Che me 109 heat transfer in electronics
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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

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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:


Graphical values

GRAPHICAL VALUES


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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