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Course: ME 353, Fall 2009
School: W. Alabama
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OF DEPARTMENT MECHANICAL ENGINEERING ME 353 HEAT TRANSFER 1 UNIVERSITY OF WATERLOO December 9, 1996 M.M. Yovanovich Time: 9-12 A.M. Three-hour Closed Book Final Examination. Two crib sheets both sides are permitted. All questions are of equal value. State clearly and justify all assumptions made and label all sketches and thermal circuits clearly. Allocate your time wisely and do not spend disproportionate...

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OF DEPARTMENT MECHANICAL ENGINEERING ME 353 HEAT TRANSFER 1 UNIVERSITY OF WATERLOO December 9, 1996 M.M. Yovanovich Time: 9-12 A.M. Three-hour Closed Book Final Examination. Two crib sheets both sides are permitted. All questions are of equal value. State clearly and justify all assumptions made and label all sketches and thermal circuits clearly. Allocate your time wisely and do not spend disproportionate time on any single problem. Good luck. PROBLEM 1 20 A reclay brick of dimensions 50 mm 80 mm 180 mm is removed from a kiln at the uniform temperature Ti = 1500 K , and it is cooled in air which is at the constant temperature Tf = 300 K . The heat transfer coe cient is assumed to be uniform over all six faces of the brick and its magnitude is 60 W=m2 K . The thermophysical properties of the brick are: k = 1:0 W=m K; = 2000 kg=m3; cp = 960 J=kg K . The cooling period is 60 minutes. a Can the lumped capacitance method be used to calculate the cooling rate? b Compute the temperature at the center of the brick after 60 minutes. c Which dimension of the brick controls the cooling process, and explain why? The rst term of the series solution for the dimensionless temperature excess within a plane wall is given by 2 = A1 exp , 1 Fo cos 1 where the Fourier coe cient is given by 2 A1 = + sinsin 1 1 cos 1 1 and the rst eigenvalue which is the root of the characteristic equation: 1 sin 1 = Bi cos 1 can be computed accurately by means of the following approximation: 1 =h 1+ 1;1= Bi 1;1 p n i1=n and 1;1 = =2 corresponding to Bi ! 1. The value of the exponent is n = 2:139. The dimensionless parameters are the Fourier number Fo, the dimensionless position within the plane wall 0 = x=L 1, and the Biot number Bi = hL=k where L is the half-thickness of the plane wall. ME 353 PROBLEM 2 20 HEAT TRANSFER 1 Page 2 A 50 , W incandescent bulb is placed in a large room and it is cooled by atmospheric air whose velocity is 0:5 m=s. Its surface temperature is measured to be 140 C and the air and surrounding temperatures are 25 C . The bulb can be modeled as a sphere of diameter 50 , mm. You are given the thermophysical properties of the air at the lm temperature: k = 0:0261 W=m K; = 15:71 10,6 m2=s; Pr = 0:71, and the following correlation equations for pure forced and pure natural convection from isothermal spheres: Rance and Marshall Correlation NuD = 2 + 0:6 Re1=2Pr1=3 D which is valid for Pr 0:7. Churchill Correlation NuD = 2 + F PrRa1=4 D where the Prandtl number function is de ned as 0:589 F Pr = h i4=9 1 + 0:469=Pr9=16 which is valid for Pr 0:7 and RaD 1011. These correlation equations are reported in the 4th edition of the text of Incropera and DeWitt. Use the air properties given above for both correlation equations. a Compute the heat transfer rate for pure forced convection QFC . b Compute the heat transfer rate pure for natural convection QNC . c Compute the maximum radiation heat transfer rate QRAD from the surface of the bulb to the surroundings. d Use the above results to estimate the conduction heat transfer rate QCOND from the bulb through its support. ME 353 PROBLEM 3 20 HEAT TRANSFER 1 Page 3 To determine air velocity uctuations, it is proposed to measure the electric current required to maintain a platinum wire of 0.6 mm diameter at a constant temperature of 1170 C in a stream of air at 370 C . The air properties at 350 K are: k = 0:0300 W=m K; cp = 1009 J=kg K; = 208:2 10,7 N s=m2; Pr = 0:700; = 0:9950 kg=m3. a Assuming Reynolds numbers in the range 40 ReD 4000, develop a relationship between the wire current and the velocity of the air which is in cross ow over the wire. b Calculate the current required when the air velocity is 30 m=s and the electrical resistivity of the platinum wire is 16:67 10,6 cm. You may use the empirical correlation due to Hilpert developed for long circular cylinders in cross ow: NuD = hD = CRem Pr1=3 D k f where the correlation coe cients C and m are given below: ReD 0.4 4 4 40 40 4000 4000 40,000 40,000 400,000 C 0.989 0.911 0.683 0.193 0.027 m 0.330 0.385 0.466 0.618 0.805 ME 353 PROBLEM 4 20 HEAT TRANSFER 1 Page 4 Air at 3 10,4 kg=s and 270 C enters a rectangular duct that is 1 m long and 4 mm by 16 mm in cross-section. A uniform heat ux of 600 W=m2 is imposed on the duct surface. The air properties are: k = 0:0263 W=m K; cp = 1007 J=kg K; = 184:6 10,7 N s=m2; Pr = 0:707. a Calculate the Reynolds for this system. b Calculate the air bulk temperature at the duct outlet by means of an overall energy balance. c Calculate the duct surface temperatu...

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W. Alabama - ME - 353
SUMTABLE.TEXME 353 HEAT TRANSFER I SUMMARY OF CONVECTION CORRELATION EQUATIONS Laminar and Turbulent Forced External Flow Flat Plate, Laminar Boundary Layer Flow= 5xRe,1=2 x Cf;x = 0:664Re,1=2 x f;x = 1:328Re,1=2 C x = Pr,1=3 Nux = 0:3387Pr1=3 Re
W. Alabama - ME - 353
UNIVERSITY OF WATERLOO DEPARTMENT OF MECHANICAL ENGINEERING ME 353 HEAT TRANSFER 1 October 25, 1991M.M. YovanovichTime: 4:30-6:30 p.m.Two-hour Closed Book Mid-term Examination. You are allowed one crib sheet both sides and the solutions to part
W. Alabama - ME - 353
WK13TPCSWEB.TEXME 353 M.M. YovanovichWeek 13Last lecture of the term. Hand in laboratory writeup to the teaching assistants. Ignore the problems for Chapter 11 which deals with Heat Exchanger Design. This topic will be covered in second heat tr
W. Alabama - ME - 353
WK12TPCSWEB.TEXME 353 M.M. YovanovichWeek 12Lecture 1See website for Maple worksheets for air properties correlation equations, and natural convection calculations. Natural convection across annular space bounded by two isothermal horizontal
W. Alabama - ME - 353
WK10TPCSWEB.TEXME 353 M.M. Yovanovich Week 10 Lecture 1Pick up material on Summary of Convection Correlation Equations. Forced External Convective Heat Transfer. Correlation equations for external natural convection: vertical at plate; horizontal
W. Alabama - ME - 353
WK6TPCSWEB.TEXME 353 M.M. YovanovichWeek 6Lecture 1Cancelled for midterm exam. Friday, October 23, 4:30-6:30 PM in CPH3374 3388.Lecture 2Cancelled for midterm exam.Lecture 3Cancelled for midterm exam.
East Los Angeles College - MATH - 1825
MATH1825 Statistics Through Applications Reading listUniversity of Leeds School of Mathematics Semester 2 20091. Baxter, P. D., (2008), MATH1825 Statistics Through Applications [Online], [Accessed on 10th August 2007], Available from World Wide W
W. Alabama - ME - 353
WK5TPCSWEB.TEXME 353 M.M. Yovanovich Week 5 Lecture 1 Lecture 2Monday, October 12 lecture cancelled for Thanksgiving Day. Resistance of truncated cone of length L, and radii a; b where b a with restriction: b , a=L 1. Thermal conductivity depends
East Los Angeles College - MATH - 3802
MATH3802 Time Series Outline Solutions to Worksheet 2University of Leeds School of Mathematics Semester 2 2009Solution to Question 1 R commands:&gt; births1=ts(scan(&quot;http:/www.maths.leeds.ac.uk/pdbaxt/math3802/births1.txt&quot;) Read 365 items &gt; ts.plot
W. Alabama - ME - 353
WK8TPCSWEB.TEXME 353 M.M. Yovanovich Week 8 Lecture 1Provide midterm results. Problem 3 of midterm will be re-submitted at start of next lecture. Outline of the solution procedure to be followed.Lecture 2Hand in Problem 3. Half-space solutions
East Los Angeles College - MATH - 1825
MATH1825: Lecture 7Two sample non parametric tests1Two sample problems Suppose that we have two samples of data and we are interested in comparing their averages to see if there is a large difference between them. The samples are small in size
W. Alabama - ME - 353
WK3TPCSWEB.TEXME 353 M.M. YovanovichWeek 3ME 353 Web Site: Summary of week 2 topics are on the Web. Contact resistance: Rc = 1=hc A; see Table 3.1 for typical values of Rt;c; how to get hc, contact conductance, from Table 3.1; hc = 1=Rt;c W=m2K
East Los Angeles College - MATH - 1825
MATH1825 Statistics Through Applications Solutions to ExercisesUniversity of Leeds School of Mathematics Semester 2 2009Solution to Question 1 (a) The mean, median and quartiles are produced using the summary command: summary(midsize) Min. 1st Qu
W. Alabama - ME - 353
RADCONDWEB.TEXME 353 M.M. YovanovichRadiative ConductanceThe radiative conductance is de ned asQ hrad = A T 12 T 1 1, 2The radiative exchange between two isothermal gray surfaces is obtained from 1 Q12 = EbR, Eb2 total where Eb1 = T14, Eb2 =
East Los Angeles College - MATH - 1825
MATH1825: Lecture 4Power and sample size for the one sample t-test1How large a sample is needed? Size of sample affects: ability to detect an effect if it is present; cost of obtaining the information. We seek the smallest sample that will a
W. Alabama - ME - 353
UNIVERSITY OF WATERLOO DEPARTMENT OF MECHANICAL ENGINEERING ME 353 HEAT TRANSFER 1 October 26, 1990 M.M. YovanovichTime: 7-9 p.m.Two-hour Closed Book Mid-term Examination. You are allowed one crib sheet both sides and the solutions to partial di
W. Alabama - ME - 353
POISSONWEB.TEXME 353 M.M. YovanovichGeneral Solution of Poisson Equation for Plane Wall, Long Solid Circular Cylinder and Solid SphereThe general Poisson equation r2T = ,P =k with appropriate boundary conditions, and the general solution which
W. Alabama - ME - 353
DEPARTMENT OF MECHANICAL ENGINEERING ME 353 HEAT TRANSFER 1UNIVERSITY OF WATERLOODecember 8, 1997 M.M. YovanovichTime: 2-5 P.M.Three-hour Closed Book Final Examination. Two crib sheets both sides are permitted. Calculator is allowed. All ques
East Los Angeles College - MATH - 1825
MATH1825: Lecture 6One sample non parametric tests1Making decisions What are the key issues in hypothesis testing? the population and its properties; the hypotheses being tested; the sample properties (e.g. size); the test assumptions.2
W. Alabama - ECE - 309
UNIVERSITY OF WATERLOO DEPARTMENT OF ELECTRICAL ENGINEERING ECE 309 Thermodynamics and Heat Transfer for Electrical Engineering Mid-Term Examination M.M. Yovanovich NOTE:1. Open book examination. You are permitted to use your calculator, the text bo
East Los Angeles College - MATH - 3802
MATH3802 Time Series Background 1 (introduction &amp; time series regression)University of Leeds School of Mathematics Semester 2 2009Types of time series Figure 1 shows that lynx numbers in years close together are similar.Lynx trapped0 182030
W. Alabama - ECE - 309
CONTWEB.TEXECE 309 M.M. YovanovichThermal Interface Joint Conductance and ResistanceDe nitionsThermal interface resistance occurs whenever two solids of di erent materials are brought together to form an interface. When there is steady heat tra
East Los Angeles College - MATH - 1825
MATH1825: Lecture 5Power and sample size for the two sample t-test1Two sample problems Suppose that we have two samples of data and we are interested in comparing their averages to see if there is a large difference between them. If the sample
W. Alabama - ME - 303
Laplace Transform M.M. YovanovichLAPLACE TRANSFORMThe Laplace transform of f x; t is de ned asL ff x; tg =and its inverse is de ned asZ01 ,st e f x; tdt = F x; ss 0L,1 fF x; sg =1 2iZ c+i1c,i1F x; sest ds = f x; tSummary of L
W. Alabama - ME - 303
WK1TPCSWEB.TEXME 303 M.M. Yovanovich Week 1 Lecture 1Information: Instructor: M.M. Yovanovich, CPH 3375C X3588, E3-2133A, X6181 or X4586 email: mmyov@mhtl.uwaterloo.ca Teaching Assistants: Rabih Alkhatib, CIM 2705, X3639; email: rfalkhat@engmail.u
W. Alabama - ME - 303
PROJ1S99SOL.TEXUNIVERSITY OF WATERLOO Department of Mechanical Engineering ME 303 Advanced Engineering Mathematics M.M. Yovanovich Project 1 Solution, June 4, 1999Given the linear, second order nonhomogeneous PDE: ! 1 @ r @T + S = 1 @T ; t 0; 0 r
W. Alabama - ME - 303
WK6TPCSWEB.TEXME 303 M.M. YovanovichWeek 6Lecture 1Midterm week. Lecture cancelled.Lecture 2Midterm week. Lecture cancelled.Lecture 3Midterm week. Lecture cancelled.
W. Alabama - ME - 303
WK13TPCSWEB.TEXME 303 M.M. YovanovichWeek 13Lecture 1Sturm-Liouville Problem. This material is usually covered in an ODE Course. See Spiegel's Text, Chapter 8, Section 2 See ME 303 Web site for Note on Sturm-Liouville Problem This proves the
W. Alabama - ME - 303
WK5TPCSWEB.TEXME 303 M.M. YovanovichWeek 5Lecture 1Sturm-Liouville Problem SLP Cartesian Coordinates. u = ux; y or u = ux; t. Partial di erential equations.uxx + uyy = 0; 0 x L; 0 y H 1D Di usion Equation: uxx = 1 ut; t 0; 0 x L 1D Wave Equ
W. Alabama - ME - 303
WK9TPCSWEB.TEXME 303 M.M. YovanovichWeek 9Lecture 1Lecture cancelled.Lecture 2Lecture cancelled.Lecture 3Lecture cancelled.
W. Alabama - ME - 303
WK8TPCSWEB.TEXME 303 M.M. YovanovichWeek 8Lecture 1Section 1.2: 1D Di usion equation Heat equation with homogeneous Neumann BCs. Section 1.3: 2D Laplace equation conduction problem in a semi-in nite plate with homogeneous Dirichlet BCs. Demons
W. Alabama - ME - 303
WK2TPCSWEB.TEXME 303 M.M. YovanovichWeek 2Lecture 1Hand out Problem Set 1. ODEs in cartesian, polar and spherical coordinates; TAs will discuss some solutions in the tutorials. Discuss how to obtain solution of homogeneous ODE in spherical co
W. Alabama - ME - 303
WK7TPCSWEB.TEXME 303 M.M. YovanovichWeek 7Lecture 1Return Project 1 Return Midterm Exam Exam and its solution are posted on Web site Examination Statistics Table 1: Midterm Exam Summary Q1 Q2 Q3 Exam Max. 30 40 30 98 Min. 8 8 10 46 Avg. 24.5
W. Alabama - ME - 303
WKxTPCSWEB.TEXME 303 M.M. YovanovichWeek 10Lecture 1Discussed the physics of the problem of Project 2. Used Maple to show the temperature plots as a function of dimensionless time. Solution procedure is based on the material covered in Sectio
Neumont - IFT - 3820
W. Alabama - ME - 303
WK12TPCSWEB.TEXME 303 M.M. Yovanovich Week 12 Lecture 1Solution of ODEd + m = n; t 0; IC 0 = i dt where t = T t , T1, and the constants are: m = hA and n = qciA cpV pV where A = surface area, V = volume, qi = incident heat ux. Units are: h W=m
W. Alabama - ME - 303
WK3TPCSWEB.TEXME 303 M.M. YovanovichWeek 3Lecture 1Vibrating String and Membranes Rectangular and Circular. The 1-D wave equation for the string in cartesian coordinates is uxx = c12 utt; t 0; 0 x L It can be modi ed to include vibrations of
W. Alabama - ME - 303
ME 303 Advanced Engineering MathematicsSYMBOLIC MATHEMATICSSymbolic mathematics software packages have been developed over the past 25 years. The best known packages are MACSYMA, MAPLE, MATHEMATICA, MATHCAD, MATHSCRIBE, MuMATH,and DERIVE, REDUCE, S
W. Alabama - ME - 303
LPTTABLE.TEXME 303 Advanced Engineering MathematicsTable of Laplace Transforms Some inverse Laplace transforms for solutions of the one-dimensional di usion equation.F sp e,a s ;f t a01 e,aps; a 0 s 1 ps e,apspa 3 exp, at 4 2 t ! a er
Allan Hancock College - COMP - 3101
Objective of Subject COMP3101 Digital System Design IDr Adam Postula 47-313 Dr Mark Schulz 47-309 adam@itee.uq.edu.au marks@itee.uq.edu.au You will be able to design a small digital system for to the specified functionality . You will be able to use
W. Alabama - ME - 303
CLASSIFICATION OF LINEAR PDEs OF SECOND ORDERSecond order linear PDEs with two independent variables x; y have the general form:Au + Bu + Cu + Du + Eu + Fu = Gxx xy yy x ywhere the coe cients A; B; C; D; E; F; and G are functions of x and y or
W. Alabama - ME - 303
STURMLIOUVILLEPROB.TEXSTURM-LIOUVILLE PROBLEM SLPThe separation of variables method when applied to second-order linear homogeneous PDEs frequently leads to second-order homogeneous ODEs of the type:d px dyx + qx + rx yx = 0; dx dx or in the equ
W. Alabama - ME - 303
ME 303 Advanced Engineering Mathematics Nondimensional Di usion Equation Boundary Conditions and Initial ConditionM.M. YovanovichDIMENSIONLESS PDE, BCs and ICTo illustrate how a Partial Di erential Equation PDE, and its Boundary Conditions BCs an
W. Alabama - ME - 303
ME 303 Advanced Engineering MathematicsM.M. YovanovichOrdinary Di erential Equations in Spherical CoordinatesWhen certain partial di erential equations formulated in spherical coordinates are separated by the separation of variables method, or th
W. Alabama - ME - 303
ME 303 Advanced Engineering Mathematics Fourier Cosine and Sine SeriesM.M. YovanovichFourier series. The Fourier series of a periodic function f x with period 2Lis de ned as the trigonometric series1 X 1 nx + X B sin nx f x = A0 + An cos L n
W. Alabama - ECE - 309
LUMPWEB.TEXECE 309 M.M. YovanovichLumped Capacitance Model With Ohmic HeatingLumped capacitance model valid for Bi 0:2 for a system long constant cross-section wire which has uniformly distributed heat sources due to ohmic heating, and convectiv
W. Alabama - ECE - 309
30996FESOL.TEXUNIVERSITY OF WATERLOODEPARTMENT OF ELECTRICAL ENGINEERING ECE 309 Thermodynamics Electrical EngineeringFinal Examination Solutions M.M. Yovanovich Problem 1Spring 1996 August 8, 1996 2:00 - 5:00 P.M.Incompressible liquid. 1a a
W. Alabama - ECE - 309
RADEXCHGWEB.TEXECE 309 M.M. YovanovichRadiation Exchange Between Black and Gray SurfacesWhen radiation leaves a black convex surface whose area is A1 at absolute temperature T1, a certain fraction F12 will be absorbed by a second convex surface
W. Alabama - ECE - 309
DEPARTMENT OF ELECTRICAL ENGINEERING ECE 309 Thermodynamics Electrical EngineeringUNIVERSITY OF WATERLOOMid-Term Examination M.M. Yovanovich NOTE:Spring 1996 June 22, 1996 9:00-11:00 A.M.1. Open book examination. You are permitted to use your
W. Alabama - ECE - 309
RADLAWSWEB.TEXECE 309 M.M. YovanovichRadiation LawsPlanck's Distribution LawThe relation for the spectral blackbody emissive power Eb was developed by Planck 1901. The relation is known as Planck's distribution law, and it is expressed asWien
W. Alabama - ECE - 309
HEATWEB.TEXHeat Transfer Relationships Conduction, Convection and Radiation Laws of Heat Transfer Fourier's Law of Conduction _ Q = ,k rTA Newton's Law of Cooling _ Q = hATwall , T uid Stefan-Boltzmann Law of Radiation for Black Bodies _ Q = A1T14
W. Alabama - ECE - 309
USUFWEB.TEXECE 309 M.M. YovanovichUniform-State, Uniform-Flow Process USUFThe following assumptions lead to a useful model called the uniformstate, uniform- ow process USUF. The control volume is stationary relative to some coordinate frame. The
W. Alabama - ECE - 309
REVIRR WEB.TEXECE 309 M.M. YovanovichReversible and Irreversible ProcessesReversible ProcessesThe following processes are frequently idealized as reversible processes. Restrained compression and expansion Frictionless motion Elastic extension
W. Alabama - ECE - 309
PROCESWEB.TEXECE 309 M.M. YovanovichTypes of ProcessesA xed mass simple compressible substance system can undergo di erent types of processes between state 1 and state 2: Some types are given below:Isothermal process - constant temperature = I
W. Alabama - ECE - 309
GIBBS EQUATIONThe Gibbs equation for a simple compressible substance SCS comes from: = . The di erential change in the speci c entropy is: ! ! = + v u Introducing the thermodynamic de nitions of temperature and pressure: 1 = ! v and ! = u we obt
W. Alabama - ECE - 309
PRANDTLWEB.TEXECE 309 M.M. YovanovichTypical Ranges of Prandtl Numbers for Selected FluidsThe Prandtl number is a dimensionless group de ned as Pr = molecular di usion of momentum = = Cp molecular di usion of heat kFluidPrLiquid metals 0:0
W. Alabama - ECE - 309
SYSTEMWEB.TEXECE 309 M.M. YovanovichThermodynamic Systems De nitionA thermodynamic system is a de nite quantity of matter occupying a volume which is bounded by a closed surface which is impervious to the ow of matter. The surface is called the
W. Alabama - ECE - 309
TEMPWEB.TEXECE 309 M.M. YovanovichTemperature Scales and ConversionsThere are four thermodynamic temperature scales: Celsius, Fahrenheit, Kelvin, Rankine. The Kelvin and Rankine temperature scales are absolute scales. The relations and conversio
W. Alabama - ECE - 309
ZEROWEB.TEXECE 309 M.M. YovanovichZeroth Law of ThermodynamicsWhen two bodies A and B are in thermal equilbrium with a third body C: TA = TC and TB = TC then the two bodies also have equality of temperature:TA = TB
W. Alabama - ECE - 309
CONVWEB.TEXECE 309 M.M. YovanovichTypical Ranges of Convective Heat Transfer Coe cients Type of ConvectionFree convection of gases Free convection of liquids Forced convection of gases Forced convection of liquids Boiling and condensation h;W=
W. Alabama - ECE - 309
WK12TPCSWEB.TEXECE 309 M.M. YovanovichWeek 12 Lecture 1Final Exam will be open book. Discussed this with Prof. Wilson. Entropy and the Second Law of Thermodynamics SLOT Read Chapter 6: Sections 1 through 5. See ECE 309 Web site for notes on Ent