## Transport Phenomena

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vChemical kinetics studies the rates of chemical reactions and their dependencies.

Authors: Curt Breneman, Joan Warren Keywords: calculus, chemistry, chemical kinetics, chemical equilibrium Learning Level: College Platform: Project Links base technical requirements Applets: [ Full Metadata ]

v The most important unit operation in a chemical process is generally a chemical reactor. Chemical reactions are either exothermic (release energy) or endothermic (require energy input) and therefore require that energy either be removed or added to the reactor for a constant temperature to be maintained. Exothermic reactions are the most interesting systems to study because of potential safety problems (rapid increases in temperature, sometimes called "ignition" behavior) and the possibility of exotic behavior such as multiple steady-states (for the same value of the input variable there may be several possible values of the output variable). In this module we consider a perfectly mixed, continuously stirred tank reactor (CSTR).

Authors: B. Wayne Bequette Keywords: Learning Level: College Platform: Project Links base technical requirements Applets: [ Full Metadata ]

v In this module, simple differential equations are used to study the effects of the "drag" force which slows the motion of a body moving through a fluid (in this case: air) and is responsible for the safe landing of the skydiver.

Authors: Howard Littman, Bernard Fleishman Keywords: calculus, drag, fluid mechanics Learning Level: College Platform: Project Links base technical requirements Applets: Drag Forces, Skydiver [ Full Metadata ] ## Flux and Surface Integration

v Through the use of interactive materials, involving practical examples, notions of flux and the associated concept of surface integration are presented.

Authors: Ashwani Kapila, Curt Breneman, Karen Cummings, Bruce Buhler Keywords: flux, surface integration, projected area, flow Learning Level: college Platform: Project Links base technical requirements Applets: Induction, Simple Uniform Flux, Simple Non-Uniform Flux, Wing [ Full Metadata ]

v

vTo develop the mathematical description of a physical process in which the gradient plays a central role. To formulate problems in steady state one-dimensional heat conduction which provide practice in solution of ordinary differential equations, physical interpretation, and interaction via manipulation of parameters. To derive the partial differential equations for heat conduction in two dimensions and solve the equation governing steady states under various boundary conditions.

Authors: Howard Littman, Bernard Fleishman Keywords: calculus, gradient, heat transfer Learning Level: College Platform: Project Links base technical requirements Applets: [ Full Metadata ]

v This module on lake pollution is about using differential equations to model lake pollution. To model lake pollution can be complicated, because there are many different factors which can be taken into account. We will use a simplified model, and consider only a few basic factors.

Authors: Robert Wheeler, Kenneth Hannsgen, John Little, John Hoggard Keywords: differential equations Learning Level: College Platform: Project Links base technical requirements Applets: [ Full Metadata ]

v There are many instances in biology and in the environment where mass transport is an important phenomenon. Everything from cellular osmosis to glucose uptake to pollution in lakes and ponds can be related to mass transport. The Mass Transport module introduces the ideas of concentration and concentration difference and formalizes how these concepts are responsible for many common phenomena. The module contains a series of related demonstrations and exercises that build on one another, allowing students an incremental understanding of the subject through increasing levels of complexity.

Authors: Jonathan Newell, Russell Manson, Donald Drew, Jason Hylan, Elisa Barney Smith Keywords: concentration, differential equations, diffusion, dilution, mass transport, semi-permeable membrane, solute, solvent Learning Level: college Platform: Project Links base technical requirements Applets: Single Chamber, Two Sources to Single Chamber, Washout Dilution, Chamber and Sink, Two Chamber, Two Chambers Plus Sink, N Chamber (N=10), N Chamber (N=10) Plus Sink [ Full Metadata ]

v Linear systems of ODEs are introduced via the chemical reactions leading to the chlorination of benzene. One of the goals is to maximize the output of certain chlorinated benzene products.

Authors: Gilberto Schleiniger, Andrew Zydney, L. P. Cook, B. Lenhoff Keywords: differential equations, linear systems, ODE, eigenvalues, eigenvectors, order reactions, initial value problems, kinetics Learning Level: college Platform: Project Links base technical requirements Applets: [ Full Metadata ]

vThe gradient, its interrelations with other math concepts, and its applications to science and engineering. Rapid-change vector; normal vector to level surface. The gradient and gradient operator in Cartesian and other coordinate systems. The gradient as related to differentiability and the directional derivative.

Authors: Edith Luchins, Tom Rousseau, Steven Irving, Sara Schubert Keywords: calculus, gradient Learning Level: College Platform: Project Links base technical requirements Applets: Visualizing the Gradient (2D), Visualizing the Gradient (3D) [ Full Metadata ]

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