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The equation for the turbulent flow in a tube is given by [16] where n = 0.4 for heating n = 0.3 for cooling (3.54) The following equation applies to laminar flow in a tube with a constant wall temperature [3] where d{ = inside tube diameter / = tube length The expression for the laminar flow heat transfer to flat plate is [3] Equation 3.56 is valid for Pr = 0.6 to 2000 and Re < 10 5 . The equation for turbulent flow heat transfer to flat plate is given as [3] Equation 3.57 applies for the conditions: Pr = 0.6 to 2000 and 5 • 10 5 < Re < 10 7 . (3.55) (3.56) (3.57) The properties of the fluids in the equations above are to be found at a mean fluid temperature. Example A flat film is moving in a coating equipment at a velocity of 130 m/min on rolls that are 200 mm apart. Calculate the heat transfer coefficient a if the surrounding medium is air at a temperature of 50 0 C. Solution The properties of air at 50 0 C are: Kinematic viscosity v = 17.86 • 10" 6 m 2 /s Thermal conductivity A = 28.22 • 10" 3 W/(m • K) Prandtl number Pr = 0.69
The Reynolds number ReL, based on the length L = 200 mm is Substituting ReL = 24262 and Pr = 0.69 into Equation 3.56 gives As the fluid is in motion on both sides of the film, the Nusselt number is calculated according to [3] For turbulent flow Nu111^ follows from Equation 3.57: The resulting Nusselt number Nu is Heat transfer coefficient a results from 3.6 Heat Transfer by Radiation Heating by radiation is used in thermoforming processes to heat sheets or films, so that the shaping process can take place. Because at temperatures above 300 0 C a substantial part of the thermal radiation consists of wavelengths in the infrared range, heat transfer by radiation is also termed as infrared radiation [14]. According to the Stefan-Boltzmann law the rate of energy radiated by a black body per unit area es is proportional to the absolute temperature T to the fourth power (Figure 3.13) [I]: The Stefan-Boltzmann constant has the value (3.58)
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Natti S. Rao Gunter Schumacher D e
Page 3 and 4:
Preface Today, designing of machine
Page 5 and 6:
Figure 1.1 Deformation of a Hookean
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Figure 1.4 Shear flow The shear or
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where c and m are empirical constan
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Apparent viscosity 7\Q True viscosi
Page 13 and 14: Pa Shear stress T Figure 1.11 Deter
Page 15 and 16: Shift Factor for Crystalline Polyme
Page 17 and 18: The power law exponent is obtained
Page 19 and 20: 1.3.7.5 Klein's Viscosity Formula [
Page 21 and 22: where Mw = molecular weight JC —
Page 23 and 24: Steady state shear compliance J°t
Page 25 and 26: Ig 6\ Ig G" lga; Figure 1.22 Storag
Page 27 and 28: Characterization of the Transient S
Page 29 and 30: Time/ Figure 1.28 Tensile creep at
Page 31 and 32: 1.4.2.2 Nonlinear Viscoelastic Beha
Page 33 and 34: Figure 1.37 Maxwell fluid [1 ] The
Page 35 and 36: Die swel B1 Figure 1.40 Dependence
Page 37 and 38: 2 Thermodynamic Properties of Polym
Page 39 and 40: where u = internal energy T = tempe
Page 41 and 42: Enthalpy /7-/720 kWh kg Kl kg polyn
Page 43 and 44: Table 2.1 Approximate Values for th
Page 45 and 46: Analogous to Ohm's law in electric
Page 47 and 48: Figure 3.3 One-dimensional heat tra
Page 49 and 50: Figure 3.5 Heat flow in a multilaye
Page 51 and 52: The combination of convection and c
Page 53 and 54: The equation for an infinite cylind
Page 55 and 56: The foregoing equations apply to ca
Page 57 and 58: Figure 3.11 Midplane temperature fo
Page 59 and 60: Figure 3.12 Temperature distributio
Page 61 and 62: For drag flow the velocity gradient
Page 63: Lewis number: ratio of thermal diff
Page 67 and 68: At thermal equilibrium according to
Page 69 and 70: The rate of heat generation in a pl
Page 71 and 72: The mass of the fluid permeating th
Page 73 and 74: 4 Designing Plastics Parts The defo
Page 75 and 76: The parabolic failure criterion is
Page 77 and 78: Figure 4.3 Secant modulus [4] Stres
Page 79 and 80: where P = load (N) Lybyd = dimensio
Page 81 and 82: 5 Formulas for Designing Extrusion
Page 83 and 84: for values of the ratio n (R0 + R1)
Page 85 and 86: melt density pm = 0.7 g/cm 3 Soluti
Page 87 and 88: and finally the pressure drop Ap fr
Page 89 and 90: Pressure drop Ap from Equation 5.2
Page 91 and 92: Proportionality factor K from Equat
Page 93 and 94: n = 3.043 RTh= 1.274 mm Shear rate
Page 95 and 96: The relation of a slit is H = heigh
Page 97 and 98: Shear stress (N/m 2 ) Figure 5.5 Ef
Page 99 and 100: Figure 5.7 Surface distortion on a
Page 101 and 102: Residence time t (s) LDPE m = 40 kg
Page 103 and 104: Table 5.1 Dimensions of Square Scre
Page 105 and 106: Pressure drop in screen Mesh size F
Page 107 and 108: In practice, this efficiency is als
Page 109 and 110: 5.2.2 Melt Conveying Starting from
Page 111 and 112: md = 46.42 kg/h Equation 5.31 and E
Page 113 and 114: Solution Power Zc in the screw chan
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Indices: m: melt f: melt film b: ba
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Example with symbols and units a) S
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X- Q Figure 5.24 Velocity and tempe
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(5.54) As seen from the equations a
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Figure 5.26 Three-zone screw [8] Th
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The profiles of stock temperature a
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where HF = feed depth H = metering
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Screw speed (rpm) Screw diameter D
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5.2.6 Mechanical Design of Extrusio
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Next Page Screw Vibration When the
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5.3.1 Pressure Drop in Runner As th
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Examples of calculating pressure dr
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Example with symbols and units The
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Flow length L mm Spiral height H Fi
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Solution The conversion factors for
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Figure 5.43 shows a sample plot of
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With the values for the properties
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Cooling time mm Distance between mo
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Table 5.2 Results of Optimization o
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Per cent unmelted Axial distance al
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A* [%] LDPE Axial length (screw dia
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A* [%] A* [%] LDPE LDPE Axial lengt
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Flow length (mm) Flow length (mm) F
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Flow length L (mm) Flow length L (m
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[26] VDI Warmeatlas, VDI Verlag, Du
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A Final Word The aim of this book i
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166 Index terms Links Index terms L
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168 Index terms Links Index terms L
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viii Contents 1.4 Viscoelastic Beha
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x Contents 5.2 Extrusion Screws ...
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