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Calculating heat flow Rearranging Fourier's law: Since T and x are the only variables, we will have: B is the thickness of the wall. 52. Hamrin, Jr., University of Kentucky; Richard W. Polymer rheology, transport phenomena, thermodynamics, membranes, conducting polymers, surfaces, interfaces and processing. ( CHEN 3620 and CHEN 5410 require a grade of C or better). Six of the required technical courses are electives, which provide each student the opportunity to tailor the program to her/his individual interests such as environmental concerns, materials, bio-processes, entrepreneurship, etc.

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The slope is related to the derivative as follows: R I S E dT SLOqE=-----=--R U N dr (13.88) Let the “RUN” in the x direction be Ax and in the f-direction be At: AX=Xi+l-Xi At=q+l-ti The transient heat equation for one direction is $T 1dT -z-e ax* (Y at Let the quantity T(xi, tj) be the temperature at location Xi and time 4. (13.6) (13.89) (13.90) Explicit method. ISBN: 0-471-43819-7 We have previously discussed two of the three modes of heat transfer (conduction and convection).

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The tangential component is not restricted, since in po- tential flow the fluid is presumed to be able to slide freely along the surface (the complete-slip assumption). (a) Show that the complex potential describes the potential flow around a circular cylinder of radius R, when the approach veloc- ity is v, in the positive x direction. (b) Find the components of the velocity vector. (c) Find the pressure distribution on the cylinder surface, when the modified pressure far from the cylinder is 9,. (a) To find the stream function and velocity potential, we write the complex potential in the form w(z) = +(x, y) + i$(x, y): J.

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Relationship between structure/morphology of dense and porous membranes and their separation characteristics. V2/2 is the contraction loss at the entrance of the pipe Ke. The kinetic theory provides estimates of the transport properties k, D, and p from molecular considerations. At time t = 0 the stopcock is opened, and diffusion begns; then the concentrations of A in the two well-stirred bulbs change. There are three forces acting on the sphere: the Stokes drag Fp, the buoyancy force FB, and the weight Fw: xF=Fp-l-FB+Fw=ma=o (12.69) where at steady-state the acceleration is zero.

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If 10 amperes of current pass through the rod. A block of metal (emissivity of 0.7"C.102 m in diameter and are set on 0. Transcripts: Applicants may upload unofficial transcripts with your application for the departmental initial review. For II,, Eq. (iii) becomes L”MbL-bB-b~cL-3cMdLde-3dT-dMee-3eT-e = dimensionless The equations are L: 0: M: T: O=a-b-3c+d 0=-b-3d-3e O=b+c+d+e 0=-d-e d=-e From Eq. (viii): b=-3d-3e=3e-3e=O From Eq. (ix): c=-b-d-e=e-e=O From Eq. (vii): a=b+3c-d=-d=e Thus I-I, = @do/k) or from Eq. (8.21) for the Nusselt number: l-I, = @do/k)’ = Nhu (x9 (xv) W) (xiii) (xii) (vii) (viii) (ix) (x) (4 (vi) These equations can be solved in terms of e.

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The transition will be assumed to occur at NRc.= equal to 5 x ld (for a typical flat plate), although this number can be lowered if a disturbance is introduced into the flow. Application for the department is available at www.engr.washington.edu/uapp. To have dynamic similarity, we must choose conditions such that Re, = ReI. A similar calculation using data from Appendix A.1 at 325 K and 330 K yields B/R= 1646 Thus, from Eq. (2.52): p(T = 53°C) = 3.336 x A = 3.336 x lo-* N s me2 x (vii) W8exp(1646/326.15) = 5.19 10e4 N s m-* (viii) = 0.519 CP These can be compared to handbook values of 0.01% and 0.523cP respectively at 53°C. 2.6 A COMPARISON OF THE TRANSPORTS At the beginning of this chapter a set of analogous equations for heat, mass, and momentum transfer was developed.

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Steam leaves the boilers at the highest pressure required by the process units or electrical generation. Show how to generalize Example 20.1-2 to flow systems, by using Eq. 20.4-26 for the two re- action-free zones. We would then observe the color moving from the point where the dissolution took place ( c = C O ) to the rest of the liquid ( c = 0). Class Work For a diffusion of solute A through a layer of gas to an absorbing liquid, we have: yA,1= 0.20 and yA,2= 0.10. 1) Compare the transfer rate NA between one-way diffusion and the equi-molar diffusion ( hint: calculate the ratio of the two fluxes) 2) What is the composition of A half way through the layer for one-way diffusion and equi-molar diffusion? 72.

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Visual studies have indicated the presence of secondary flow patterns in which fluid flows outward from the center of the tube to the top of the bend and then around the outside in a pair of loops, as sketched to the right in Fig. 10.6 [P3]. This result is correct for the limits Pr = 0.73 and Pr = and hence can include the evaporation of solvents in air. Select three parameters from the list of eight parameters. There can be heat generation through electrical means or nuclear reactions.

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Equation (F) for the L component has non-zero terms. A mixture of isobutane and n-butane is to be stripped (i.e., concentrate the isobutane). For momentum transfer, $I represents the rectangular vector components (pU,, pUY, or ~0,) when V is substituted for in the rectangular coordinate column. Show that the natural frequency of the system is o, = l/iTTI, in which I is the moment of inertia of the bob, and k is the spring constant for the torsion wire. (b) Next, apply Newton's second law when there is a fluid of viscosity p in the annular space.

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Applications to electrophoresis, filtration, floatation, sedimentation, and suspension rheology. Two dissimilar metals, such as copper and constantan, an alloy composed of 60 percent copper and 40 percent nickel, when in contact will generate a small potential difference that is a function of temperature. Assume the operation to be isothermal and isobaric. (c) Determine the interfacial conditions at each end of the column. (d) Determine the required tower height using Eq. 23.5-24 if k!a = 0.32 moles/hr. ft3, kia = 14.2 moles/hr. ft3, and the tower cross section S is 2.00 fi?. (e) Repeat part (d), using Eq. 23.5-25.