Mass flux

Abstract: The bulk properties of tropical cloud clusters, such as the vertical mass flux, the excess temperature, and moisture and the liquid water content of the clouds, are determined from a combination of 1) the observed large-scale heat and moisture budgets over an area covering the cloud cluster, and 2) a model of a cumulus ensemble which exchanges mass, heat, water vapor and liquid water with the environment through entrainment and detrainment The method also provides an understanding of how the environmental air is heated and moistened by the cumulus convection An estimate of the average cloud cluster properties and the heat and moisture balance of the environment, obtained from 1956 Marshall Islands data, is presented

Abstract: A General Theory.- 1 The Porous Medium.- 1.1 Definition and Classification of Porous Media.- 1.1.1 Definition of a porous medium.- 1.1.2 Classification of porous media.- 1.1.3 Some geometrical characteristics of porous media.- 1.1.4 Homogeneity and isotropy of a porous medium.- 1.2 The Continuum Model of a Porous Medium.- 1.2.1 The need for a continuum approach.- 1.2.2 Representative Elementary Volume (REV).- 1.2.3 Selection of REV.- 1.2.4 Representative Elementary Area (REA).- 1.3 Macroscopic Values.- 1.3.1 Volume and mass averages.- 1.3.2 Areal averages.- 1.3.3 Relationship between volume and areal averages.- 1.4 Higher-Order Averaging.- 1.4.1 Smoothing out macroscopic heterogeneity.- 1.4.2 The hydraulic approach.- 1.4.3 Compartmental models.- 1.5 Multicontinuum Models.- 1.5.1 Fractured porous media.- 1.5.2 Multilayer systems.- 2 Macroscopic Description of Transport Phenomena in Porous Media.- 2.1 Elements of Kinematics of Continua.- 2.1.1 Points and particles.- 2.1.2 Coordinates.- 2.1.3 Displacement and strain.- 2.1.4 Processes.- 2.1.5 Material derivative.- 2.1.6 Velocities.- 2.1.7 Flux and discharge.- 2.1.8 Gauss' theorem.- 2.1.9 Reynolds' transport theorem.- 2.1.10 Green's vector theorem.- 2.1.11 Pathlines, transport lines and transport functions.- 2.1.12 Velocity potential and complex potential.- 2.1.13 Movement of a front.- 2.2 Microscopic Balance and Constitutive Equations.- 2.2.1 Derivation of balance equations.- 2.2.2 Particular cases of balance equations.- 2.2.3 Constitutive equations.- 2.2.4 Coupled transport phenomena.- 2.2.5 Phase equilibrium.- 2.3 Averaging Rules.- 2.3.1 Average of a sum.- 2.3.2 Average of a product.- 2.3.3 Average of a time derivative.- 2.3.4 Average of a spatial derivative.- 2.3.5 Average of a spatial derivative of a scalar satisfying ?2G = 0.- 2.3.6 The coefficient T?*.- 2.3.7 Average of a material derivative.- 2.4 Macroscopic Balance Equations.- 2.4.1 General balance equation.- 2.4.2 Mass balance of a phase.- 2.4.3 Volume balance of a phase.- 2.4.4 Mass balance equation for a component of a phase.- 2.4.5 Balance equation for the linear momentum of a phase.- 2.4.6 Heat balance for a phase and for a saturated porous medium.- 2.4.7 Mass balance in a fractured porous medium.- 2.4.8 Megascopic balance equation.- 2.5 Stress and Strain in a Porous Medium.- 2.5.1 Total stress.- 2.5.2 Effective stress.- 2.5.3 Forces acting on the solid matrix.- 2.6 Macroscopic Fluxes.- 2.6.1 Advective flux of a single Newtonian fluid.- 2.6.2 Advective fluxes in a multiphase system.- 2.6.3 Diffusive flux.- 2.6.4 Dispersive flux.- 2.6.5 Transport coefficients.- 2.6.6 Coupled fluxes.- 2.6.7 Macrodispersive flux.- 2.7 Macroscopic Boundary Conditions.- 2.7.1 Macroscopic boundary.- 2.7.2 The general boundary condition.- 2.7.3 Boundary conditions between two porous media in single phase flow.- 2.7.4 Boundary conditions between two porous media in multiphase flow.- 2.7.5 Boundary between two fluids.- 2.7.6 Boundary with a 'well mixed's vector theorem.- 2.1.11 Pathlines, transport lines and transport functions.- 2.1.12 Velocity potential and complex potential.- 2.1.13 Movement of a front.- 2.2 Microscopic Balance and Constitutive Equations.- 2.2.1 Derivation of balance equations.- 2.2.2 Particular cases of balance equations.- 2.2.3 Constitutive equations.- 2.2.4 Coupled transport phenomena.- 2.2.5 Phase equilibrium.- 2.3 Averaging Rules.- 2.3.1 Average of a sum.- 2.3.2 Average of a product.- 2.3.3 Average of a time derivative.- 2.3.4 Average of a spatial derivative.- 2.3.5 Average of a spatial derivative of a scalar satisfying ?2G = 0.- 2.3.6 The coefficient T?*.- 2.3.7 Average of a material derivative.- 2.4 Macroscopic Balance Equations.- 2.4.1 General balance equation.- 2.4.2 Mass balance of a phase.- 2.4.3 Volume balance of a phase.- 2.4.4 Mass balance equation for a component of a phase.- 2.4.5 Balance equation for the linear momentum of a phase.- 2.4.6 Heat balance for a phase and for a saturated porous medium.- 2.4.7 Mass balance in a fractured porous medium.- 2.4.8 Megascopic balance equation.- 2.5 Stress and Strain in a Porous Medium.- 2.5.1 Total stress.- 2.5.2 Effective stress.- 2.5.3 Forces acting on the solid matrix.- 2.6 Macroscopic Fluxes.- 2.6.1 Advective flux of a single Newtonian fluid.- 2.6.2 Advective fluxes in a multiphase system.- 2.6.3 Diffusive flux.- 2.6.4 Dispersive flux.- 2.6.5 Transport coefficients.- 2.6.6 Coupled fluxes.- 2.6.7 Macrodispersive flux.- 2.7 Macroscopic Boundary Conditions.- 2.7.1 Macroscopic boundary.- 2.7.2 The general boundary condition.- 2.7.3 Boundary conditions between two porous media in single phase flow.- 2.7.4 Boundary conditions between two porous media in multiphase flow.- 2.7.5 Boundary between two fluids.- 2.7.6 Boundary with a 'well mixed' domain.- 2.7.7 Boundary with fluid phase change.- 2.7.8 Boundary between a porous medium and an overlying body of flowing fluid.- 3 Mathematical Statement of a Transport Problem.- 3.1 Standard Content of a Problem Statement.- 3.1.1 Conceptual model.- 3.1.2 Mathematical model.- 3.2 Multicontinuum Models.- 3.3 Deletion of Nondominant Effects.- 3.3.1 Methodology.- 3.3.2 Examples.- 3.3.3 Concluding remarks.- B Application.- 4 Mass Transport of a Single Fluid Phase Under Isothermal Conditions.- 4.1 Mass Balance Equations.- 4.1.1 The basic equation.- 4.1.2 Stationary rigid porous medium.- 4.1.3 Deformable porous medium.- 4.2 Boundary Conditions.- 4.2.1 Boundary of prescribed pressure or head.- 4.2.2 Boundary of prescribed mass flux.- 4.2.3 Semipervious boundary.- 4.2.4 Discontinuity in solid matrix properties.- 4.2.5 Sharp interface between two fluids.- 4.2.6 Phreatic surface.- 4.2.7 Seepage face.- 4.3 Complete Mathematical Model.- 4.4 Inertial Effects.- 5 Mass Transport of Multiple Fluid Phases Under Isothermal Conditions.- 5.1 Hydrostatics of a Multiphase System.- 5.1.1 Interfacial tension and capillary pressure.- 5.1.2 Capillary pressure curves.- 5.1.3 Three fluid phases.- 5.1.4 Saturation at medium discontinuity.- 5.2 Advective Fluxes.- 5.2.1 Two fluids.- 5.2.2 Two-phase effective permeability.- 5.2.3 Three-phase effective permeability.- 5.3 Mass Balance Equations.- 5.3.1 Basic equations.- 5.3.2 Nondeformable porous medium.- 5.3.3 Deformable porous medium.- 5.3.4 Buckley-Leverett approximation.- 5.3.5 Flow with interphase mass transfer.- 5.3.6 Immobile fluid phase.- 5.4 Complete Model of Multiphase Flow.- 5.4.1 Boundary and initial conditions.- 5.4.2 Complete model.- 5.4.3 Saturated-unsaturated flow domain.- 6 Transport of a Component in a Fluid Phase Under Isothermal Conditions.- 6.1 Balance Equation for a Component of a Phase.- 6.1.1 The dispersive flux.- 6.1.2 Diffusive flux.- 6.1.3 Sources and sinks at the solid-fluid interface.- 6.1.4 Sources and sinks within the liquid phase.- 6.1.5 Mass balance equation for a single component.- 6.1.6 Variable fluid density and deformable porous medium.- 6.1.7 Balance equations with immobile liquid.- 6.1.8 Fractured porous media.- 6.2 Boundary Conditions.- 6.2.1 Boundary of prescribed concentration.- 6.2.2 Boundary of prescribed flux.- 6.2.3 Boundary between two porous media.- 6.2.4 Boundary with a body of fluid.- 6.2.5 Boundary between two fluids.- 6.2.6 Phreatic surface.- 6.2.7 Seepage face.- 6.3 Complete Mathematical Model.- 6.4 Multicomponent systems.- 6.4.1 Radionuclide and other decay chains.- 6.4.2 Two multicomponent phases.- 6.4.3 Three multicomponent phases.- 7 Heat and Mass Transport.- 7.1 Fluxes.- 7.1.1 Advective flux.- 7.1.2 Dispersive flux.- 7.1.3 Diffusive flux.- 7.2 Balance Equations.- 7.2.1 Single fluid phase.- 7.2.2 Multiple fluid phases.- 7.2.3 Deformable porous medium.- 7.3 Initial and Boundary Conditions.- 7.3.1 Boundary of prescribed temperature.- 7.3.2 Boundary of prescribed flux.- 7.3.3 Boundary between two porous media.- 7.3.4 Boundary with a 'well mixed' domain.- 7.3.5 Boundary with phase change.- 7.4 Complete Mathematical Model.- 7.5 Natural Convection.- 8 Hydraulic Approach to Transport in Aquifers.- 8.1 Essentially Horizontal Flow Approximation.- 8.2 Integration Along Thickness.- 8.3 Conditions on the Top and Bottom Surfaces.- 8.3.1 General flux condition on a boundary.- 8.3.2 Conditions for mass transport of a single fluid phase.- 8.3.3 Conditions for a component of a fluid phase.- 8.3.4 Heat.- 8.3.5 Conditions for stress.- 8.4 Particular Balance Equations for an Aquifer.- 8.4.1 Single fluid phase.- 8.4.2 Component of a phase.- 8.4.3 Fluids separated by an abrupt interface.- 8.5 Aquifer Compaction.- 8.5.1 Integrated flow equation.- 8.5.2 Integrated equilibrium equation.- 8.6 Complete Statement of a Problem of Transport in an Aquifer.- 8.6.1 Mass of a single fluid phase.- 8.6.2 Mass of a component of a fluid phase.- 8.6.3 Saturated-unsaturated mass and component transport.- References.- Problems.

Abstract: A simple dimensionless correlation for predicting heat-transfer coefficients during film condensation inside pipes is presented. It has been verified by comparison with a wide variety of experimental data. These include fluids water, R-11, R-12, R-22, R-113, methanol, ethanol, benzene, toluene, and trichloroethylene condensing in horizontal, vertical, and inclined pipes of diameters ranging from 7 to 40mm. One data set for condensation inside an annulus has also been analyzed. The range of parameters covered includes reduced pressures from 0.002 to 0.44, saturation temperatures from 21 to 310°C, vapor velocities from 3 to 300m/s, vapor qualities from 0 to 100%, mass flux 39000-758 000kg/m2 h, heat flux from 158 to 1 893000W/m2, all liquid Reynolds numbers from 100 to 63 000, and liquid Prandtl numbers from 1 to 13. The mean deviation for the 474 data points analyzed was found to be 15.4%.

Abstract: : This manual describes the next generation of the modular three-dimensional transport model, MT3D, with significantly expanded capabilities, including the addition of (a) a third-order total-variation-diminishing (TVD) scheme for solving the advection term that is mass conservative but does not introduce excessive numerical dispersion and artificial oscillation, (b) an efficient iterative solver based on generalized conjugate gradient methods and the Lanczos/ORTHOMIN acceleration scheme to remove stability constraints on the transport time-step size, (c) options for accommodating nonequilibrium sorption and dual-domain advection-diffusion mass transport, and (d) a multicomponent program structure that can accommodate add-on reaction packages for modeling general biological and geochemical reactions MT3DMS can be used to simulate changes in concentrations of miscible contaminants in groundwater considering advection, dispersion, diffusion, and some basic chemical reactions, with various types of boundary conditions and external sources or sinks The basic chemical reactions included in the model are equilibrium-controlled or rate-limited linear or nonlinear sorption and first-order irreversible or reversible kinetic reactions MT3DMS can accommodate very general spatial discretization schemes and transport boundary conditions, including: (a) confined, unconfined, or variably confined/unconfined aquifer layers, (b)inclined model layers and variable cell thickness within the same layer, (c) specified concentration or mass flux boundaries, and (d) the solute transport effects of external hydraulic sources and sinks such as wells, drains, rivers, areal recharge, and evapotranspiration

Abstract: The convection scheme used at the UK Meteorological Office in large-scale numerical models is described. The scheme uses a “bulk” cloud model to represent an ensemble of convective clouds and aims to represent shallow, deep and midlevel convection. A simple closure is employed, the initial convective mass flux being related to the stability of the initial convecting layer. The ability of the scheme to represent convective processes in a variety of situations is evaluated using GATE, BOMEX, and ATEX data. In each case realistic heating rates are simulated and although the closure of the scheme does not demand a balance between convective and large-scale forcings as in many other types of convection scheme (for example the Arakawa–Schubert scheme), a quasi-equilibrium is established while retaining realistic atmospheric structure. The performance of the scheme in an 11-layer atmospheric general circulation model used in climate research at the UK Meteorological Office is also evaluated by comparing...