lecture+8+integrating+factor+ode

lecture+8+integrating+factor+ode - Problem Solving Approach...

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Unformatted text preview: Problem Solving Approach 1. Read and think 2. Draw a diagram and label 3. Choose CV(s) (and later basis) 4. Apply balance(s) 5. Incorporate constitutive information 6. Solve quantitatively Step 6 requires mathematics to solve the governing eqns. For unsteady state, we must solve 1 st oder odes. For steady state, we must solve simultaneous algebraic eqns. Solution of First Order ODEs Three Techniques: Separation Of Variables , Homogeneous and Particular, and Integrating Factors (1) Separation of variables is straightforward for both linear & nonlinear (2) We will discuss general solutions to linear first order by homogeneous and particular and integrating factions ) ( ) ( t g y t a dt dy = + 1 1 t H t y (t ) c exp[ a( )d ] ξ ξ =- ∫ ) ( ) ( ) ( t y t y t y P H + = Homogeneous and Particular Method y P (t) = guess by method of families (also called undetermined coefficients) When g(t)= 0, we have the Homogeneous Solution that Particular Solution Final Solution = ξ dummy variable 1 1 t...
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This note was uploaded on 07/05/2010 for the course CHEME 140 taught by Professor Radke during the Fall '09 term at University of California, Berkeley.

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lecture+8+integrating+factor+ode - Problem Solving Approach...

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