Stagnation-Point Flow Dynamics in Non-Newtonian Fluids

Stagnation-point flow occurs where a fluid stream impinges on a surface or obstacle and the local velocity falls to zero, creating strong gradients in pressure and shear. In non-Newtonian fluids, whose viscosity and normal stress responses depend on shear rate and elastic effects, the classical stagnation-point problem acquires additional complexity through viscoelasticity, shear-thinning or shear-thickening characteristics, and stress relaxation. Mathematical models often invoke boundary-layer approximations and similarity transformations to reduce the governing conservation equations to ordinary differential form. Numerical methods such as finite-difference schemes, spectral techniques and homotopy analyses then yield solutions for velocity, stress and temperature fields. These solutions underpin applications ranging from polymer processing and microfluidic mixing to thermal management in renewable-energy systems. Key phenomena include the influence of fluid relaxation on flow separation, the coupling of heat and mass transport under external fields, and the role of surface slip or lubrication layers in tailoring shear stresses at solid boundaries.

Research from Nature Portfolio

Recent studies have elucidated the oblique stagnation-point flow of a viscoelastic Maxwell fluid over a stretchable surface subject to a transverse magnetic field and convective thermal conditions. Incorporating a finite-speed thermal model, the analysis shows that the thermal relaxation parameter markedly reduces heat-transfer rates while the magnetic field alters the momentum boundary layer and modifies tangential and normal velocity profiles. The Deborah number, representing the ratio of relaxation time to flow time scale, is found to suppress both components of velocity in the vicinity of the stagnation point. These results pave the way for optimising cooling and extrusion processes in viscoelastic suspensions under magnetic control.

Stagnation-Point Flow Dynamics in Non-Newtonian Fluids publication trend

The graph below shows the total number of articles in stagnation-point flow dynamics in non-newtonian fluids across all publications each year (not limited to Nature Index journals).

Technical terms

Stagnation point: A location in a flow field where fluid velocity is zero and pressure reaches a local maximum.

Non-Newtonian fluid: A fluid whose viscosity or stress response varies with shear rate, time or deformation history.

Maxwell fluid: A viscoelastic fluid model characterised by a single relaxation time, combining viscous and elastic behaviour.

Jeffrey fluid: A generalised viscoelastic model incorporating both relaxation and retardation times to capture complex stress responses.

Cattaneo–Christov heat flux: A modification of Fourier’s law introducing finite thermal propagation speed and material frame indifference.

Deborah number: A dimensionless number giving the ratio of fluid relaxation time to a characteristic flow time.

Slip: A boundary condition allowing relative motion between a fluid and solid surface, reducing shear stress at the interface.

References

1. Heat transfer in Jeffrey fluid flow over a power law lubricated surface inspired by solar radiations and magnetic flux. Case Studies in Thermal Engineering (2023).
2. Oblique stagnation point flow of magnetized Maxwell fluid over a stretchable Riga plate with Cattaneo-Christov heat flux and convective conditions. Scientific Reports (2023).
3. Mathematical modeling and computational outcomes for the thermal oblique stagnation point investigation for non-uniform heat source and nonlinear chemical reactive flow of Maxwell nanofluid. Case Studies in Thermal Engineering (2023).
4. Thermal performance comparative analysis of nanofluid flows at an oblique stagnation point considering Xue model: a solar application. Journal of Computational Design and Engineering (2022).