Heat Transfer II ENGR 7901 Spring, Dr. Y. Muzychka EN 3058
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1 Heat Transfer II ENGR 7901 Spring, 2010 Dr. Y. Muzychka EN 3058
2 Course Materials Text: Fundamentals of Heat Transfer Incropera and DeWiP, 6 th EdiRon Course Notes and Handouts Most Course Material on Webpage Power Point will posted every week or two Office Hours: Thursday 2-4 PM Outside of this Rme, by appointment only. y.s.muzychka@mun.ca TA: To be announced.
3 Important Dates Midterm Break: June 21/22/23 Quizzes: June 17/July 15, 2010 No Class June 1 st and June 3 rd Last Day of Classes: July 30th, 2010 Make Up Classes for June 1/3 will be held in the week of June 7 th and 14 th Lab is due two weeks ader the lab session.
4 Course Grading Quizzes (2): 30% (Total) Labs (1 or 2): 10% Final Exam: 60% Lab Groups Composed of 4 Members
5 Text SecRons for this Course Chapter 4 - MulRdimensional ConducRon: Chapter 11 - Heat Exchangers: * * Basic Theory Only, More details in 7903 Chapter 6 - ConvecRon: Chapter 7 External Flow: Chapter 8 Internal Flow: Chapter 9 Natural ConvecRon: Chapter 10 CondensaRon: AddiRonal Review Topics from Chapters 1-3,5
6 Review of Heat Transfer I Fundamentals
7 The Review: The Three Modes
8 Dimensionless Groups Recall, the following dimensionless groups: Biot Number (Bi) Fourier Number (Fo)
9 Dimensionless Groups We will encounter many other dimensionless groups such as: Nusselt # (Nu), Reynolds # (Re), Grashof # (Gr), Rayleigh # (Ra), Prandtl # (Pr), Jakob # (Ja), Eckert # (Ec), Peclet # (Pe), Stanton # (St), Stefan # (Ste), Colburn factor (j), and Fanning fricbon factor (C f or f). In general, the subscript used on the dimensionless number indicates the length scale used in its definiron, i.e.
10 ConducRon Review One Dimensional Steady ConducRon
11 Unsteady ConducRon Semi- Infinite Domains, αt < L
12 Unsteady ConducRon AddiRonal results for the plane wall, cylinder, and spherical regions, i.e. the Heisler charts or single term approximarons. See the notes.
13 Other Concepts for Review Please review the Lumped Capacitance formularons. SecRon Also, review concepts related to extended surfaces (fins). SecRon 3.6 Review the supplied materials carefully.
14 MulRdimensional ConducRon Shape Factors, Moving Heat Sources, and Numerical SoluRons
15 Shape Factors Shape factors are a simple means of accounrng for the geometric factors affecrng conducron in 1D, 2D and 3D systems. The shape factor S is defined such that: Q = Sk(T 1 T 2 ) The shape factor is related to the thermal resistance through: R = 1 S k Shape factors are determined from analyrc solurons to Laplace s equaron and using the field to calculate S or R. 2 T x T y T z 2 = 0
16 Shape Factors Shape factors are convenient for determining thermal resistance in simple systems such as:
17 Shape Factors Shape factors are convenient for determining thermal resistance in complex systems such as:
18 Shape Factors Shape factors can easily be used in thermal circuits: where R Total = 1 h i A i + 1 Sk + 1 h o A o Q = T i T o R Total Here is a sample of shape factors from your text:
19
20
21 Shape Factors Shape factors are tabulated in a number of Heat Transfer Handbooks. Here is a sample of some useful factors:
22 Shape Factors
23 Shape Factors Shape factors can also be approximated from many one dimensional solurons. Other solurons can be used to approximate situarons where no shape factor is available. Two rules for shape factor equivalence : Rule #1 Preserve the smaller surface area (inside or outside). Rule #2 Preserve the volume of the material in the system.
24 Example 1.1 Calculate the heat transfer rate from the cubical oven enclosure having an outside side length of W=5 m, and a wall thickness of t=0.35 m. The thermal conducrvity of the wall is 1.4 W/mK, and there is an outside heat transfer coefficient of h o =5 W/m 2 k and an ambient temperature of 25 C. The inside surface is constant at 1100 C. Use two approaches: 1) Find appropriate shape factors from the table in your text or from the tables provided. 2) Using the two modelling rules approximate the cubical enclosure as a spherical enclosure.
25 Example 1.2 Compare the shape factor for the system composed of a circular hole in a square bar, with that approximated using a circular hole in a circular bar.
26 Example 1.3 Compare the shape factor for a spherical enclosure in an infinite medium to that of a cubical enclosure in an infinite medium. Using the soluron for the spherical enclosure approximate the shape factor for the cubical enclosure and compare the error. Why? So that we can test the two rule method!
27 Example 1.4 You are asked to analyze the liquid cooled heat sink, which is produced by machining triangular grooves in two matching plates which eventually form a diamond shaped holes when the plates are assembled as shown in the sketch. Calculate the overall heat transfer coefficient for the system shown below assuming that the internal convecrve heat transfer coefficient is 1000 W/m 2 K. You will need to approximate the shape factor using sound physical principles as no exact soluron is available to this configuraron. Assume that the plate is aluminum with a thermal conducrvity of k = 180 W/mK. If the surface temperature is limited to T s = 50 C and coolant has a mean bulk temperature of 30 C, what heat transfer rate is permissible, when the sink contains four channels of length 15 cm?
28 Moving Fins: Extrusion In Heat Transfer I you learned about fins. Here we wish to extend the concept of fins to extrusion of wires and plates. In these cases the fins are moving. What does moron do to the temperature profile in a conrnuous flow? Why would we need to calculate the temperature of a moving wire? To appreciate the problem, we will tackle the issue from first principles and re- derive the fin equaron, but this Rme including moron.
29 Example 1.5 Copper wire is formed by means of an extrusion process. Calculate the temperature of the wire as a funcron of posiron from the die. The wire is 1 mm in diameter, and leaves the die at 500 C at a rate of 0.5 kg/hr. If the heat transfer coefficient is approximately 25 W/m2K in an environment of 25 C, find the distance from the die where the wire reaches 50 C. How does this compare to the case when the system is not moving, i.e. a staronary fin?
30 Moving Heat Sources Moving heat sources are found in many applicarons: heat trearng, welding, sliding fricron, etc. Several fundamental solurons exist for simple configurarons: Plane heat source, line heat source, and point heat source. Plane heat source models the upstream and downstream porrons of the system. The line heat source and point heat source are useful in welding analysis of thin and thick plates depending upon the weld penetraron depth. In all three cases the temperature field is measured from the center of the heat source, i.e. we are following it.
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