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Internal Flow

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  1. Internal Flow Chapter 8 Section 8.1 through 8.9 Lecture 13

  2. 1. Flow in Tubes Hydrodynamics Entrance & Fully Developed Regions

  3. Hydrodynamic Entrance ReD,c< 2300, Laminar Flow

  4. Mean Velocity

  5. Velocity Profile

  6. Friction Factor & Pressure Drop Moody Factor: ReD≤2300 2300≤ReD≤20000 ReD>20000

  7. Friction Factor & Pressure Drop 3000 ≤ ReD< 5x106

  8. Friction Factor & Pressure Drop

  9. Thermal Entrance

  10. Thermal Entrance

  11. Mean Temperature

  12. Fully Developed Conditions

  13. Fully Developed Conditions

  14. 2. Energy Balance

  15. Energy Balance

  16. Energy Balance For constant heat flux:

  17. Energy Balance For constant Ts:

  18. Energy Balance

  19. 3. Laminar Flow in Circular Tubes For fully developed conditions

  20. 3. Laminar Flow in Circular Tubes

  21. Laminar Flow in Circular Tubes For the entry region: Ts=Constant 0.48 < Pr <16,700 0.0044 < ( ) < 9.75 [ReDPr/(L/D)]1/3 (μ/μs)0.14 ≥2 All properties at average Tm

  22. 4. Turbulent Flow in Circular Tubes Colburn Equation

  23. Turbulent Flow in Circular Tubes Dittus-Boelter Equation n = 0.4 for heating, Ts > Tm n = 0.3 for cooling, Ts < Tm 0.7 < Pr <160 ReD≥10,000 L/D ≥ 10

  24. 5. Flow in Noncircular Tubes Effective Diameter For turbulent flow, correlations for circular tubes can be used. For laminar flow, Nu values can be found in Table 8.1, page519

  25. 6. Convection Mass Transfer

  26. Fully Developed Conditions

  27. Fully Developed Conditions Laminar Flow: Turbulent Flow: Correlations for Nu can be used for Sh by replacing Pr with Sc

  28. 7. Methodology for Convection Calculation • Identify the flow geometry, calculate Dh • Specify reference T for fluid properties • Calculate Re, laminar or turbulent ? • Flow entrance or fully developed region? • Select appropriate correlation

  29. Example 1 Steam condensing on the outer surface of a thin-walled circular tube of 50-mm diameter and 6-m length maintains a uniform surface temperature of 100C. Water flows through the tube at a rate of =0.25 kg/s, and its inlet and outlet temperatures are Tm,i=15C and Tm,o=57C. What is the average convection coefficient associated with the water flow?

  30. Example 1 Known:Flow rate and inlet and outlet T of water flowing through a tube of 100 C Find: Average convection heat transfer coefficient Schematic:

  31. Example 1 Assumptions: 1. Negligible outer surface resistance and tube wall conduction; 2. Negligible kinetic and potential energy and flow work change; 3. Constant properties. Properties: Table A.6, for water at (15+57)/2=36 C, cp = 4178 J/kgC Analysis: For constant Ts, Eqn. 8.42b

  32. = 756 W/m2K Example 1 Analysis: P = D

  33. Example 2 Freon is being transported at 0.1 kg/s through a Teflon tube of inside diameter Di=25mm and outside diameter Do=28 mm, while atmospheric air at V=25 m/s and 300K is in cross flow over the tube. What is the heat transfer per unit of length of tube to Freon at 240K?

  34. Example 2 Known:Flow rate and temperature of Freon passing through a Teflon tube of prescribed inner and outer diameter. Velocity and temperature of air in cross flow over tube. Find: Heat transfer per unit length of tube Schematic:

  35. Example 2 Assumptions: (1) Steady-state conditions, (2) One-dimensional radial conduction, (3) Constant properties, (4) Fully developed flow. Properties:

  36. Example 2 Analysis:

  37. Example 2 Analysis: Lecture 13