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
B. Ostwald de Waele model can describe shear thickening (Dilatant) or shear
thinning (Pseudoplastic), where
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
viscoelastic material. What is the result of deformation in terms of energy for the
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:
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
Shear Rate (1/s)
Viscosity (Pa s)
Viscosity (Pa s)
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)
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)?
Conductivity (W/mK) at
(a, S/m) 300K
5.) (1 point) Inphotovoltaics, contributions to photocurrent can arise from both drift
(mobile charges under an electric field) and diffusion of photogenerated carriers:
] anne qD
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
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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”)....