Note on the Early Thermoelastic Stage Preceding Rayleigh–Bénard Convection in Soft Materials
Abstract
:1. Introduction
1.1. Rayleigh–Bénard Convection in a Yield–Stress Fluid: Literature Review
1.2. Objectives, Methodology and Outline of the Paper
2. Problem Formulation
2.1. Governing Equations
2.2. Boundary Conditions
3. Thermal Stresses and Strains Induced by a Temperature Gradient
4. Strain and Stress Fields Induced by Gravity Combined with a Temperature Gradient
5. Onset of Plastic Deformation: Main Yield Criteria
5.1. Tresca Criterion
5.2. Von Mises Yield Criterion
5.3. Drucker–Prager Yield Criterion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
specific heat constant volume | ||
thermal diffusivity | ||
E | Young’s modulus | Pa |
g | acceleration of gravity | |
H | thickness of the viscoplastic fluid layer | |
first invariant of the Cauchy stress tensor | ||
second invariant of the deviatoric stress tensor | ||
K | thermal conductivity | |
T | temperature | |
temperature difference between top and bottom walls | ||
displacement vector | ||
z | vertical coordinate | |
volume expansion coefficient | ||
strain tensor | ||
dynamic viscosity | ||
first Lamé’s parameter | ||
second Lamé’s parameter | ||
Poisson’s ratio | ||
fluid density | ||
reference value of the fluid density | ||
maximum value of shear-stress | ||
Cauchy stress tensor | ||
yield stress |
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Rahouadj, R.; Nouar, C.; Pereira, A. Note on the Early Thermoelastic Stage Preceding Rayleigh–Bénard Convection in Soft Materials. Fluids 2022, 7, 231. https://doi.org/10.3390/fluids7070231
Rahouadj R, Nouar C, Pereira A. Note on the Early Thermoelastic Stage Preceding Rayleigh–Bénard Convection in Soft Materials. Fluids. 2022; 7(7):231. https://doi.org/10.3390/fluids7070231
Chicago/Turabian StyleRahouadj, Rachid, Chérif Nouar, and Antonio Pereira. 2022. "Note on the Early Thermoelastic Stage Preceding Rayleigh–Bénard Convection in Soft Materials" Fluids 7, no. 7: 231. https://doi.org/10.3390/fluids7070231