By Richard G. Rice
Bridges the distance among classical research and glossy functions. Following the bankruptcy at the version construction level, it introduces conventional ideas for fixing usual differential equations, including new fabric on approximate answer equipment corresponding to perturbation thoughts and trouble-free numerical strategies. additionally comprises analytical ways to care for very important periods of finite-difference equations. The final part discusses numerical answer options and partial differential equations.
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Extra info for Applied Mathematics and Modeling for Chemical Engineers
43 • 10~4 kcal/(s • m • K) Since the Reynolds number is in the turbulent range, use the correlation of Sieder and Tate (Bird et al. 32. Dissolution of Benzoic Acid Initially pure water is passed through a tube constructed of solid benzoic acid. Since benzoic acid is slightly soluble in water (denote solubility as C* moles acid/cm3 solution), the inner walls of the tube will dissolve very slowly. By weighing the dried tube before and after exposure, it is possible to calculate the rate of mass transfer.
62) If we scale time by replacing 0 = k2t, the above expression becomes identical to the special form of the Riccati equation. Thus, on comparing with Eq. 63) If we make the Riccati transformation Cfi u d6 we finally obtain We have thus transformed a nonlinear first order equation to a solvable, linear second order equation. CASE (b) n = 2, m =1 The simultaneous equations for this case are ^A _ _k C2 . 66) where C is the constant of integration. 71) = kxCA - k2CB This also yields the I-factor equation, if the time variation is desired.
The reaction is new and the rate constant is nonstandard, that is, its value does not fall into the range of values known to your group of design engineers. Your first attempt, therefore, is to model the reactor in the simplest possible way so that you can develop some intuition about the system before any further modeling attempts are made to describe it exactly. (a) For simplicity, assume that there is no appreciable diffusion inside the catalyst and that diffusion along the axial direction is negligible.
Applied Mathematics and Modeling for Chemical Engineers by Richard G. Rice