Thermal Convection of an Ellis Fluid Saturating a Porous Layer with Constant Heat Flux Boundary Conditions
Abstract
:1. Introduction
2. Mathematical Formulation
2.1. Rheological Model
2.2. Modified Darcy’s Law
2.3. Governing Equations
2.4. Basic State
2.5. Linear Stability Analysis
3. Asymptotic Analysis for Vanishing Wavenumber
4. Results and Discussion
5. Conclusions
- There exists a suitable variable transformation that yields a compact representation of the stability eigenvalue problem;
- The critical conditions hold always for . The threshold values can be obtained entirely analytically due to an asymptotic analysis performed for ;
- The non-Newtonian character of the fluid plays a destabilizing effect on the convective flow, namely an increasing value of the Ellis number yields a destabilization of the basic flow;
- For , the Ellis index a does not affect the stability conditions and the results coincide with those for the limit of Newtonian fluid already available in the literature ( and );
- For large values of the Ellis number, the power-law behavior is recovered. This means that the critical Rayleigh number tends to zero.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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k | |
---|---|
12.0114 | |
12.0001 | |
12.0000 | |
0 | 12 |
0 | 12 | 12 | 12 | 12 |
10.666667 | 10.285714 | 9.6 | 8 | |
7.3846154 | 6.5454545 | 5.3333333 | 3.4285714 | |
1 | 5.3333333 | 4.5 | 3.4285714 | 2 |
10 | 0.88888889 | 0.67924528 | 0.46153846 | 0.23529412 |
100 | 0.095238095 | 0.071570577 | 0.047808765 | 0.023952096 |
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Brandão, P.V.; Celli, M.; Barletta, A.; Lazzari, S. Thermal Convection of an Ellis Fluid Saturating a Porous Layer with Constant Heat Flux Boundary Conditions. Fluids 2023, 8, 54. https://doi.org/10.3390/fluids8020054
Brandão PV, Celli M, Barletta A, Lazzari S. Thermal Convection of an Ellis Fluid Saturating a Porous Layer with Constant Heat Flux Boundary Conditions. Fluids. 2023; 8(2):54. https://doi.org/10.3390/fluids8020054
Chicago/Turabian StyleBrandão, Pedro Vayssière, Michele Celli, Antonio Barletta, and Stefano Lazzari. 2023. "Thermal Convection of an Ellis Fluid Saturating a Porous Layer with Constant Heat Flux Boundary Conditions" Fluids 8, no. 2: 54. https://doi.org/10.3390/fluids8020054