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### hw12

Course: ME 3333, Spring 2012
School: University of Minnesota...
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Word Count: 342

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Sciences Thermal III, Spring Semester 2011 Instructor: Teaching assistants: Prof. Wojciech Lipiski Marc Dunham Krithiga Ganesan Vivek Ghosh HOMEWORK 12 Due to May 5, 2011 Problem 1 The spectral distribution of the radiation emitted by a diuse surface may be approximated as shown in Fig. 1. Figure 1 Questions: (a) Calculate the total hemispherical emissive power. (b) Calculate the total intensity of the...

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Sciences Thermal III, Spring Semester 2011 Instructor: Teaching assistants: Prof. Wojciech Lipiski Marc Dunham Krithiga Ganesan Vivek Ghosh HOMEWORK 12 Due to May 5, 2011 Problem 1 The spectral distribution of the radiation emitted by a diuse surface may be approximated as shown in Fig. 1. Figure 1 Questions: (a) Calculate the total hemispherical emissive power. (b) Calculate the total intensity of the radiation emitted in the normal direction. (c) Calculate the total intensity of the radiation emitted at an angle of 45 from the normal. (d) Determine the fraction of the emissive power leaving the surface in the directions 30 60 . Problem 2 A diuse and opaque surface at 1000 K has spectral emissivities of = 0 for 0 2 m, = 0.6 for 2 m 8 m, and = 0.8 for 8 m . A radiative ux of 1000 W m2 , which is uniformly distributed between 1 and 6 m, is incident on the surface at an angle of 30 (Fig. 2). Radiation leaving the surface is acquired by a detector. The aperture of the detector is 105 m2 , and its distance from the surface is 1 m. Consider a surface element of area 104 m2 that is positioned on-axis the with detector. Question: Calculate the total radiative power from the surface element that reaches the detector aperture. Thermal Sciences III, Spring Semester 2011 Figure 2 Problem 3 An isothermal, diuse-gray, and innitely long equilateral-triangle bar of side a is enclosed by an isothermal, diuse-gray, and innitely long square duct of side 2a. The temperatures and emissivities of the bar and the duct are, respectively, T1 = 2900 K, 1 = 0.7, and T2 = 500 K, = 0.9. Assume uniform radiative heat uxes on each surface. Questions: (a) Derive all view factors Fij , where i, j = 1, 2. (b) Sketch the radiation network. (c) Calculate the net radiative heat transfer rate per unit length of the enclosure from the bar to the duct. Problem 4 Consider enclosures shown in Fig. 3. Figure 3 Questions: Calculate the view factors F12 and F21 for: (a) a sphere of diameter D inside a cubical box of side L = D (three-dimensional geometry), (b) a diagonal partition with a long square duct (two-dimensional geometry), (c) two concentric spheres of diameters D1 and D2 = 10D1 (three-dimensional geometry).
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University of Minnesota Crookston - ME - 3333
Thermal Sciences III, Spring Semester 2011Instructor:Teaching assistants:Prof. Wojciech LipiskiMarc DunhamKrithiga GanesanVivek GhoshSOLUTION TO HOMEWORK 4Problem 1Known:Diameter and thermophysical properties of alumina particles. Convection con
University of Minnesota Crookston - ME - 3333
Thermal Sciences III, Spring Semester 2011Instructor:Teaching assistants:Prof. Wojciech LipiskiMarc DunhamKrithiga GanesanVivek GhoshSOLUTION TO HOMEWORK 5Problem 1Known:Wire geometry, velocity of crossow, wire and ow temperatures, and Nusselt c
University of Minnesota Crookston - ME - 3333
Thermal Sciences III, Spring Semester 2011Instructor:Teaching assistants:Prof. Wojciech LipiskiMarc DunhamKrithiga GanesanVivek GhoshSOLUTION TO HOMEWORK 6Problem 1Known:Engine oil ows on the upper surface of a at plate. Surface and free-stream
University of Minnesota Crookston - ME - 3333
Thermal Sciences III, Spring Semester 2011Instructor:Teaching assistants:Prof. Wojciech LipiskiMarc DunhamKrithiga GanesanVivek GhoshSOLUTION TO HOMEWORK 7Problem 1Known:A tube bank 5 rows deep and and 15 rows wide. Upstream ow velocity and temp
University of Minnesota Crookston - ME - 3333
Thermal Sciences III, Spring Semester 2011Instructor:Prof. Wojciech LipiskiTeaching assistants: Marc DunhamKrithiga GanesanVivek GhoshSOLUTION TO HOMEWORK 8Problem 1Known:A plate heater dissipates constant power of 1500 W. The plate width and max
University of Minnesota Crookston - ME - 3333
Thermal Sciences III, Spring Semester 2011Instructor:Teaching assistants:Prof. Wojciech LipiskiMarc DunhamKrithiga GanesanVivek GhoshSOLUTION TO HOMEWORK 9Problem 1Known:A steel tube transfers heat from a hot gas to cold water owing inside the t
University of Minnesota Crookston - ME - 3333
Thermal Sciences III, Spring Semester 2011Instructor:Teaching assistants:Prof. Wojciech LipiskiMarc DunhamKrithiga GanesanVivek GhoshSOLUTION TO HOMEWORK 10Problem 1Given:A shell and tube heat exchanger consisting of one shell and one pass of ft
University of Minnesota Crookston - ME - 3333
Thermal Sciences III, Spring Semester 2011Instructor:Teaching assistants:Prof. Wojciech LipiskiMarc DunhamKrithiga GanesanVivek GhoshSOLUTION TO HOMEWORK 11Problem 1Find:Boiling curve for water at 1 atm, showing all boiling regimes and character
University of Minnesota Crookston - ME - 3333
Thermal Sciences III, Spring Semester 2011Instructor:Teaching assistants:Prof. Wojciech LipiskiMarc DunhamKrithiga GanesanVivek GhoshSOLUTION TO HOMEWORK 12Problem 1Find:(a) Total emissive power E .(b) Total intensity associated with directions
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
ME3281 Spring 2010 - Final ExamTuesday May 11th. 5:45-7:45pmRoom ME 102 (different room than regular classroom)The exam will cover everything learned in ME3281. Suggested Topics for Review:Power variables in Mechanical Translating, Mechanical Rotating
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
Feb 9 2010ME 3281 Spring 2010PROBLEM SET 54.20Wilson Santiago
University of Minnesota Crookston - ME - 3281
Feb 9 2010ME 3281 Spring 2010PROBLEM SET 6Wilson SantiagoFeb 9 2010ME 3281 Spring 2010Wilson SantiagoFeb 9 2010ME 3281 Spring 2010Wilson SantiagoFeb 9 2010ME 3281 Spring 2010Wilson Santiago
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
Mar22010me3281spring2010ProblemSet10Mar22010me3281spring2010Mar22010me3281spring2010
University of Minnesota Crookston - ME - 3281
7.24
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
s=tf('s');H1 = (s-1)/(s+1);subplot(321)bode(H1);grid onsubplot(322)pzmap(H1);grid onH2 = (s+1)*(s+1)/s/(s+5);subplot(323)bode(H2);grid onsubplot(324)pzmap(H2);grid onH3 = s/(s*s+.2*s+100)/(s*s+.2*s+100);subplot(325)bode(H3);grid onsubplot(32
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
March292010me3281spring2010WilsonSantiagoMarch292010me3281spring2010WilsonSantiago
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
University of Minnesota Crookston - ME - 3281
April132010me3281spring2010WilsonSantiagoApril132010me3281spring2010WilsonSantiagoApril132010me3281spring2010WilsonSantiago
University of Minnesota Crookston - ME - 3281
GivenJ_loadGear RatioOn time0.1341 lb*in*s^2 Load Revs4Motor Revs0.25 secMotor Revs312 revolutions75.4 radiansMotor Propertiesmotor642643644721722J loadreflected J totalJ totalT peak T peakW max WeightJ rotorlb*in*s^2 lb*in*s^2 lb
University of Minnesota Crookston - ME - 3281
Obtain a root-locus plot for KF ( s ) =14.24 a)K.( s + 1)( s + 6 2 j ) s + 6 + 2 jSolution:&gt; rlocus(zpk([],[-1, -6+2*i, -6-2*i],[1])Root Locus1510Imaginary Axis50-5-10-15- 18-16-14-12-10-8Real Axis-6-4-202Obtain a root-locus pl
University of Minnesota Crookston - ME - 3281
April272010spring2010me3281PROBLEMSET22SOLUTIONSApril272010spring2010me3281April272010spring2010me3281April272010spring2010me3281April272010spring2010me3281April272010spring2010me3281April272010spring2010me3281c)DrawrootlocusandverifytheCLp
Oakland University - MTH - 122
MTH 122: SI WorksheetAverage Rate of ChangeThe Average Rate of Change of f over the interval [a, b] isf (b)f (a)baThe Average Rate of Change of f over the interval [a, a + h] isf (a + h ) f (a )a+ ha=f ( a + h ) f (a )h1. Calculate the average
Oakland University - MTH - 122
MTH 122 HandoutInstantaneous Rate of Change: An Algebraic Viewpoint1. Compute the derivative of the function f (x) = 2x2 + x algebraically. Use your resultto nd f (2).2. Compute the derivative of the function f (x) =f (5).2xalgebraically. Use your
Oakland University - MTH - 122
MTH 122 SI WorksheetApplications of the Derivative1. Daily oil imports to the United States from Mexico can be approximated byI (t) = 0.015t2 + 0.1t + 1.4 million barrels (0 t 8)where t is time in years since the start of 2000. Find the derivative fun
Oakland University - MTH - 122
Oakland University - MTH - 122
Oakland University - MTH - 122
FINAL EXAMMTH 122Print Name CLEARLYWinter, 2011Student Number (last 3 digits)April 22, 2011SignatureShow all work. Put answers in the spaces provided for them. Correct answers not supported bycorrect and complete work may not receive full credit.
Oakland University - MTH - 122
Oakland University - MTH - 122
Oakland University - MTH - 122
MTH 122: SI WorksheetDerivatives of Powers, Sums, and Constant MultiplesThings to know:If n is any constant and f (x) = xn , then f (x) = nxn1 .as y = xn before attempting to nd its derivative.Rewrite a function of the form y =1xnRewrite a functio
Oakland University - MTH - 122
MTH 122Practice ExamShow all work for full credit. Correct answers not supported by correct work/justicationwill receive little or no credit.1. Find the derivative of each function.a) f (x) = ln(3x1)22x+5b) y = x2 e73xc) y = x4 x2 +1204x+112
Oakland University - MTH - 122
MTH 122: SI Practice ExamExam 11. Compute the average rate of change of the function f (x) = 4x2 [1, 4]. Simplify your answer.1xover the interval2. Compute the derivatives of the function g (x) = 2x2 + 3x using the denition of thederivative.13.
Oakland University - MTH - 122
Oakland University - MTH - 122
MTH 122: SI WorksheetIndenite Integral/ AntiderivativeThe notationf (x)dx is traditionally used for an antiderivative of f and is called anindenite integral.Sof (x)dx = F (x) + C means F (x) = f (x) .You can check that you found the antiderivative
Oakland University - MTH - 122
MTH 122 SI WorksheetLHospitals RuleThings to know and think about:If f and g are dierentiable functions such that substituting x = a into the expressiongives the indeterminate form00or,f ( x)g ( x)thenf (x)f (x)= limxa g (x)xa g (x)limLH
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870
Western Michigan - ECON - 3870