integrating the airborne particles collected by the BSNE sampler. Soil analyses showed no significant differences in all measured properties, ensuring that soil inherent erodibility is similar. Both models were significantly effective (P < 0.001) in predicting airborne sediment loads as indicated by their high associated R2 and low root-mean-square error (RMSE). The results also showed that trapped airborne dust decreases with height, where maximum fluxes were generally at lowest height, indicating that saltation is the dominant transport mode. Average erosion from the disturbed site is almost double the undisturbed site, (6.6 and 3.9 t/ha, respectively). The suggested management plan is to set the area aside as a land reserve or at least performing better grazing management, which will insure lower disturbance of surface soil, result in better plant recover rate leading to stronger soil cover, and allow soil aggregates to develop and be more stable.

A new sub-grid surface mass balance and flux model for continental-scale ice sheet modelling: testing and last glacial cycle

Abstract. To investigate ice sheet evolution over the timescale of a glacial cycle, 3-D ice sheet models (ISMs) are typically run at "coarse" grid resolutions (10–50 km) that do not resolve individual mountains. This will introduce to-date unquantified errors in sub-grid (SG) transport, accumulation and ablation for regions of rough topography. In the past, synthetic hypsometric curves, a statistical summary of the topography, have been used in ISMs to describe the variability of these processes. However, there has yet to be detailed uncertainty analysis of this approach. We develop a new flow line SG model for embedding in coarse resolution models. A 1 km resolution digital elevation model was used to compute the local hypsometric curve for each coarse grid (CG) cell and to determine local parameters to represent the hypsometric bins' slopes and widths. The 1-D mass transport for the SG model is computed with the shallow ice approximation. We test this model against simulations from the 3-D Ice Sheet System Model (ISSM) run at 1 km grid resolution. Results show that none of the alternative parameterizations explored were able to adequately capture SG surface mass balance and flux processes. Via glacial cycle ensemble results for North America, we quantify the impact of SG model coupling in an ISM. We show that SG process representation and associated parametric uncertainties, related to the exchange of ice between the SG and CG cells, can have significant (up to 35 m eustatic sea level equivalent for the North American ice complex) impact on modelled ice sheet evolution.

An anisotropic Reynolds mass flux model for the simulation of chemical reaction in gas-particle CFB risers

A model is proposed for numerical simulation of the multiphase flow coupled with chemical reaction in gas-particle circulating fluidized bed (CFB) risers. The proposed model is based on the newly developed computational mass transfer (CMT) methodology (Yu and Yuan, 2014) featuring the use of Reynolds mass flux equation to close the turbulent mass transfer equation, so that the anisotropic turbulent mass diffusion in CFB riser can be realized in the simulation. The proposed model consists of the turbulent mass transfer equation for the species with its Reynolds mass flux closure and the relevant formulations of computational fluid dynamics (CFD). With the proposed model, the species concentration and solid volume fraction as well as the velocity distributions along the CFB riser can be predicted. To validate the proposed model, simulation is carried out for the catalytic ozone decomposition in a gas-particle CFB riser. The simulated results are compared with the experimental data and satisfactory agreement is found in both axial/radial distributions of ozone concentration and solid volume fraction. Furthermore, the anisotropic turbulent mass diffusivities are also predicted and validated by the experimental data reported in literature.

An anisotropic turbulent mass transfer model for simulation of pilot-scale and industrial-scale packed columns for chemical absorption

An anisotropic turbulent mass transfer model, namely the Reynolds mass flux model (RMF), for simulating the chemical absorption process in packed column is introduced by the use of combined computational methodology. With the present model, the concentration and temperature as well as velocity distributions can be simultaneously obtained. The feature of the proposed model is that the modeled Reynolds mass flux equation is adopted to close the turbulent mass transfer equation so that the Boussinesq’s postulation is abandoned and consequently the anisotropy of turbulent mass diffusion can be characterized. The present model is accompanied by the formulations of computational fluid dynamics (CFD) and computational heat transfer (CHT). In mathematical expression of CFD and CHT, the Reynolds stress and Reynolds heat flux equations are used to close the turbulent momentum and heat transfer equations. The simulated results are validated with experimental data for pilot-scale and industrial-scale packed columns and satisfactory agreement is found between them. Furthermore, the Reynolds mass flux and the anisotropic turbulent mass diffusion are characterized and discussed.

A Reynolds mass flux model for gas separation process simulation: II. Application to adsorption on activated carbon in a packed column

Simulations of adsorption process using the Reynolds mass flux model described in Part I of these serial articles are presented. The object of the simulation is the methylene chloride adsorption in a packed column (0.041m id, packed with spherical activated carbon up to a length of 0.2m). With the Reynolds mass flux model, breakthrough/regeneration curves, concentration and temperature as well as the velocity distributions can be obtained. The simulated results are compared with the experimental data reported in the literature and satisfactory agreement is found both in breakthrough/regeneration curves and temperature curves. Moreover, the anisotropic turbulent mass diffusion is characterized and discussed.

A Reynolds mass flux model for gas separation process simulation: I. Modeling and validation

Separation process undertaken in packed columns often displays anisotropic turbulent mass diffusion. The anisotropic turbulent mass diffusion can be characterized rigorously by using the Reynolds mass flux (RMF) model. With the RMF model, the concentration and temperature as well as the velocity distributions can be simulated numerically. The modeled Reynolds mass flux equation is adopted to close the turbulent mass transfer equation, while the modeled Reynolds heat flux and Reynolds stress equations are used to close the turbulent heat and momentum transfer equations, so that the Boussinesq postulate and the isotropic assumption are abandoned. To validate the presented RMF model, simulation is carried out for CO2 absorption into aqueous NaOH solutions in a packed column (0.1m id, packed with 12.7mm Berl saddles up to a height of 6.55m). The simulated results are compared with the experimental data and satisfactory agreement is found both in concentration and temperature distributions. The sequel Part II extends the model application to the simulation of an unsteady state adsorption process in a packed column.

Comparison of different analytical models for heat and mass transfer characteristics of an evaporating meniscus in a micro-channel

Based on the augmented Young–Laplace equation and lubrication theory, a detailed analytical model predicting the heat and mass transport characteristics of the evaporating meniscus in a micro-channel is developed. The present model solves the third-order differential equation of the film thickness and the first-order differential equation of the liquid average velocity simultaneously. The different models for thermal performance of the evaporating meniscus are also compared to each other. It is found that both the film thickness and cumulative heat flux by the present model are in good agreement with the results by the previous models. The total heat flux of evaporating meniscus based on interface temperature calculated by Clausius–Clapeyron equation is far higher than that obtained by Wayner's interface mass flux model.

A Reynolds Mass Flux Model for the Simulation of Chemical Absorption of CO2 into 2-Amino-2-methyl-1-propanol in a Packed Column

A Reynolds mass flux model is proposed for the simulation of CO2 absorption into aqueous 2-amino-2-methyl-1-propanol (AMP) solutions in a packed column. With the proposed model, distributions of concentration and temperature as well as velocity can be obtained. In the mathematical expression of the proposed model, the modeled Reynolds mass flux equation is used to close the turbulent mass transfer equation so that the generalized Boussinesq’s postulation is abandoned. The feature of the closure method is that the anisotropy of turbulent mass diffusion can be characterized. To validate the proposed model, a simulation is carried out for CO2-AMP absorption in a randomly packed column. The simulated results are compared with the experimental data in literature, and satisfactory agreement is found between them. Besides, the anisotropy of turbulent mass diffusion characterized by the proposed model is discussed and found to be consistent with that from experimental correlations. Finally, the simulations reveal...

Experimental constraints on the composition and dynamics of Titan's polar lakes

Titan's polar lakes are thought to be predominantly composed of liquid ethane and methane; however, little is known on the ratio of these hydrocarbons in the lakes, and the stability and dynamics of these mixtures. Here we provide the first experimental constraints under Titan surface conditions of liquid hydrocarbon mixture evaporation. Our results are relevant to Titan's polar temperatures and pressures (∼92 K and 1.5 bar), and cover a wide range of methane–ethane compositions. We show that evaporation is negligible for pure ethane, but increases nearly linearly with increasing methane concentration. Early dissolution of N2 results in ternary mixtures evaporating, which is modeled by a ‘hybrid’ thermodynamic equilibrium approach combining Perturbed-Chain Statistical Associating Fluid Theory with a diffusion and buoyancy-driven mass flux model. The approach follows the experimental evaporation rate measurements presented in this study, and allows for the calculation of the corresponding liquid methane–ethane–nitrogen ratios. Such results along with Cassini inferred lake evaporation rates can be used to estimate the composition of Titan's polar liquids, and may have implications on their origin. Our results suggest that Ontario Lacus is predominantly composed of ethane (>50–80 mol%), indicating it may be a residual lake following extensive seasonal methane evaporation, and/or might be in contact with a subsurface liquid reservoir.

A Unified Model for Moist Convective Boundary Layers Based on a Stochastic Eddy-Diffusivity/Mass-Flux Parameterization

Abstract A single-column model (SCM) is developed for representing moist convective boundary layers. The key component of the SCM is the parameterization of subgrid-scale vertical mixing, which is based on a stochastic eddy-diffusivity/mass-flux (EDMF) approach. In the EDMF framework, turbulent fluxes are calculated as a sum of the turbulent kinetic energy–based eddy-diffusivity component and a mass-flux component. The mass flux is modeled as a fixed number of steady-state plumes. The main challenge of the mass-flux model is to properly represent cumulus clouds, which are modeled as moist plumes. The solutions have to account for a realistic representation of condensation within the plumes and of lateral entrainment into the plumes. At the level of mean condensation within the updraft, the joint pdf of moist conserved variables and vertical velocity is used to estimate the proportion of dry and moist plumes and is sampled in a Monte Carlo way creating a predefined number of plumes. The lateral entrainment rate is modeled as a stochastic process resulting in a realistic decrease of the convective cloudiness with height above cloud base. In addition to the EDMF scheme, the following processes are included in the SCM: a pdf-based parameterization of subgrid-scale condensation, a simple longwave radiation, and one-dimensional dynamics. Note that in this approach there are two distinct pdfs, one representing the variability of updraft properties and the other one the variability of thermodynamic properties of the surrounding environment. The authors show that the model is able to capture the essential features of moist boundary layers, ranging from stratocumulus to shallow-cumulus regimes. Detailed comparisons, which include pdfs, profiles, and integrated budgets with the Barbados Oceanographic and Meteorological Experiment (BOMEX), Dynamics and Chemistry of Marine Stratocumulus (DYCOMS), and steady-state large-eddy simulation (LES) cases, are discussed to confirm the quality of the present approach.

Mass transfer of toluene vapor through protective polymer gloves

Abstract A series of solvent vapor permeation tests are conducted to investigate the diffusion of toluene vapor through two types of common chemical-resistant polymer gloves. The measured concentration–time data are fitted using a two-parameter regression equation, and an empirical mass flux model derived from the fitted concentration–time curve is proposed to explain the mass transfer behavior of toluene vapor through polymer gloves. The mass transfer behavior of toluene vapor through the tested polymers is initially dominated by case-II diffusion for the solvent sorption followed by anomalous diffusion. The mass transfer coefficient of toluene vapor in the polymers and the breakthrough time are found to vary as a function of the inlet surface concentration. Analogous desorption experiments reveal that desorption initially occurs by Fickian diffusion, followed by an anomalous diffusion, and finally by case-II diffusion. Although the initial rate of desorption is considerably faster than that of sorption, a low rate of desorption continues for many hours after solvent saturation. An investigation of the mechanical properties of new and artificially aged polymer gloves through stress relaxation experiments revealed that aging can have a pronounced effect on the mechanical properties with an associated change in the solvent vapor mass transfer behavior.

Effectiveness of Explosive Reactive Armor

Explosive reactive armor (ERA) is a type of add-on armor that usually consists of tiles made of two metal plates with an explosive layer in between. The ERA is placed at a certain distance from the main armor to enhance its performance. ERA design is optimized based on the required effectiveness of the tiles. Various methods of defining ERA effectiveness are described. The effectiveness parameters of the mass-flux model and its derivatives, the effect of material properties, the escape length of the jet tip precursor, the explosive layer thickness, and the edge effects are analyzed, and correlations between them are presented. Analysis results are compared with available experimental data and a very good correlation is found.

A Mass Flux Model of Nocturnal Cold-Air Intrusions into a Closed Basin

AbstractObservations made during the Meteor Crater Experiment (METCRAX) field campaign revealed unexpected nighttime cooling characteristics in Arizona’s Meteor Crater. Unlike in other natural closed basins, a near-isothermal temperature profile regularly develops over most of the crater depth, with only a shallow stable layer near the crater floor. A conceptual model proposed by Whiteman et al. attributes the near-isothermal stratification to the intrusion, and subsequent detrainment, of near-surface air from outside the crater into the crater atmosphere. To quantify and test the hypothesis, a mass flux model of the intrusion process is developed. It is found that the observed temperature profile can be reproduced, providing confirmation of the conceptual model. The near-isothermal stratification can be explained as a result of progressively cooler air entering the crater and detraining into the atmosphere, combined with the finite time of ascent in the compensating rising motion. The strength of detrainment largely determines the characteristics of the cooling process. With weak detrainment, most of the cooling arises from an adiabatic rising motion (“filling-up” mode). Stronger detrainment leads to reduced rising motion and enhanced cooling at upper levels in the crater (“destabilization” mode). Of interest is that the detrainment also reduces the total cooling, which, for a given intrusion mass flux, is determined by the temperature difference between the intruding air and the crater atmosphere at rim height.