By Richard G. Rice
Bridges the space among classical research and smooth functions. Following the bankruptcy at the version development level, it introduces conventional concepts for fixing usual differential equations, including new fabric on approximate resolution equipment reminiscent of perturbation suggestions and hassle-free numerical recommendations. additionally contains analytical the right way to take care of very important sessions of finite-difference equations. The final part discusses numerical answer suggestions and partial differential equations.
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Additional info for Applied Mathematics and Modeling for Chemical Engineers
N. Lightfoot. Transport Phenomena. , New York (1960). 2. , Oxford University Press, New York (1959). 3. , "Approximate Solutions for Batch, Packed Tube and Radial Flow Adsorbers—Comparison with Experiment," Chem. Eng. Sci. 37, 83-97 (1982). 4. , Modeling with Differential Equations in Chemical Engineering, Butterworth-Heinemann, Boston (1991). I1. Length Required for Cooling Coil A cooling coil made of copper tube is immersed in a regulated constant temperature bath held at a temperature of 20 0 C.
90) Substituting this into Eq. 89, we will obtain Eq. 63a. 91) In summary, we have illustrated how proper model hierarchy sets limits on the lower levels. In particular, one can derive criteria (like Eq. 91) to show when the simpler models are valid. Some solutions for the simpler models can be found in Walas (1991). The obvious question arises: When is a model of a process good enough? This is not a trivial question, and it can only be answered fully when the detailed economics of design and practicality are taken into account.
7 Schematic diagram of shell for heat balance. 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 = T1 when x < 0. This then leaves only the portion above the solvent surface to study. Setting up the annular shell shown in Fig. >-'&-o Next, insert the two forms of Fourier's laws Qr- k d r ; Qx- k d x and get finally, Here we have assumed that the conductivity of the steel rod is isotropic and constant, that is, the thermal conductivity k is uniform in both x and r directions, and does not change with temperature.
Applied Mathematics and Modeling for Chemical Engineers by Richard G. Rice