Review: Convection and Heat Exchangers. Reminders

Transcription

1 CH EN 3453 Heat Transfer Review: Convection and Heat Exchangers Chapters 6, 7, 8, 9 and 11 Reminders Midterm #2 Wednesday at 8:15 AM Review tomorrow 3:30 PM in WEB L104 (I think) Project Results and Discussion due Friday at 4:00PM Turn in to Chem Engineering office Write text, not just equations! Target words. Explain it to e.g. your manager (a non-engineer) Project Intro and Conclusions due Friday, Nov 21 Use separate paper for each Put your name on each section Many homework assignments have not been picked up

2 CHAPTER 6: Introduction to Convection Boundary layers Velocity Thermal Boundary layer equations Three Boundary Layers

3 Laminar and Turbulent Flow Laminar and Turbulent Flow Figure 6.8 Variation of velocity boundary layer thickness δ and the local heat transfer coefficient h for flow over an isothermal flat plate.

4 CHAPTER 7: External Flow Geometries Flat plate Cylinder in cross flow Sphere Banks of tubes Heat transfer Constant surface temperature Constant heat flux Flat Plate Critical Reynolds number: 5 x 10 5 Local Nusselt number (use Tfilm): Laminar Turbulent

5 Flat Plate Average Nusselt number Laminar Turbulent (tripped at leading edge) Transition Unheated starting length Example: Problem 7.16 Consider a rectangular fin that is used to cool a motorcycle engine. The fin is 0.15 m long and at a temperature of 250 C, while the motorcycle is moving at 80 km/h in air at 27 C. The air is in parallel flow over both surfaces of the fin, and turbulent flow conditions may be assumed to exist throughout. What is the rate of heat removal per unit width of the fin?

6 Cylinder in Cross Flow Average Nusselt number (all ReD) Example: Problem 7.45 A pin fin of 10-mm diameter dissipates 30 W by forced convection to air in cross flow with a Reynolds number of If the diameter of the fin in doubled and all other conditions remain the same, estimate the fin heat rate. Assume the fin to be infinitely long.

7 Flow over a Sphere Average Nusselt number Flow Across Banks of Tubes

8 Banks of Tubes (cont.) Example: Problem 7.88 A tube bank uses an aligned arrangement of 30 mm diameter tubes with ST = SL = 60 mm and a tube length of 1 m. There are 10 tube rows in the flow direction and 7 tubes per row. Air with upstream conditions of T = 27 C and V = 15 m/s is in cross flow over the tubes, while a tube wall temperature of 100 C is maintained by steam condensation inside the tubes. Determine the temperature of air leaving the tube bank.

9 Table Bookmark It! CHAPTER 8: Internal Flow Basics Velocity profiles Mean velocity, mean temperature Geometries Circular tubes Non-circular tubes Concentric annulus Heat transfer Constant surface temperature Constant heat flux

10 Internal Flow Internal Flow Calculations Reynolds number (critical = 2300) Hydraulic diameter for non-circular tubes For uniform surface temperature

11 Laminar Flow in a Circular Tube Laminar Flow: Non-Circular Tube

12 Turbulent Flow Circular or noncircular tube with small temperature diffs (Dittus-Boelter)

13 Example: Problem 8.26 Ethylene glycol flows at 0.01 kg/s through a 3 mm diameter, thin-walled tube. The tube is coiled and submerged in a well-stirred water bath maintained at 25 C. If fluid enters the tube at 85 C, what heat rate and tube length are required for the fluid to leave at 35 C? CHAPTER 9: Free (Natural) Convection Fundamentals Buoyancy Boundary layer development Geometries Vertical surface Horizontal plates Long horizontal cylinder Spheres Vertical parallel plate channels Enclosures/cavities

14 Types of Free Convection Plume Buoyant Jet Boundary Layer Empirical Correlations Similar to approach used previously for forced convection Correlation for Nusselt number Nu Instead of Re, we use Ra Careful on which expression to use Fluid properties determined at film temp. ( ) / 2 T film = T s + T Thermal expansion coefficient β Gases: Liquids: Look up in appendix

15 Flow over Vertical Plate Rayleigh Number: (9.25) Laminar Flow (Ra L < 10 9 ): (9.27) All Conditions: (9.26) Example: Problem 9.13 A household oven door of 0.5-m height and 0.7-m width reaches an average surface temperature of 32 C during operation. Estimate the heat loss to the room with ambient air at 22 C.

16 CHAPTER 11: Heat Exchangers Basics Overall heat transfer coefficient Phase change heat transfer one one side Heat exchanger configurations Parallel flow Counterflow Multiple shells Multiple tube passes Cross-flow Analysis approaches Log-mean temperature difference (design) Effectiveness-NTU (performance and design) Modified LMTD (design - fancy configurations) Overall Heat Transfer Coefficient Contributing factors Convection between the two fluids and solid Conduction of the solid separator Potential use of fins in one or both sides Time-dependent surface fouling General expression (c and h = cold and hot)

17 Log-Mean Temperature Difference q = UAΔT lm Cocurrent flow (parallel flow) Countercurrent flow Special Operating Conditions "heat capacity rate"

18 Effectiveness-NTU Approach Effectiveness: NTU (Number of Transfer Units):

19 Parallel-Flow Heat Exchanger

20 Counterflow Heat Exchanger Shell-and-Tube Heat Exchanger (One Shell)

21 Shell-and-Tube Heat Exchanger (Multiple Shells) Cross-Flow Heat Exchanger (Unmixed-Unmixed)

22 Cross-Flow Heat Exchanger (Mixed-Unmixed) Solid curves: C min mixed C max unmixed Dashed curves: C min unmixed C max mixed Example: Problem In a dairy operation, milk at a flow rate of 250 liter/hour and a cow body temperature of 38.6 C must be chilled to a safeto-store temperature of 13 C or less. Ground water at 10 C is available at a flow rate of 0.72 m 3 /h. The density and specific heat of water are 1030 kg/m 3 and 3860 J/kg K. (a) Determine the UA product of a counterflow heat exchanger required for the chilling process. Determine the length of the exchanger if the inner pipe has a 50 mm diameter and the overall heat transfer coefficient is U = 1000 W/m 2 K. (b) Determine the outlet temperature of the water. (c) using the UA from part a, determine the milk outlet temperature if the water flow rate is doubled.