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Chapter_6_Homework

# Chapter_6_Homework - The liquid and plates are initially at...

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Chapter 6: Partial Differential Equations Homework Assignment I. Rework Example 6.1, part (c) (pp. 382-395, in text) using a thin square plate of dimensions (0.20 m × 0.20 m). This is the microprocessor chip in your computer. The microprocessor is subject to an electric current that creates a uniform heat source within the plate. Use the same thermal conductivity, 16 W/m.K, and the same heat generated Q'=100,000 W/m 3 . All four edges of the plate are in contact with air at 25 ° C. The set of Robbins boundary conditions are given in the text (p. 383). Examine the temperature profile within the plate. What is the maximum temperature reached and at what point in the plate? Why is the maximum temperature different than the one on Figure E6.1d (p. 395)? Make sure you use the latest version of Example6_1.m and elliptic.m (download these from http://sol.rutgers.edu/~constant ). II. Examine the unsteady-state flow of a liquid between two moving plates that are 1 m apart.
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Unformatted text preview: The liquid and plates are initially at rest. At t ≥ 0, the bottom plate begins to move with a velocity of 1.5 m/s in the x-direction, and the top plate moves with a velocity of 1 m/s. No pressure gradient is applied on the fluid. Compare the velocity profiles for the following four liquids, and explain why the profiles are different: a) Water: viscosity = 0.001 kg/m.s b) Tallow: viscosity = 0.01 kg/m.s c) Olive oil: viscosity = 0.1 kg/m.s d) Glycerol: viscosity = 1 kg/m.s For simplicity, assume that all liquids have the same density: (1000 kg/m 3 ) and that they are all Newtonian fluids. Integrate the differential equation to t = 2,000 s. Use the program fluid_flow.m (download from http://sol.rutgers.edu/~constant ). III. Solve problem 6.7 (p. 439, text). Do part (c) using pdetool (in MATLAB 7.1 in C-233). Print a contour plot and a 3-D plot of your results showing the displacement of the membrane above the horizontal plane. y x 1 m...
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