HANSER Hanser Publishers, Munich • Hanser Gardner Publications ...
HANSER Hanser Publishers, Munich • Hanser Gardner Publications ...
HANSER Hanser Publishers, Munich • Hanser Gardner Publications ...
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Nomenclature:<br />
a: thermal diffusivity (m 2 /s)<br />
g: acceleration due to gravity (m/s 2 )<br />
/: characteristic length (m)<br />
p: ressure (N/m )<br />
t. time (s)<br />
Indices<br />
D, P: memory and process of polymer respectively<br />
AT: Temperature difference (K)<br />
w: Velocity of flow (m/s)<br />
O1: Outside heat transfer coefficient [W/(m 2 <strong>•</strong> K)]<br />
/J: Coefficient of volumetric expansion (K" )<br />
/J1: Temperature coefficient in the power law of viscosity (KT 1 )<br />
(5S: Mass transfer coefficient (m/s)<br />
& Diffusion coefficient (m 2 /s)<br />
Tj: Viscosity (Ns/m 2 )<br />
A: Thermal conductivity (Index i refers to the inside value) [W/(m K)]<br />
v: Kinematic viscosity (m 2 /s)<br />
tv: Residence time (s)<br />
p: Density (kg/m 3 )<br />
3.4.1 Physical Meaning of Dimensionless Groups<br />
Biot number: Ratio of thermal resistances in series: (/ / A1) / (1 / oQ<br />
Application: heating or cooling of solids by heat transfer through conduction and<br />
convection<br />
Brinkmann number: ratio of heat dissipated (T] w ) to heat conducted (AAT)<br />
Application: polymer melt flow<br />
Fourier number: ratio of a characteristic body dimension to an approximate temperature<br />
wave penetration depth for a given time [16]<br />
Application: unsteady state heat conduction<br />
Deborah number: ratio of the period of memory of the polymer to the duration of<br />
processing [13]. At Deb > 1 the process is determined by the elasticity of the material,<br />
whereas at Deb < 1 the viscous behavior of the polymer influences the process remarkably.<br />
Grashof number: ratio of the buoyant force g /5 <strong>•</strong> AT f to factional force (v)<br />
Application: heat transfer by free convection<br />
Graetz number: ratio of the time to reach thermal equilibrium perpendicular to the<br />
flow direction (I 2 Ia) to the residence time (tv)<br />
Application: heat transfer to fluids in motion