CU Journal of Non-Linear Fluid Mechanics

A Computational Study on the Radiative Thermal Transport of Nanofluids Past a Stretching Boundary

2026-08-17T03:48:24+00:00

The present study deals with the thermal analysis of a nanofluid past the stretching sheet in
presence of radiation. Thermal and mass transport are also modelled considering viscous
dissipation and the effects of chemical reaction. Additionally, temperature-dependent and
concentration-dependent heat source terms are incorporated into the energy equation to
examine their influence on the thermal transport characteristics of the nanofluid. An increase
in the internal heat generation parameter enhances the temperature distribution within the
boundary layer due to the additional volumetric heat supplied to the fluid, thereby thickening
the thermal boundary layer and reducing the wall temperature gradient. Thus, this is
incorporated into the energy equation. The governing equations were formulated using partial
differential equations (PDEs). These equations are then transformed into ODEs through the
application of similarity transformations to obtain the solution. The resulting system of ODEs
is subsequently solved using the Runge–Kutta–Fehlberg (RKF45) method. The effect of the
dimensionless parameters on the nanofluid's temperature, concentration, and velocity profiles
is presented graphically using the numerical solutions. The outcomes of the study depicts that
the temperature profile upsurges when the heat source dependent on temperature and the
concentration increases. It was noted that there is a lowering in the velocity profile with rise
in the velocity slip parameter while the thermal profile increases with increase in thermal
radiation.

The Clay Navier–Stokes Problem as a Boundary of Effective Fluid Theories: A Conceptual Perspective

2026-06-24T05:58:57+00:00

The Clay Millennium Prize Problem on the Navier–Stokes equations asks whether smooth solutions to the three-dimensional incompressible system on R3 remain globally regular or can exhibit finite-time blow-up. This paper offers a conceptual perspective rather than a new mathematical theorem. We situate the Clay problem within a hierarchy of physical breakdowns: continuum failure at high Knudsen number, non-Newtonian rheology, limitations of numerical closures, and transitions to relativistic or quantum hydrodynamics. We then formalize the notion of an analytic “boundary of effective description” and relate it to known mathematical results—Leray–Hopf weak solutions, Prodi–Serrin regularity criteria, partial regularity theory (Caffarelli–Kohn–Nirenberg), and scaling criticality. Our central claim, stated carefully, is that if finite-time blow-up occurs for the 3D Navier–Stokes equations, the singularity would occur at scales where the continuum hypothesis itself becomes physically suspect; conversely, global regularity would confirm the self-consistency of this effective model. Neither outcome affects the logical independence of the mathematical problem. The paper aims to bridge the mathematical theory of Navier–Stokes regularity with the physics of effective descriptions, without conflating the two domains.

The Clay Navier–Stokes Problem as a Boundary of Effective Fluid Theories

2026-06-24T05:58:14+00:00

The Clay Millennium Prize Problem on the Navier–Stokes equations asks whether smooth solutions to the three-dimensional incompressible Navier–Stokes system on R3 remain globally regular or can exhibit finite-time blow-up. Although posed as a purely analytical question, the Navier–Stokes equations are not fundamental laws of nature but rather an effective continuum model derived from more microscopic descriptions. In this paper, we situate the Clay problem within a hierarchy of physical breakdowns: continuum failure at high Knudsen number, non-Newtonian or complex rheology, limitations of numerical and turbulence closures, and the transition to relativistic or quantum hydrodynamics. We argue that the Clay question probes the internal self-consistency of one specific effective layer in this hierarchy. Any eventual blow-up or regularity result should be interpreted against the backdrop of the known physical regimes where the Navier–Stokes equations cease to apply. From this perspective, the Navier–Stokes system neither describes all fluids nor claims to be a UV-complete theory; the Clay problem is best understood as a test of how far this macroscopic idealization can be pushed before it signals its own limits.

Retention of Axially Input Arsenic Contaminants in a Heterogeneous Groundwater System under Sorption Isotherm Models

2026-08-22T06:01:28+00:00

The presence of arsenic contaminants in groundwater poses a risk to the surrounding ecosystem. The retention of contaminants in the soil medium leads to soil degradation and affects vegetation, with the risk of desorption. This research focuses on the retention strength of arsenic contaminant onto the soil medium under different sorption models (Henry, Freundlich,
Langmuir and Tóth). It presents a two-dimensional numerical model for contaminant transport in groundwater, governed by the advection-dispersion equation (ADE). A concentration-dependent retardation factor is considered for the sorption models to introduce nonlinearity into the system. An Alternating Direction Implicit (ADI) scheme, combined with the Thomas algorithm, is employed to ensure numerical stability and computational efficiency for long-term simulations. The
numerical results demonstrate that nonlinear sorption significantly attenuates contaminant migration and modifies arsenic plume evolution compared to non-sorbing cases. The spatial concentration maps of arsenic contaminants, compared with unit retardation, reveal substantial accumulation within the soil matrix. This highlights the significance of accounting for nonlinear sorption effects in the realistic transport and fate of groundwater contamination. A study on a soil medium revealed that the amount of arsenic retained in the medium is directly proportional to the soil’s Al/Fe content, offering insights for environmental studies and understanding the harmful effects of arsenic retention. The research is aligned with SDG 3 (Good Health and Well-being), SDG 6 (Clean Water and Sanitation), and SDG 14 (Life Below Water).

Chief Editor’s note on behalf of the editorial board

2026-09-04T08:21:33+00:00