Numerical Modeling of Thermal Flows in Entrance Channels for Polymer Extrusion: A Parametric Study
Abstract
:1. Introduction
2. Mathematical Model of Temperature Distribution of the Casson Fluid Flow
2.1. Derivation of the Velocity Profile
2.2. Temperature Distribution of the Flow in Parallel-Plate Channel
2.3. Temperature Distribution of the Flow in Circular Tube Channel
Finite Element Model
3. Description of the Parametric Study
4. Results and Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
Constants and variables | |
,g | pressure drop in the channel |
Casson viscosity | |
shear rate in circular tube | |
shear rate in parallel-plate | |
element domain | |
boundary domain | |
fluid density | |
shear stress | |
Casson yield stress | |
wall stress constant | |
specific heat capacity of the fluid | |
increment in y | |
increment in z | |
k | fluid thermal conductivity |
L | distance from the inlet to exit |
optimal length of the channel to reach the steady state | |
for inlet pressure, for pressure at exit | |
Q | flow rate |
dimensional, and non-dimensional radial coordinates of the circular tube | |
maximum radius of the circular tube | |
critical radius of the circular tube | |
T | temperature of the fluid |
temperature of the fluid at or for , and at for | |
temperature of the fluid at the inlet | |
wall temperature | |
u | velocity of the fluid flow |
y | axis coordinate perpendicular to z in parallel-plate |
, | critical length from the center to the critical point along y in parallel-plate |
distance from the center to the wall in parallel-plate | |
dimensional, and non-dimensional axial coordinates in the direction of the flow | |
F,{F} | local and global load vectors |
K,K | local and global stiffness matrices |
W | vector of three linear shape functions |
Superscripts and subscripts | |
evaluation of the entity referring to the particular element | |
p | evaluation of the corresponding function at the particular point |
T | matrix transpose |
J | Jacobian matrix |
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Amangeldi, M.; Wei, D.; Perveen, A.; Zhang, D. Numerical Modeling of Thermal Flows in Entrance Channels for Polymer Extrusion: A Parametric Study. Processes 2020, 8, 1256. https://doi.org/10.3390/pr8101256
Amangeldi M, Wei D, Perveen A, Zhang D. Numerical Modeling of Thermal Flows in Entrance Channels for Polymer Extrusion: A Parametric Study. Processes. 2020; 8(10):1256. https://doi.org/10.3390/pr8101256
Chicago/Turabian StyleAmangeldi, Medeu, Dongming Wei, Asma Perveen, and Dichuan Zhang. 2020. "Numerical Modeling of Thermal Flows in Entrance Channels for Polymer Extrusion: A Parametric Study" Processes 8, no. 10: 1256. https://doi.org/10.3390/pr8101256