Thermal Convection in Non-Newtonian Fluid Systems

Thermal convection in non-Newtonian fluids arises when buoyancy forces induced by temperature gradients drive motion through media whose viscosity depends on shear rate or stress history. Unlike Newtonian fluids, these materials can exhibit yield stress, shear-thinning or shear-thickening behaviour, and viscoelastic effects, leading to complex flow patterns, delayed onset of motion and multiple stable or metastable states. Governing equations often combine the Boussinesq approximation with constitutive models such as the Bingham, Carreau or Herschel-Bulkley formulations. Key features include the formation of plug or unyielded regions, modification of critical Rayleigh numbers, and subcritical bifurcations that permit convective states beyond classical stability limits. Such phenomena play a pivotal role in polymer processing, geophysical flows in magma and ice, and heat management in yield-stress suspensions. Advances in numerical methods and stability theory have illuminated how rheological parameters tune heat-transfer rates, threshold conditions for onset and the transition between conduction-dominated and convective regimes.

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Thermal Convection in Non-Newtonian Fluid Systems publication trend

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Technical terms

Rayleigh number: Dimensionless measure of buoyancy relative to viscous damping in a thermal boundary layer.

Bingham fluid: Viscoplastic material exhibiting a yield stress below which it behaves as a rigid body.

Carreau fluid: Non-Newtonian model in which viscosity decreases or increases with shear rate, capturing shear-thinning and shear-thickening behaviour.

Bingham number: Ratio of yield stress to characteristic viscous stress, governing plug formation.

Nusselt number: Dimensionless heat-transfer coefficient quantifying convective enhancement over conduction.

Hartmann number: Ratio of electromagnetic Lorentz forces to viscous forces in magnetohydrodynamic flows.

References

1. Magnetohydrodynamic Flow of a Bingham Fluid in a Vertical Channel: Mixed Convection. Fluids (2021).
2. Rayleigh–Bénard flow for a Carreau fluid in a parallelepiped cavity. Journal of Fluid Mechanics (2022).
3. 3D-Numerical simulation of free convection inside a cubical cavity filled with non-Newtonian-Bingham fluid. Al-Qadisiyah Journal for Engineering Sciences (2024).