 # Transport Phenomena Questions

## Transcribed Text

1.) (1 point) We discussed in class that Newtoniar fluids have a shear stress (z) that is a linear function of the shear rate (Y) with the proportionality constant termed the viscosity Examples of common Newtonian fluids are water, gases, and most organic solvents However, many fluids do not follow Newtonian behavior A.) Bingham plastic/fluid Newtonian fluid that has a yield stress To For all the fluid does not flow. but flows with constant viscosity for all other stress T B. Ostwald de Waele model can describe shear thickening (Dilatant) or shear thinning (Pseudoplastic), where T= -k(Iy))-1(y) where behavior is dilatant if n)1 and pseudoplastic if n<1 C.) Viscoeleastic fluids that undergo creep demonstrate that the stress is held constant, strain increases with time, as described by: where Yis Young's modulus. Likewise, if the strain is held constant, the stress decreases with time (relaxation) For the fluids describe in A and B above, give some common examples and plot the shear stress, as function of shear rate. Include a Newtonian fluid in your plot as well, for reference. For Part C. plot the stress strain curves for purely elastic material and a viscoelastic material. What is the result of deformation in terms of energy for the viscoelastic material? 2.) (1 point) Below is data set of brand of mayonnaise, which uses modified starches and xanthan gum to stabilize the water and oil emulsion. Note for reference, the effective or apparent viscosity (pett), can be described as function of the shear rate: du Veff dx Data was taken from Donatella, P et al Food Eng 35, 409, 1998 A.) Plot the data and discuss whether the mayonnaise is shear- thinning or shear thickening fluid (as described by Problem 1B above) B. Determine the exponent and the flow consistency index (K) by fitting the data to power law expression Apparent Shear Rate (1/s) Apparent Shear Rate Viscosity (Pa s) Viscosity (Pa s) (1/s) 0.396 249 096 2.207 51.413 0.598 167.090 2.413 47.971 0.790 133.307 2.580 44.767 0.988 108.264 2.790 41.064 1.194 91.034 3.017 38.983 1.412 77.892 3.227 37.010 1.596 67.828 3.450 35.138 1.805 61.132 3.649 33.363 1.996 55.107 3.859 31.678 2.207 51.413 4.080 30.078 3.) (1 point) A slab of uniform thickness (d 50cm) with an initial temper ature of 293K is placed in a furnace. At 500 after being placed in the furnace, the temperature gradient can be described as T(x) +bx +cx² where a b. and are constants, and is the distance from the centerline of the slab A.) Solve for the constants in terms of the surface (Ts) and centerline (TO) temperature. B.) Solve for the heat flux as a function of if Ts 750K and To 293K. 4.) (1 point) For metals and semiconductors. the thermal conductivity is dependent upon two mechanisms. energy transfer by lattice vibrations (phonon conduction) and energy transfer by the motion of free electrons in the conduction band. Because phonon transport is independent of energy transport by the motion of free electrons, the overall thermal conductivity of metallic solid can be written as the sum of contributions fromphonon and electron transport k = kph ke The Wiedemann Franz law states that the thermal conductivity ke can be related to the electrical conductivity by: For the following materials and measured conductivities, calculate the electronic (ke. W/mK) and phonon (kph W/mK) contributions to total thermal conductivity at 300K. Remember, conductivities cannot be negative. What can you say about dominant factors in metals? What about semiconductors (such as Si)? Material Net Thermal Electronic Conductivity Conductivity (W/mK) at (a, S/m) 300K 300K Copper 401 5.80x107 Gold 317 4.10x107 Nickel 90.7 1.28x107 Mercury 8.69 1.04x106 Silicon 148 1000 5.) (1 point) Inphotovoltaics, contributions to photocurrent can arise from both drift (mobile charges under an electric field) and diffusion of photogenerated carriers: dn ] anne qD dx where is the charge of an electron, is the mobility, Eis the internal electric field, D is the diffusion coefficient, and in is the carrier density. For nanoparticle devices mobilities are on the order of 10-¹ to 10-4 cm2/Vs, depending on the ligand length used Calculate the drift current contribution for film of nanoparticles with a mobility of 5x10³ cm2/Vs at internal fields of 0.1, 0.5, and V. for film of 100 nm thick and 0. cm² area. for white light intensity that generates 1017 e-/cm³. Determine the diffusion coefficient. When do you anticipate drift currents will dominate? What about diffusion currents?

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Question 1)
Classic example of Newtonian fluid is water (it flows easily).
(A) Classic example of plastic (Bingham) fluid is tooth paste (it stays on the toothbrush and preserve its shape so it is “plastic”)....
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