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Fundamental Concepts
Published in Nicholas P. Cheremisinoff, Polymer Mixing and Extrusion Technology, 2017
Rheology is a subject which addresses the deformation of fluids. By this it is meant that whenever surface forces, called stresses, are applied to a body of fluid, that body deforms or flows. We can describe this behavior mathematically by means of a set of constitutive equations. A constitutive equation defines the cause and effect relationships in terms of the properties or characteristics of the fluid material. To develop such relationships balance equations must be derived. A balance equation is merely a mathematical statement of the universal laws of conservation of mass, energy, and momentum that are specific to the system of interest. By way of a simple example found in many fluid dynamic textbooks (Cheremisinoff, 1982; Azbel and Cheremisinoff, 1983), consider a shearing force applied to a rectangular body of incompressible fluid as illustrated in Figure 1. For steady-state, isothermal flow conditions we may write the following mass balance (continuity equation) and momentum balance (equation of motion): Mass balance: () ddxρVx=0=ρdVxdx
Sara Section 313 Reporting
Published in Bell John W., Proceedings of the 44th Industrial Waste Conference May 9, 10, 11, 1989, 1990
John A. Lytle, Katherine E. Imbrock
The objective of the release calculations is to estimate the amount of a listed chemical which is released to the air, water and/or the land. Figure 3 shows the possible releases from a process. In most processes, the majority of material will leave the process as part of the product, but some inputs will exit the process in wastewater, as waste escapes into the solids or air. Release determinations are most often made using a mass balance equation. A mass balance equation states that the amount of a material entering a process must equal the amount leaving, provided no accumulation occurs. Process inputs may consist of raw materials, recirculated material, or clean up material. Input amounts should be totaled for each listed chemical entering a particular process. Process outputs typically consist of wastewater, waste solids, air emissions and products. Process outputs should also be totalled for each listed chemical, and should equal the total inputs of that chemical entering the process.
One-Dimensional, Steady-State, Diffusive Transport
Published in Joel L. Plawsky, Transport Phenomena Fundamentals, 2020
Formally the momentum balance equation states that: the rate of change of momentum within the control volume is equal to the net force applied across the upper and lower faces. We write this and the other balance equations referencing the plane at z as the In term and z + Δz as the Out term regardless of whether v∞ < vo or vice versa. If the recipe for deriving the equation and getting the solution is followed, the final result should tell us which directions are the correct ones.
Dynamic model-based feature extraction for fault detection and diagnosis of a supermarket refrigeration system†
Published in Science and Technology for the Built Environment, 2023
Jian Sun, Teja Kuruganti, Brian Fricke, Yanfei Li, Shenglan Xuan, Wenhua Li
The mass balance equation, energy balance equation, and momentum balance equation are listed as follows. where T denotes the display case air temperature, ṁa,s and ma,r denote the display case supply and return air mass flow rate, ṁa,inf denotes the infiltration air mass flow rate, ṁcond denotes the condensed water mass flow rate, ha,s and ha,r denote the display case supply and return air enthalpy, ha,inf denotes the infiltration air enthalpy, hvap denotes the water vaporization enthalpy, Pa,s and Pa,rdenote the display case supply and return air pressure, and Pa,inf denotes the infiltration air pressure.
Investigation of Normal and Abnormal States of the Molten Salt Experimental Loop Using Computational Fluid Dynamics
Published in Nuclear Science and Engineering, 2023
Michal Cihlář, Pavel Zácha, Jan Uhlíř, Martin Mareček, Václav Dostál, Jan Prehradný
The governing equations comprise the basic balance equation for the conservation of mass, momentum, and energy. The energy equation is solved together with pressure-velocity states using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE). The solver is pressure-based with absolute velocity formulation. Spatial discretization is performed using the Least Squares Cell Based method for gradient, the Second Order method for pressure, and the Second Order Upwind method for momentum and energy. The First Order Implicit transient formulation was employed. The viscous model was set to laminar due to very low velocities (v 0.05 m·s−1, Re 100). For heat transfer, the conjugate heat transfer model was applied.