Thermal radiation reshapes heat flow in bioconvective Casson nanofluid study

Engineers have long sought a complete picture of how heat, mass and momentum move together in exotic fluids, and a new theoretical study published in Results in Chemistry delivers one of the most comprehensive treatments to date. A team led by V. Madhusudanan, with collaborators including L. Guerrini, D. Iranian, Raja R., Ilyas Khan and Ilker Ozsahin, has built a unified three-dimensional model of a Casson nanofluid flowing over a stretching sheet, layering in thermal radiation, viscous dissipation, magnetohydrodynamic effects with Hall currents, Soret–Dufour cross-diffusion, Arrhenius-type chemical reactions, gyrotactic bioconvection and four distinct slip mechanisms at the surface. The work, published under DOI 10.1016/j.rechem.2026.103888, stands out because previous three-dimensional Casson-flow studies had each tackled only fragments of this physics, never all of it at once.

Casson fluids occupy a special place in rheology. Unlike simple Newtonian liquids such as water, they possess a yield stress: below a critical applied stress they behave like solids, and only above that threshold do they flow. Blood is the canonical example, but polymer melts, printing inks and industrial suspensions also fall into this class. The Casson parameter in the new model quantifies how strongly the yield-stress behavior manifests, and the researchers found that raising it lets the fluid flow more freely along the stretching sheet, accelerating both the primary streamwise velocity and, to a much lesser degree, the secondary cross-flow induced by Hall currents. The secondary component barely responds to yield-stress changes, a subtle but telling sign that Casson rheology dominates the direction aligned with the stretching motion while the magnetically driven cross-flow marches to a different physical drumbeat.

The magnetic side of the problem introduces its own drama. A transverse magnetic field applied perpendicular to the sheet generates a Lorentz force that resists fluid motion, and the team captured this through a Hall-modified magnetic parameter that accounts for the fact that, under strong fields, the classical Ohm’s law breaks down. As this parameter grows, both velocity components decline because the magnetic damping force actively opposes forward motion. Yet the same magnetic field heats the fluid through Joule heating, the electrical resistance of the conducting nanofluid converting electromagnetic work into thermal energy. The result is a striking asymmetry: magnetic fields slow the flow while warming it, a combination that designers of electromagnetic pumping systems and metallurgical casting operations must weigh carefully.

The paper’s most counterintuitive finding concerns thermal radiation. Modeled through the Rosseland diffusion approximation for optically thick media, radiation increases the effective thermal diffusivity of the fluid, thickening the thermal boundary layer and raising temperatures throughout. But the tabulated Nusselt numbers tell a paradoxical story: as the radiation parameter climbs from 0.1 to 2, the wall heat transfer rate falls from 0.42871 to 0.1945. Radiation spreads thermal energy through the bulk of the fluid, flattening the temperature gradient right at the wall, and it is that near-wall gradient that determines how much heat actually escapes the surface. For engineers designing combustion chambers, solar receivers or glass manufacturing lines, where radiative effects dominate, this means that simply increasing radiative transport can quietly undermine heat removal, and mitigation strategies such as low-emissivity coatings or enhanced forced convection become essential.

Viscous dissipation compounds the thermal challenge. Quantified by the Eckert number, it represents the irreversible conversion of mechanical energy into heat through internal friction, and it grows severe in high-speed flows, polymer extrusion and microfluidic channels. In the new calculations, raising the Eckert number from zero to 0.5 drives the Nusselt number down from 0.35639 to 0.19763, because the internally generated heat erodes the temperature difference that drives wall heat transfer. In extreme cases, dissipation can push fluid temperatures above the wall temperature itself, creating thermal overshoots that threaten material integrity. The study’s quantitative tables give designers concrete numbers for anticipating when these overshoots become dangerous.

Cross-diffusion effects, the reciprocal coupling between temperature and concentration fields, add another layer of complexity. The Soret effect describes how temperature gradients drive mass flux, while the Dufour effect describes how concentration gradients drive heat flux. In the energy equation, the Dufour term acts as an additional heat sink in the boundary layer, and the results show that increasing the Dufour number from zero to 0.5 boosts the Nusselt number from 0.29273 to 0.4523, a genuinely beneficial coupling that enhances heat removal beyond what conduction and convection alone can achieve. The Soret effect, by contrast, slightly impairs mass transfer, nudging the Sherwood number downward as it rises, while modestly elevating concentration profiles through thermodiffusion. The authors note that these effects become order-unity corrections in high-gradient environments such as chemical vapor deposition, isotope separation and geothermal energy extraction, and cannot be neglected there even though they are secondary in milder settings.

Chemical reactions with Arrhenius activation energy intensify the thermal-concentration coupling because reaction rates depend exponentially on temperature, so small thermal fluctuations can produce order-of-magnitude swings in reaction kinetics. This nonlinearity matters enormously in catalytic reactors, combustion chambers and reactive separation processes. Meanwhile, the bioconvection component of the model captures the behavior of gyrotactic microorganisms, which swim in directed ways in response to gravitational and viscous torques and migrate toward nutrient-rich regions. Their collective motion generates density gradients that induce convective flow, and the study shows that the bioconvection Lewis number and Peclet number exert dramatic control over microorganism distributions. As the Lewis number climbs from 0.1 to 2, the motile microorganism density number rises from 0.30252 to 1.0326, reflecting how low-motility organisms become sharply confined near surfaces, potentially triggering bioconvective instabilities marked by collective upwelling.

The numerical machinery behind these findings is rigorous. The team transformed the full set of coupled nonlinear partial differential equations into ordinary differential equations via similarity transformations, then solved them with a fourth-order Runge–Kutta-Fehlberg method paired with a shooting technique and Newton–Raphson iteration, converging to a tolerance of ten to the minus six. Crucially, they validated the code against an exact analytical solution available in a simplified limiting case, achieving agreement to better than one part in ten thousand across a range of Casson parameters, and confirmed that their computational domain and far-field residuals were fully converged. This kind of benchmark-anchored validation lends real credibility to the parametric tables that form the study’s practical core.

Those tables reveal a clear hierarchy of influence that could streamline engineering design. Momentum transport is governed chiefly by the Casson parameter, magnetic damping and porous-medium permeability, with the permeability parameter showing nonmonotonic behavior in skin friction as Darcy resistance first concentrates momentum near the wall and then slows the flow entirely. Thermal transport is dominated by the Prandtl number, which at a fixed height cuts dimensionless temperature by 82 percent as it rises from 0.71 to 2.0, followed by radiation and dissipation. Mass transfer hinges on the Schmidt number, which lifts the Sherwood number from 0.1968 to 0.59234 across its tested range, while bioconvection is steered by the Lewis and Peclet numbers. Slip conditions and cross-diffusion act as secondary but non-negligible corrections, important chiefly in microscale and rarefied applications where the no-slip assumption fails.

The practical reach of the work spans heat exchangers, electronic cooling, nuclear reactor thermal management, biomedical therapies, bioreactors, wastewater treatment and drug delivery systems, wherever simultaneous control of momentum, heat, mass and living microorganisms is required. In algae photobioreactors, for instance, maintaining moderate Lewis and Peclet numbers prevents excessive wall accumulation that would shade cells and form biofilms, while microbial fuel cells benefit from the opposite regime, maximizing electrode colonization. The authors caution that their model assumes constant thermophysical properties, steady forcing and classical Fourier heat conduction, and they flag unsteady effects, nanoparticle aggregation and experimental validation as the natural next steps. Even so, by quantifying how radiation, dissipation, cross-diffusion, magnetism and bioconvection compete within a single validated framework, the study offers engineers a rational map for navigating some of the most tangled multiphysics in modern thermal design.

Subject of Research: Thermal radiation and coupled transport mechanisms in bioconvective Casson nanofluid flow over a stretching sheet

Article Title: Impact of thermal radiation in bioconvection Casson nanofluid flow with cross-diffusion

Article References: Madhusudanan, V., Guerrini, L., Iranian, D., R., R., Khan, I., & Ozsahin, I. (2026). Impact of thermal radiation in bioconvection Casson nanofluid flow with cross-diffusion. Results in Chemistry, 31, Article 103888. https://doi.org/10.1016/j.rechem.2026.103888

Image Credits: AI Generated

DOI: 10.1016/j.rechem.2026.103888

Keywords: Casson nanofluid, thermal radiation, bioconvection, Soret-Dufour, magnetohydrodynamics, Hall current, viscous dissipation, stretching sheet, boundary layer, Nusselt number, gyrotactic microorganisms, heat transfer