transport-master

transport-master - Prof Dr May-Britt Kallenrode Fachbereich...

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Unformatted text preview: Prof. Dr. May-Britt Kallenrode Fachbereich Physik Modeling Transport Osnabr¨uck, 13th November 2006 Contents 1 What is Transport? 1 1.1 What is transport? – A Guided Tour . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Help, I still can’t define Transport . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.2 Classification – Questions on our Way to a Transport Model . . . . . 10 1.2.3 Why should I Model at All? . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 Modeling 14 2.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.1 Types of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.2 When Not to Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Creating a model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.1 Make a Sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.2 Draw an Envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.3 Simplifying Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.4 Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.1 Discharge of a Plant Effluent into a River . . . . . . . . . . . . . . . . 24 2.3.2 Newton’s Law of Cooling . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.3 Evaporation of a Pollutant into the Atmosphere . . . . . . . . . . . . 26 2.3.4 Thermal Balance of a Building . . . . . . . . . . . . . . . . . . . . . . 28 2.4 If Inspiration Refuses to Help . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.4.1 Mass Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.4.2 Energy Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.4.3 Conservation of Momentum (Equation of Motion) . . . . . . . . . . . 38 2.5 Selling and Borrowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3 Constant Flow with Reactions 41 3.1 Chemical Reactor in Steady-State . . . . . . . . . . . . . . . . . . . . . . . . 41 3.1.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.1.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.1.3 Solving the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.1.4 Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2 Time-Dependent Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.2.1 Numerical Method 1: Implicit Method . . . . . . . . . . . . . . . . . . 47 3.2.2 Numerical Method 2: Crank–Nicolsen . . . . . . . . . . . . . . . . . . 48 3.2.3 Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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This note was uploaded on 09/16/2011 for the course ME 563 taught by Professor Staff during the Spring '11 term at Auburn University.

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transport-master - Prof Dr May-Britt Kallenrode Fachbereich...

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