Heat Transfer Models in Viscoelastic Fluid Dynamics

Heat transfer in viscoelastic fluids examines the coupled influence of viscous dissipation and elastic energy storage on thermal transport. Classical Fourier conduction has been augmented by hyperbolic models—most notably the Cattaneo–Christov heat flux theory—to incorporate finite thermal propagation speeds and relaxation effects. These heat‐flux models are typically combined with simple rheological constitutive equations such as the Maxwell or Oldroyd-B models to capture fluid elasticity. Solutions often employ similarity transformations and numerical schemes to resolve boundary‐layer equations under diverse forcing conditions, including magnetic fields, chemical reactions and variable wall dynamics. Key dimensionless parameters—Deborah number, Prandtl number and thermal relaxation time—govern the thickness of momentum and thermal boundary layers, Nusselt number distributions and entropy generation. Such insights inform the design of polymer processing units, biomedical devices, energy systems and advanced cooling strategies.

Research from Nature Portfolio

Recent studies have addressed the flow of an upper-convected Maxwell fluid over an exponentially stretching sheet, introducing a chemical reaction on the Cattaneo–Christov heat flux model. Using similarity transformations and successive linearisation, the governing nonlinear equations yield detailed velocity, temperature and concentration profiles. Results demonstrate that increasing thermal relaxation time leads to thinner thermal boundary layers and higher local Nusselt numbers, while reaction rates modulate concentration thickness. These findings carry direct implications for optimising heat and mass transport in biological fluids and industrial processing of complex polymer solutions.

Heat Transfer Models in Viscoelastic Fluid Dynamics publication trend

The graph below shows the total number of articles in heat transfer models in viscoelastic fluid dynamics across all publications each year (not limited to Nature Index journals).

Technical terms

Viscoelastic fluid: A fluid exhibiting both viscous flow and elastic deformation under applied stress.

Maxwell fluid: A linear viscoelastic model combining a Newtonian dashpot and elastic spring in series, characterised by a single relaxation time.

Cattaneo–Christov heat flux model: A non-Fourier constitutive relation that incorporates thermal relaxation time and fluid frame indifference for hyperbolic heat conduction.

Thermal relaxation time: The characteristic time delay between the imposition of a temperature gradient and the resulting heat flux in non-Fourier models.

Nusselt number: A dimensionless measure of convective heat-transfer rate relative to conductive heat transfer across a boundary layer.

References

1. Impact of chemical reaction on the Cattaneo–Christov heat flux model for viscoelastic flow over an exponentially stretching sheet. Scientific Reports (2024).
2. Entropy generation analysis on Darcy-Forchheimer Maxwell nanofluid flow past a porous stretching sheet with threshold Non-Fourier heat flux model and Joule heating. Case Studies in Thermal Engineering (2023).
3. Natural convection of a viscoelastic Cattaneo–Christov fluid bounded by thick walls with finite thermal conductivity. Journal of Non-Equilibrium Thermodynamics (2023).
4. Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper-convected Maxwell fluid. AIP Advances (2015).