By Richard G. Rice, Duong D. Do
This moment variation of the go-to reference combines the classical research and sleek purposes of utilized arithmetic for chemical engineers. The e-book introduces conventional thoughts for fixing usual differential equations (ODEs), including new fabric on approximate answer equipment similar to perturbation strategies and trouble-free numerical suggestions. it is also analytical ways to take care of vital periods of finite-difference equations. The final part discusses numerical answer options and partial differential equations (PDEs). The reader will then be outfitted to use arithmetic within the formula of difficulties in chemical engineering. just like the first variation, there are lots of examples supplied as homework and labored examples
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Extra info for Applied Mathematics And Modeling For Chemical Engineers, Second Edition
6 A plot of the effectiveness factor versus mL2. that the heat flow through area pR2 at x ¼ 0 must be equal to the heat released into the atmosphere, that is, @T Q ¼ ÀpR k @x x¼0 2 ð1:138Þ Applying Eq. 136 to Eq. 138 gives Q ¼ 2pRhG L2 hðT 1 À T 0 Þ ð1:139aÞ tanhðmL2 Þ mL2 tanhðmL2 Þ %1 mL2 L2 hG ðT À T 0 Þ ð2pRdxÞ ð1:141Þ 0 Level 3 In this level of modeling, we relax the assumption (a) of the first level by allowing for temperature gradients in the rod for segments above and below the solvent–air interface.
While simple to design and construct, bubble columns sustain rather large eddy dispersion coefficients, and this must be accounted for in the modeling process. For concurrent operation, liquid of superficial velocity u0L is injected in parallel with gas superficial velocity u0G. The liquid velocity profile can be taken as plug shaped, and the gas voidage can be treated as uniform throughout the column. We wish to model a column used to aerate water, such that liquid enters with a composition C0.
The next level of modeling is by now obvious: At what point and under what conditions do radial gradients become significant? This moves the modeling exercise into the domain of partial differential equations. Level 4 Let us investigate the fourth level of model where we include radial heat conduction. This is important if the rod diameter is large relative to length. Let us assume in this model that there is no resistance to heat flow underneath the solvent interface, so as before, take temperature T ¼ T1 when x 0.
Applied Mathematics And Modeling For Chemical Engineers, Second Edition by Richard G. Rice, Duong D. Do