Natural Convection Dynamics of Non-Newtonian Fluids

Natural convection in non-Newtonian fluids arises when buoyancy forces induced by temperature or concentration gradients drive flow in complex viscous media whose rheology departs from Newton’s law. Such fluids include shear-thinning or shear-thickening power-law liquids, viscoplastic suspensions exhibiting yield stress, and nanofluids with enhanced thermal properties. The coupling between variable viscosity, temperature-dependent density, and geometry produces rich flow patterns, often characterised by asymmetric circulations, multiple vortices and altered heat transport rates. Mathematical modelling typically employs the Boussinesq approximation together with constitutive equations such as the Ostwald-de Waele or Bingham models. Numerical methods—finite element, finite difference and lattice Boltzmann approaches—enable detailed resolution of velocity, temperature and yielded/unyielded regions. Key dimensionless groups include the Rayleigh and Prandtl numbers, power-law index and yield number, which govern the onset and intensity of convection as well as transitions between conduction-dominated and convection-dominated regimes. Understanding these dynamics is critical for applications ranging from polymer extrusion and electronic cooling to geothermal energy recovery and biochemical reactors, where efficient thermal management and control of flow instabilities are paramount.

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Natural Convection Dynamics of Non-Newtonian Fluids publication trend

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Technical terms

Rayleigh number: Dimensionless ratio of buoyancy to viscous and thermal diffusivity forces that dictates the onset and strength of convection.

Power-law index: Exponent in the Ostwald-de Waele model describing the degree of shear-thinning (n<1) or shear-thickening (n>1) behaviour of a fluid.

Bingham model: Constitutive relation for viscoplastic fluids incorporating a yield stress below which the fluid behaves as a rigid solid.

Nusselt number: Dimensionless heat transfer coefficient representing the ratio of convective to conductive heat transport across a boundary.

Boussinesq approximation: Simplification that treats density as constant except where it contributes to buoyancy, facilitating analysis of natural convection.

References

1. Numerical analysis of permeability and Darcy effect in heat transfer of pyramid-shaped structure. International Communications in Heat and Mass Transfer (2024).
2. Lattice Boltzmann simulation of cavity flows driven by shear and internal heat generation for both Newtonian and viscoplastic fluids. Physics of Fluids (2023).
3. Natural Convection of Non-Newtonian Power-Law Fluid in a Square Cavity with a Heat-Generating Element. Energies (2019).