A computational investigation has evaluated the coupled momentum and heat transfer mechanisms in an electrically conducting five-component nanofluid flowing past a vertically stretched sheet. Conducted by researchers including Iqra Karim, Mustefa Abduletif Mamud, Mohamed Arbi Khlifi, Adnan, Walid Abdelfattah, Heba G. Mohamed, Yasir Khan, and Muhammad Nasir Bashir, the study modeled how combined physical influences—specifically magnetic fields, Joule heating, viscous dissipation, and thermal radiation—alter the dynamic and thermal behavior of the fluid. The authors converted the governing nonlinear boundary layer formulations into a dimensionless system using similarity transformations and subsequently evaluated the transport phenomena across parameter ranges using an Artificial Neural Network framework.
Blending multiple distinct nanoparticle species into a single base fluid creates hybrid suspensions where synergistic interactions between particle types can augment effective thermal conductivity, dynamic viscosity, heat capacity, and thermal expansion. Understanding these complex transport behaviors under multi-physical constraints provides a theoretical foundation for regulating thermal electromagnetic operations in high-temperature surface processes.
The mathematical formulation treats the flow of the five-component suspension, designated as a penta nanofluid, as a steady, two-dimensional, laminar, and incompressible boundary layer problem adjacent to an impermeable vertical sheet. In the physical coordinate system, the surface stretches along the vertical x-direction with an exponential velocity distribution while subject to an external free-stream velocity and an exponential wall temperature distribution. A uniform ambient temperature and reference temperature establish the thermal environment, while a magnetic field acts normally to the surface with a position-dependent intensity. The fluid components are assumed to be in thermal equilibrium without chemical reactions, and the nanoparticles are treated as homogeneously dispersed throughout the conventional base liquid.
To capture the multi-physical dynamics, the governing continuity, momentum, and energy conservation equations incorporate viscous diffusion, convective acceleration, electromagnetic interaction, internal viscous dissipation, resistive Ohmic heating, and radiative transport. The momentum formulation accounts for the Lorentz force arising from the interaction between the electrically conducting nanofluid and the transverse magnetic field, introducing electromagnetic drag relative to the external stream. In the thermal energy balance, the model accounts for conductive diffusion alongside kinetic energy dissipation due to fluid shear, electrical resistive dissipation via Joule heating, and radiative flux modeled through the Rosseland approximation.
By applying similarity transformations and stream functions, the authors reduced the governing partial differential equations into a set of ordinary differential equations. These equations incorporate key dimensionless groups: the stretching parameter lambda, the Hartmann number representing magnetic field strength, the Eckert number denoting viscous dissipation intensity, the thermal radiation parameter, the Prandtl number, and individual nanoparticle volume fractions ranging from 0.1 percent to 0.4 percent. The resulting boundary value system was initially solved by conversion into an initial value problem using the bvp4c scheme, generating reference data across parameter ranges to train, validate, and test the neural network algorithm.
The artificial neural network scheme processed the generated datasets to predict the velocity profiles and temperature fields across different operating conditions. Computational assessments indicated high agreement across training, validation, and testing phases, with regression values demonstrating consistent convergence and minimal error histograms. Validation of the mathematical model against previously published limiting cases for conventional nanofluids in the absence of a magnetic field confirmed consistent skin friction results, confirming the accuracy of the numerical and learning framework in reproducing physical boundary layer trends.
Analysis of the velocity distribution revealed that surface stretching strongly accelerates fluid motion within the boundary layer. As the stretching parameter lambda increases from 0.1 to 0.4, the momentum transferred from the moving wall into the fluid intensifies, causing the velocity near the surface to rise noticeably before matching the external stream. Conversely, increasing the Hartmann number from 0.2 to 0.8 opposes the flow. The transverse magnetic field interacts with the moving conducting fluid to generate opposing Lorentz forces, which act as electromagnetic resistance, suppressing the velocity distribution across the boundary layer.
The addition of nanoparticles also influences fluid momentum. Increasing the concentration of the constituent nanoparticles between 0.1 percent and 0.4 percent progressively reduces fluid velocity due to elevated effective density and dynamic viscosity, which together increase resistance to flow. This deceleration is particularly evident at lower particle concentration stages, while remaining systematic across all components. These findings confirm that while higher particle loading alters hydrodynamic resistance, surface movement remains the dominant driver of boundary layer acceleration.
In contrast to the opposing effects observed on velocity, thermal analysis demonstrated that several physical parameters substantially enhance the temperature distribution within the boundary layer. Elevating the Eckert number from 0.1 to 0.4 triggers a rapid increase in fluid temperature. Because the Eckert number represents the conversion of kinetic energy into internal thermal energy through fluid friction, stronger viscous dissipation produces additional heat within the moving fluid. Thermal radiation similarly augments the thermal field; increasing the radiation parameter from 1.0 to 7.0 contributes extra radiative heat flux relative to pure conduction, thereby thickening the thermal boundary layer.
The concentration of the five nanoparticle types showed a consistently positive contribution to the heat transfer mechanism. As individual volume fractions varied from 0.001 to 0.004, the temperature profiles rose steadily across the domain. The authors observed that changes in nanoparticle concentration generate a more pronounced impact on thermal profiles than on velocity profiles, reflecting altered thermal conductivity and energy storage capacity in the composite medium. Meanwhile, strengthening the Hartmann number produced only a mild thermal increase via Joule heating, indicating that magnetic resistive dissipation contributes modestly to overall thermal enhancement relative to direct radiation and viscous shear.
The researchers noted specific theoretical constraints governing the study’s scope. The mathematical formulation is restricted to steady, laminar, single-phase boundary layer flow and does not encompass turbulent, transient, or multi-phase phenomena such as particle sedimentation, agglomeration, or thermophoresis. Additionally, the analysis adopts the Rosseland approximation for thermal radiation and excludes induced secondary magnetic fields. Future investigations may expand upon this foundation by modeling non-Newtonian behavior, temperature-dependent thermophysical properties, variable magnetic fields, and deep learning or metaheuristic optimization strategies.
The mathematical architecture of the boundary layer relies on exact exponential distributions that govern the interfacial kinematics along the vertical sheet. The wall stretches with a surface velocity defined by the product of a dimensional rate parameter and an exponential function of the coordinate distance relative to the reference length, while the free stream accelerates in parallel with its own exponential velocity. The ratio of the surface stretching rate to the free-stream velocity parameter establishes the dimensionless stretching parameter lambda, distinguishing positive stretching behavior from negative shrinking motions. By defining a specialized stream function dependent on the kinematic viscosity of the base fluid, the reference length, and the external flow rate, the researchers expressed the horizontal and vertical velocity distributions through the dimensionless stream variable F and its first derivative. Concurrently, the surface temperature varies exponentially from the uniform reference value above ambient conditions, scaling the dimensionless temperature function beta across the finite boundary layer until it decays completely to ambient thermal levels at infinite distance from the surface.
To characterize the complex multi-particle medium, the mathematical model incorporates explicit formulations for each physical property of the penta nanofluid. The effective dynamic viscosity of the mixture is determined by dividing the viscosity of the base fluid by five consecutive volume fraction reduction factors, each raised to the power of two point five, capturing the progressive hydrodynamic resistance introduced by each particle addition. Sequential multi-stage relations similarly define effective density, volumetric heat capacity, electrical conductivity, and thermal conductivity, tracking the cumulative physical modification from the initial base fluid through intermediate binary, ternary, and quaternary blends to the final five-component suspension. From these relations, the authors derived the primary diagnostic quantities of industrial interest, namely the local skin friction coefficient and the local Nusselt number. These dimensionless metrics link the physical wall shear stress and interfacial heat flux to the local Reynolds number, the second derivative of the stream function at the wall, and the wall temperature gradient.
Related investigations into conducting fluids illustrate how electromagnetic fields govern liquid metal blanket flows in nuclear fusion concepts, including lithium-lead coolant architectures influenced by internal buoyancy and external magnetic drag. In industrial settings such as paper manufacturing, thin-film coating, aerodynamic extrusion of polymeric sheets, and glass fiber fabrication, fluid motion and surface heat removal operate under combined viscous shear friction and thermal radiation.
Subject of Research: Artificial intelligent computing of penta-hybrid nanofluid thermal and momentum transport
Article Title: Artificial intelligent computing of advanced nanomaterials under electrothermal heating
Article References: Karim, I., Mamud, M. A., Khlifi, M. A., Adnan, Abdelfattah, W., Mohamed, H. G., Khan, Y., & Bashir, M. N. (2026). Artificial intelligent computing of advanced nanomaterials under electrothermal heating. Discover Nano, 21(1), Article 583. https://doi.org/10.1186/s11671-026-05073-9
Image Credits: AI Generated
DOI: 10.1186/s11671-026-05073-9
Keywords: nanofluids, artificial neural networks, heat transfer, magnetohydrodynamics, thermal radiation, fluid mechanics, computational modeling, Joule heating, Artificial, intelligent, computing, advanced
News Source: Cassandra Pierce. (November 11, 2026). Neural Network Models Heat and Fluid Flow in Multicomponent Nanofluids. Scienmag.
