# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

80 Pages

### wk9tpcs

Course: ME 353, Fall 2009
School: W. Alabama
Rating:

Word Count: 879

#### Document Preview

353 WK9TPCSWEB.TEX ME M.M. Yovanovich Week 9 Makeup lecture 3. Week 8 lecture summary and several pages of summary of convective heat transfer correlations are available in Engineering Photocopy Center. Pick up and bring to future lectures. See Appendices for special functions. Table B.2 on page 857 for erf w and 0 w 3. Table B.5 on page 860 for modi ed Bessel functions: I0x; I1x; K0x; K1 x for 0 x 10. The...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Alabama >> W. Alabama >> ME 353

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
353 WK9TPCSWEB.TEX ME M.M. Yovanovich Week 9 Makeup lecture 3. Week 8 lecture summary and several pages of summary of convective heat transfer correlations are available in Engineering Photocopy Center. Pick up and bring to future lectures. See Appendices for special functions. Table B.2 on page 857 for erf w and 0 w 3. Table B.5 on page 860 for modi ed Bessel functions: I0x; I1x; K0x; K1 x for 0 x 10. The rst ve roots of characteristic equation for plane wall n sin n = Bi cos n for a range of values of the Biot number. See Maple worksheets on ME 353 Web site how to calculate Bessel functions, and to obtain the roots of the characteristic equations for plane wall, long circular cylinder and solid sphere. Multidimensional systems: i nite circular cylinder with side cooling and end cooling, ii rectangular plate, and iii cuboid parallelopiped. See Section 5.8. Finite circular cylinder of diameter D and length 2L. Temperature excess depends on r; z; t. There are two sets of Biot and Fourier numbers: Bi1 = h1 L=k; F o1 = t=L2 and Bi2 = h2 D=2=k; F o1 = t=D=22 . Here the subscripts 1; 2 denote cooling at two ends and side respectively. Dimensionless temperature excess is obtained from the plane wall and long circular cylinder solutions: ! ! ! = i cp i c i p Lecture 2 Lecture 1 and heat loss fraction is obtained from ! ! ! ! ! Q Q Q Q Q = Q + Q , Q Q Qi cp i c i p i c i p and Qi = cpD=22 2L i. Rectangular plate of dimensions: 2L1 ; 2L2; 2L3 corresponding to the x; y; zcoordinates respectively. The dimension 2L3 2L1 and 2L2 . Heat transfer coe cients are h1 on the L2L3-surfaces and h2 on the L1L3-surfaces. The surfaces perpendicular to the z,coordinate are adiabatic. The two sets of Biot and Fourier numbers are: Bi1 = h1L1=k; F o1 = t=L2 and Bi2 = h2L2=k; F o2 = 1 t=L2 . 2 Dimensionless temperature excess which depends on x; y; t is obtained from the plane wall solution applied twice: ! ! ! = i p1 p2 i p1 i p2 and heat loss fraction is obtained from ! ! ! ! ! Q Q Q Q Q = Q + Q , Q Q Qi p1 p2 i p1 i p2 i p1 i p2 and Qi = cp2L12L22L3 i. See example 5.6 transient conduction in nite cylinder and Maple worksheets on ME 353 Web site. Cuboid of dimensions: 2L1 ; 2L2; 2L3 corresponding to the x; y; z-coordinates respectively. Heat transfer coe cients are h1 on the L2L3-surfaces, h2 on the L1 L3 -surfaces, and h3 on the L1 L2 -surfaces. The three sets of Biot and Fourier numbers are: Bi1 = h1L1=k; F o1 = t=L2 , Bi2 = h2L2=k; F o2 = t=L2 and 1 2 Bi3 = h3 L3 =k; F o3 = t=L2 . 3 Dimensionless excess temperature which depends on x; y; z; t is obtained from the plane wall solution applied three times: ! ! ! ! = i p1 p2 p3 i p1 i p2 i p3 and heat loss fraction is obtained from ! ! 2 ! 3 ! 2 ! 32 ! 3 ! Q Q Q Q Q Q Q = Q + Q 41 , Q 5+ Q 41 , Q 5 41 , Q 5 Qi p1 p2 p3 i p1 i p2 i p1 i p3 i p1 i p2 and Qi = cp2L12L22L3 i. Approximations of Bessel functions J0x; J1x based on trapezoidal rule applied to integral forms of the Bessel functions. Also see B.4, page 859 for 2 short tables of J0x; J1x for 0 x 2:4. The following relations are based on 4 panels: ! 1 + 1 cos p + 1 cosx x J0x = 4 2 4 2 and ! ! 1 sin p + + 1 sinx , 1 cos p + x x J1x = 4 4 4 2 4 2 4 These approximations can be used in the single term approximate solutions for long cylinders. Lecture 3 Convective Heat Transfer. The four chapters which deal with this topic are: Chapter 6: Review of uid mechanics and de nitions. Chapter 7: External forced convection. Chapter 7: Internal forced convection. Chapter 8: External and internal natural convection. Convective heat transfer analysis is complex because, in general, one must solve 6 equations simultaneously to nd the three velocity components: u; v; w, the temperature T and the pressure: P . The six equations are: Continuity equation 1 Momentum equations 3 Energy equation 1 Equation of state 1 Correlation equations are based on i approximate analytical solutions, ii experiments and iii numerical solutions. The correlation equations relate the Nusselt number to other dime...

Textbooks related to the document above:
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

W. Alabama - ME - 353
WK7TPCSWEB.TEXME 353 M.M. YovanovichWeek 7Lecture 1Read Chapter 5: Sections 5.1 - 5.8. Lumped Capacitance Model LCM Bi = hL=k 0:2; T ~; t = T t r System parameters: _ _ V; S; ; cP ; k; ; h; Ti; Tf ; Tsurr; qin; Egen; Estorage; Qconv; Qrad Ene
W. Alabama - ME - 353
WKxTPCSWEB.TEXME 353 M.M. YovanovichWeek 11ME 353 Heat Transfer Lab begins on Monday. See signup sheet. Forced internal laminar and turbulent convection in circular and noncircular tubes, pipes and ducts. See handout for de nitions of local and
W. Alabama - ME - 353
WK1TPCSWEB.TEXME 353 M.M. Yovanovich Week 1 Lecture 1Information provided: Instructor: M.M. Yovanovich, CPH 3375C X3588, E3-2133A, X6181 or X4586 email: mmyov@mhtl.uwaterloo.ca Teaching Assistants Mirko Stevanovic, E3-2133A, X6181; email: mirko@mh
W. Alabama - ME - 353
WK2TPCSWEB.TEXME 353 M.M. Yovanovich Week 2 Lecture 1Solutions to problems are available in Engineering Photocopy Center. First makeup lecture: Thursday, 8:30 AM, CPH 3385. Discuss the ME 353 Website. Calendar, Assigments, Projects, Exams, Lecture
W. Alabama - ME - 353
DEPARTMENT OF MECHANICAL ENGINEERING ME 353 HEAT TRANSFER 1UNIVERSITY OF WATERLOODecember 9, 1996 M.M. YovanovichTime: 9-12 A.M.Three-hour Closed Book Final Examination. Two crib sheets both sides are permitted. All questions are of equal val
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