## Transport Phenomena in Porous Media II

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The energy equation, Eq. (B) of Table 5.6, in cylindrical coordinates was simplified in Example 5.4; the result was a differential equation describing the variation of T with r. The bulk flow in such an experiment is caused by a pressure gradient. To do this, it must be recognized that both x and d x / d & are zero at 6 = 6,. Copyright 1940, 1969, 1970, American Society of Mechanical Engineers.) (curve C and the points in the lower right-hand comer; references are 14, 15, and 16).

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The various contributions to the momentum balance are then obtained with the help of the quantities in the "z-component" columns of Tables 1.2-1 and 1.7-1. J.: Conduction Heat Transfer, Addison-Wesley, Cambridge, MA, 1955. Course Requirements: MATH 124, MATH 125, MATH 126; CHEM 142, CHEM 152, CHEM 162; PHYS 121; and 5 credits of English composition, chosen from C LIT 240, ENGL 109-ENGL 110, ENGL 111, ENGL 121, ENGL 131, ENGL 197, ENGL 198, ENGL 199, or ENGL 281. You’ll draw upon many topics within chemical engineering, including the others explored here.

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From this get the efflux time List all the assumptions that have been made and discuss how serious they are. The physical properties of water will be needed at temperatures of 20°C 3o”C, and 4o”C, in order to use the six methods of prediction covered in Section 11.3. Application of the techniques to areas such as petroleum reservoir simulation, chemical process industry operations and plant start-up. Equation (9.29) will be used for this procedure; the identical answers will be obtained.

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A glass rod of diameter 1.3 mm is 1 m long. This equation is appropriate for describing the diffusion in dilute liquid solutions at constant temperature and pressure. It is desired to find the rate of flow in the system as a function of the imposed pressure difference. New microreactor designs are expanding the concept of what a reactor may do, how reactions may be conducted, and what is required to scale a process from laboratory to production.

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The second half of this chapter considers the opposite limit in which Pe ≫ 1. Diffusion in systems with three or more components is a much more difficult problem than indicated by this discussion, since the various diffusion coefficients are coupled and depend on the fluxes as well [G?, LI]. Write the applicable differential equations from the tables in Chapter 5, eliminating all the zero terms. 7. In nature, the trained observer perceives that changes occur in response to imbalances or driving forces.

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Estimate the temperature at which ice will form on a clear night (sky effective radiation temperature is -73.3"C). Equilibrium data for each of the gases as Y = KX are, respectively, 23.9 (methane), 4.6 (ethane), 1.4 (propane), and 0.4 (butane). The heaters are usually designed for specific process operations, and most are of cylindrical vertical or box-type designs. Or what happens inside a water treatment plant?

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The reader may wonder how the solubility cAo and the diffusivity QAB can be de- termined experimentally if there is a chemical reaction taking place. The usefulness and comprehensiveness of Figure 3-3 can't be understated. Pigford, Nuclear Chemical Engineering, McGraw-Hill, New York (1957). 29. Comparisons were made against exact calculations of elements kxap and N,, via Eq. 22.9-19, and against a film model given by Krishna and Standart" in which each element kXop is calculated independently with the corresponding binary diffusivity gap.

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O'Connell correlation for overall efficiency. (Reproduced with permission from reference 15.296 EQUILIBRIUM STAGED OPERATIONS 100 01 I I I I I 0. Hence we need to know how the radiant energy emanating from a black body is distributed with respect to angle. Nikuradse, J.: VDI-Forschungshelf No. 356 (1932). In nature, the trained observer perceives that changes occur in response to imbalances or driving forces. However, for steady conduction these materials can be regarded as homogeneous materials with an effective thermal conductivity keff, and the temperature and heat flux components are reinterpreted as the analogous quantities av- eraged over a volume that is large with respect to the scale of the heterogeneity but small with respect to the overall dimensions of the heat conduction system.

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T. t. ) WORKED EXAMPLES Example 5-1 A cold storage room has walls constructed of 0. (Reproduced with permission from reference 3. In the following unit analysis, the momentum flux (also called shear stress) ryX is shown to be 24 BASIC CONCEPTS IN TRANSPORT PHENOMENA equivalent to a force per unit area: trx = (mass)(velocW _ E (time)(area) -A SI Mitt? (W(m s-l) (W(m) CW (s)(m”) =(s30=Nm-2 (lb,)@ s-l) (s)(ft’)(lb,,, lb;’ ft s-2) = lbf *-2 In the above equation using SI units, velocity has units of m s-l, and one newton is one kg m s-~.

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Using Eq. (15.26) the answers used to are (9 (ii) n =n’=0.8851 0.01254 = - = 0.01219 N mm2 K = [(3n +:;/4n] 1.029 NON-NEWTONIAN PHENOMENA I75 FIGURE 15.12 Pseudoshear rate, 8l&,Jd,,, s-’ Capillary shear diagram for polyisobutylene L-80 in cyclohexane. 15.4. The maximum permitted air temperature at the water surface is T, = 492"R. Steady-state conduction; transient conduction; lumped and distributed systems; thermal and hydrodynamic boundary layer concepts; forced convection (external and internal); free convection; heat exchangers; radiation properties; radiation heat transfer.