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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 .

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che me 109 heat transfer in electronics

CHE/ME 109 Heat Transfer in Electronics

LECTURE 18 –FLOW IN TUBES

laminar fluid 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
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
laminar flow mean velocity
LAMINAR FLOW - MEAN VELOCITY
  • MEAN VELOCITY FROM THE INTEGRATED AVERAGE OVER THE RADIUS:

IN TERMS OF THE MEAN VELOCITY

pressure drop
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:
pump work
PUMP WORK
  • REQUIRED TO TRANSPORT FLUID THROUGH A CIRCULAR TUBE IN LAMINAR FLOW:
heat transfer to laminar fluid flows in tubes
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
constant heat flux solutions
CONSTANT HEAT FLUX SOLUTIONS
  • BOUNDARY CONDITIONS:
  • AT THE WALL T = Ts @ r = R
  • AT THE CENTERLINE FROM SYMMETRY:
constant wall temperature solutions
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:
constant wall temperature
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
heat transfer in non circular tubes
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
turbulent flow in tubes
TURBULENT FLOW IN TUBES
  • FRICTION FACTORS ARE BASED ON CORRELATIONS FOR VARIOUS SURFACE FINISHES (SEE PREVIOUS FIGURE FOR f VS. Re)
  • FOR SMOOTH TUBES:
turbulent flow
TURBULENT FLOW
  • FOR VARIOUS ROUGHNESS VALUES (MEASURED BY PRESSURE DROP):
  • TYPICAL ROUGHNESS VALUES ARE IN TABLES 8.2 AND 8.3
turbulent flow heat transfer in tubes
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)
non circular ducts
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)
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