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The unequimolar case occurs, but any type of a solution similar to Eq. (5.68) or Eq. (v) in Example 5.12 is of doubtful value, since the product C,D varies. 5.3.5 Diffusion in Solids This section provides a brief overview of diffusion in solids. Fluid Mechanics for Chemical Systems. 3 Units. This course introduces the physical and mathematical concepts associated with the motion of material and the transfer of momentum.

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LA i k k m :A nA 12 P fG t u V X Unit vector in x direction Molar flux vector in Fick’s law, Eq. (2.4), detined with respect to a plane of no net volume flow (km01 rn-:s-l, lb mol ft-z s-l); subscripts A or B are for flus of species A or B; called J”A/A in Chapter 5 Mass flux vector of species A, defined with respect to a plane of no net volume flow (kg mm2 s-l, lb, ftw2 s-t) Unit vector in y direction Unit vector in z direction T h e r m a l c o n d u c t i v i t y (Wm-‘K-l o r J m-‘K-‘s-r, B t u ft-’ “R-‘s-l); k, is mean thermal conductivity over the range of integration Specitic reaction rate constant of order n, as given in Eq. (4.105) Length (m, ft) rate of generation of momentum in a unit volume (kgmm2sm2, N me3, lb,,, fte2 sT2, lb, ft-“) Mass (kg, lb,) Subscript denoting contribution due to molecular transport Molar flow vector for species A, defined with respect to tixed coordinates (km01 s-l, lb mol s-l); if written not as a vector, then N is subscripted for direction of transfer Mass flow vector for species A, equal to molar flow N* times molecular weight (kg s-l lb,,, s-‘) Order of reaction in Eq, (4.105) Pressure @Pa, atm, lb, inT2); P,%, is partial pressure of Species A, Eq. (2.38) Volume rate of flow (m3 s-l, ft3 s-l); also subscript denoting torque Energy (heat) flow vector (J s-l, Btu s-‘) Gas constant, see Table C. 1 for values Cylindrical coordinate Radius (m, ft); in heat transfer, ri is radius of inside tube wall and r,, is radius of outside tube wall; in momentum transfer, the convention is to, designate r,, (and d,) as the radius (and dieter) of the tube through which the fluid is flowing (i.e., the inside radius) Area perpendicular to the direction of the velocity vector U Temperature (K, “R, “C, “F); & and T2 are temperatures at locations 1 and 2; T, is temperature of the wall or surface; Tq is temperature at the center line Rate of generation of heat (J rnF3 s-l, Btu fte3 s-l) Time (s) Velocity vector (m s-l, fts-‘); V is the magnitude of U; V,, LJ,, V,, V,, V, are wmponents in directions x, y, z, t?, r; U is the mass average velocity [Eq. (3.22)], whereas U’ is molar average velocity M &WI Volume (m3, f?) Rectangular (Cartesian) coordinate; x, is thickness of Iaminar film. 92 BASIC CONCEFIX INTRANSP~RTP~IF~NOMENA.

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From Table 10.2, the absolute roughness for commercial steel pipe is 1.5 x 10m4 ft. Since most tables present molecular weights in units of g mol-‘, this SI unit is the same as the old “g-mole” unit. In these liquids, the agitation process is under laminar flow conditions, and unusual impeller shapes, such as the anchor, a helical ribbon, the screw impeller, or some other similar shape are most satisfactory. Prerequisite: C&PE 651 or C&PE 661; and invitation and permission of instructor, open to seniors only.

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Gray (eds.), Academic Press, New York, 1966, ch. 5, pp. 284-317. Kirchhoff, Chapter 7 in Handbook of Fluid Dynamics (R. Prerequisites or Corequisites: CH_ENG 2226 and CH_ENG 3235. In order to obtain the concentration of momentum that is transferred, the density is multiplied by U,. Finally, the location of the orifice with relation to other fittings in the system can be critical. Boussinesq’s idea [B4] was to express Eq. (6.61) in a form similar to the laminar shear stress-shear rate 228 BASIC C0NCEF’l-S IN TRANSPORT PHENOMENA equation, Eq. (6.60) or Eq. (4.18): rT = p(m)= -&(auz/ar) (6.62) In Eq. (6.62), the term a&/%, which is the slope of the velocity profile in the pipe or channel, is the shear rate, and E is ca$d-the eddy viscosity, Note that E is defined very similarly to p.

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Let us assume that the temperatughange in this problem is relatively small. Application to a wide range of operations in the chemical and metallurgical process industries. Gaseous nitrogen is in isothermal turbulent flow at 25°C through a straight length of horizontal pipe with 3-in. inside diameter at a rate of 0.28 1bJs. For a summary of measured values and comparisons with the Chapman-Enskog theory, see R. Reaction products enter the first stage with 0.5 kg H 2 0 k g CaCO,.

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From Eq. 8.6-9 we find for the limiting values of the viscosity For y = 0: For j + m: Hence, at high shear rates one obtains a power law behavior (Eq. 8.3-3) with n = i. Nanosystems Integration (4) Discussion of scaling issues and how to carry out the effective hierarchical assembly of diverse molecular and nanoscale components into higher order structures which retain the desired electronic/photonic, structural, mechanical or catalytic properties at the microscale and macroscale levels.

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For nonreacting binary mixtures with con- stant p and B,,, Eq. 19.1-14 takes the form Continuity of A: For the assumptions that have been made, the analogy between Eqs. 19.5-3 and 4 is clear. - - - J. 0. Instead of Eq. 20.3-19, one finds K .= 2.59,,PeAB, with the first power of the P6clet number appearing, instead of the second power and with K in- dependent of 9JAB.13 Brenner and Edwards14 have given analyses of convective disper- sion and reaction in various geometries, including tubes and spatially periodic packed beds.

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We then consider the actual rupture process of a thin film with van der Waals forces present. For isothermal conditions (260°C) and an exit pressure of 2.07 x lo5 pascals, what is the entrance pressure? 4-10. Solvent mixture fed to the system is made up of 595.0 0.5 kg of benzene and 9. A stream of gas mixture A-B of concentration XA2 flows slowly past the top of the tube, to maintain the mole fraction of A at x,, for z= z2. The constitutive equations describe how the quantity in question responds to various stimuli via transport.

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Giesekus, Phanomenologische Rheologie: Eine Einfiihrung, Springer Verlag, Berlin (1994). This course will provide an introduction to the physics and chemistry of soft matter, followed by a literature-based critical examination of several ubiquitous classes of organic nano materials and their technological applications. Turbulent systems may be included by using time-smoothed quantities and an effective turbulent diffusivity. A mixture of air (A) and carbon dioxide (B) at 0°C is diffusmg through a capillary of diameter 10m6m and 2 m long.

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Gheorghe (Author) Introductory Transport Phenomena (by R. Fane: in Handbook of Muitiphnse Systems, G. For WI. cocurrent (parallel) operation, both fluids A and B enter the equipment at the same end, as shown in Fig. ll.ll(b). Unless the problems are idealized or simplified, mixture transport phenomena are quite complicated and usually numerical techniques are re- quired. What is the thickness of the water layer for a flow rate of 0. 2-26. 2-20. bottom diameter of 0. The X and Y values for L, are Next we connect v b and L, on Figure 13-23 and note that J lies on this line.

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