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Nonlinear stability analysis of Darcy's flow with viscous heating
Michele Celli1, Leonardo S de B Alves2, Antonio Barletta1
1Department of Industrial Engineering , Alma Mater Studiorum Università di Bologna , Bologna, Italy.
Proceedings. Mathematical, Physical, and Engineering Sciences
|June 10, 2016
Summary
This study investigates the nonlinear stability of a porous channel, finding that viscous dissipation alone can induce mixed convection. High Péclet numbers cause initial overheating before settling into a steady state.
Area of Science:
- Fluid dynamics
- Heat transfer
- Porous media physics
Background:
- Investigating fluid flow and heat transfer in porous media is crucial for applications like geothermal energy and chemical reactors.
- Understanding nonlinear stability is essential for predicting complex convective phenomena.
- Viscous dissipation as an internal heat source can significantly alter stability characteristics.
Purpose of the Study:
- To analyze the nonlinear convective stability of a fluid-saturated rectangular porous channel with a variable aspect ratio.
- To examine the influence of viscous dissipation and throughflow on stability.
- To compare nonlinear results with existing linear stability analyses.
Main Methods:
- Utilizing the generalized integral transform technique (GITT) for nonlinear stability analysis.
- Performing nonlinear simulations to validate analytical findings.
- Analyzing the neutral stability curve and growth rates of unstable modes.
Main Results:
- Viscous dissipation alone is confirmed to induce mixed convection.
- Nusselt number and convective cell patterns are analyzed for supercritical configurations.
- Low Gebhart or high Péclet numbers result in transient overheating before reaching a steady state.
Conclusions:
- Nonlinear simulations corroborate linear stability analysis, highlighting the role of viscous dissipation.
- The study provides insights into the complex behavior of porous channel flow under varying conditions.
- Findings are relevant for optimizing heat and mass transfer in porous systems.
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