1 / 16

CHE/ME 109 Heat Transfer in Electronics

CHE/ME 109 Heat Transfer in Electronics. LECTURE 18 – FLOW IN TUBES. LAMINAR FLUID FLOW IN TUBES. FORCE BALANCE OVER A CYLINDRICAL VOLUME IN FULLY DEVELOPED LAMINAR FLOW PRESSURE FORCES = VISCOUS FORCES THE DIFFERENTIAL BALANCE IS: . LAMINAR FLUID FLOW .

onawa
Télécharger la présentation

CHE/ME 109 Heat Transfer in Electronics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CHE/ME 109 Heat Transfer in Electronics LECTURE 18 –FLOW IN TUBES

  2. LAMINAR FLUID FLOW IN TUBES • FORCE BALANCE OVER A CYLINDRICAL VOLUME IN FULLY DEVELOPED LAMINAR FLOW • PRESSURE FORCES = VISCOUS FORCES • THE DIFFERENTIAL BALANCE IS:

  3. LAMINAR FLUID FLOW • INTEGRATING TWICE, WITH BOUNDARY CONDITIONS • V = 0 @ r = R (ZERO VELOCITY AT THE WALL) • (dV/dr) = 0 @ r = 0 (CENTERLINE SYMMETRY) • PARABOLIC VELOCITY PROFILE

  4. LAMINAR FLOW - MEAN VELOCITY • MEAN VELOCITY FROM THE INTEGRATED AVERAGE OVER THE RADIUS: IN TERMS OF THE MEAN VELOCITY

  5. PRESSURE DROP • PRESSURE REQUIRED TO TRANSPORT FLUID THROUGH A TUBE AT A SPECIFIED FLOW RATE IS CALLED PRESSURE DROP, ΔP • UNITS ARE TYPICALLY (PRESSURE/LENGTH PIPE) • USING RESULTS FROM THE FORCE BALANCE EQUATION, A CORRELATION FOR PRESSURE DROP AS A FUNCTION OF VELOCITY USES THE FORM: • FOR LAMINAR FLOW:

  6. GRAPHICAL VALUES

  7. PUMP WORK • REQUIRED TO TRANSPORT FLUID THROUGH A CIRCULAR TUBE IN LAMINAR FLOW:

  8. HEAT TRANSFER TO LAMINAR FLUID FLOWS IN TUBES • ENERGY BALANCE ON A CYLINDRICAL VOLUME IN LAMINAR FLOW YIELDS: • SOLUTION TO THIS EQUATION USES BOUNDARY CONDITIONS BASED ON EITHER CONSTANT HEAT FLUX OR CONSTANT SURFACE TEMPERATURE

  9. CONSTANT HEAT FLUX SOLUTIONS • BOUNDARY CONDITIONS: • AT THE WALL T = Ts @ r = R • AT THE CENTERLINE FROM SYMMETRY:

  10. CONSTANT WALL TEMPERATURE SOLUTIONS • STARTING WITH THE FLUID HEAT BALANCE IN THE FORM: • BOUNDARY CONDITIONS: • AT THE WALL: T = Ts @ r = R • AT THE CENTERLINE:

  11. CONSTANT WALL TEMPERATURE • SUBSTITUTING THE VELOCITY PROFILE INTO THIS EQUATION YIELDS AN EQUATION IN THE FORM OF AN INFINITE SERIES • RESULTING VALUES SHOW: Nu = 3.657

  12. HEAT TRANSFER IN NON-CIRCULAR TUBES • USES THE SAME APPROACH AS DESCRIBED FOR CIRCULAR TUBES • CORRELATIONS USE Re AND Nu BASED ON THE HYDRAULIC DIAMETER: • SEE TABLE 8-1 FOR LIMITING VALUES FOR f AND Nu BASED ON SYSTEM GEOMETRY AND THERMAL CONFIGURATION

  13. TURBULENT FLOW IN TUBES • FRICTION FACTORS ARE BASED ON CORRELATIONS FOR VARIOUS SURFACE FINISHES (SEE PREVIOUS FIGURE FOR f VS. Re) • FOR SMOOTH TUBES:

  14. TURBULENT FLOW • FOR VARIOUS ROUGHNESS VALUES (MEASURED BY PRESSURE DROP): • TYPICAL ROUGHNESS VALUES ARE IN TABLES 8.2 AND 8.3

  15. TURBULENT FLOW HEAT TRANSFER IN TUBES • FOR FULLY DEVELOPED FLOW DITTUS-BOELTER EQUATION: • OTHER EQUATIONS ARE INCLUDED AS (8-69) & (8-70) • SPECIAL CORRELATIONS ARE FOR LOW Pr NUMBERS (LIQUID METALS) (8-71) AND (8-72)

  16. NON-CIRCULAR DUCTS • USE THE HYDRAULIC DIAMETER: • USE THE CIRCULAR CORRELATIONS: • ANNULAR FLOWS • USE A DEFINITION FOR HYDRAULIC DIAMETER Dh = Do -Di • USE THE CIRCULAR CORRELATIONS • HAVE LIMITING VALUES FOR LAMINAR FLOW (TABLE 8-4) • HAVE LIMITING FLOWS FOR ADIABATIC WALLS (8-77 & 8-78)

More Related