Machine Learning Model Predicts Engine Oil Heat Transfer Under Thermo-Diffusion Conditions

A computational investigation led by Abdulhadi A. Altherwi and colleagues demonstrates that an artificial neural network trained with the Levenberg-Marquardt algorithm can accurately model the coupled heat and mass transfer characteristics of a 10W40 engine oil hybrid nanofluid. Reporting in Discover Nano, the research team analyzed how cross-diffusion mechanisms, specifically the Dufour and Soret phenomena, influence automotive engine cooling dynamics across a stretching sheet embedded in a porous medium. By incorporating local thermal non-equilibrium formulations, the numerical computing framework accounts for distinct thermal profiles within the fluid and solid matrix phases, providing predictive capabilities aimed at developing energy-efficient vehicular lubrication systems that reduce operational friction and improve overall engine durability.

Conventional heat transfer analysis in permeable environments often relies on the local thermal equilibrium assumption, which treats the circulating fluid and the solid porous structure as sharing identical temperatures at every spatial point. The authors emphasize that when substantial thermal disparities arise between the liquid and solid phases, the single-equation equilibrium assumption fails to capture true transport physics. To resolve this limitation, the researchers implemented a two-equation local thermal non-equilibrium framework requiring separate thermal boundary conditions. Their governing mathematical model simulates steady two-dimensional fluid movement over a stretched surface subjected to a uniform transverse magnetic field, capturing the intricate coupled dynamics of fluid velocity, ambient thermal fields, and chemical species concentration.

The mathematical formulation translates physical conservation laws into a set of ordinary differential equations using similarity transformations. The model incorporates the Hamilton-Crosser formulation to describe the effective thermal conductivity of the hybrid nanofluid, alongside non-dimensional parameters including the magnetic interaction parameter, Prandtl number, Schmidt number, Dufour number, Soret number, radiation parameter, and the interphase heat transfer coefficient. These coupled formulations track how boundary layer thicknesses and transport rates respond to simultaneous variations in particle loading, magnetic strength, and cross-diffusion gradients, laying the groundwork for high-precision simulation data.

To overcome the intensive computational expense associated with traditional computational fluid dynamics and direct numerical simulations, the authors constructed a supervised machine learning framework. Operating on labeled numerical datasets generated across distinct parametric scenarios, the neural network optimizes internal connection weights via the Levenberg-Marquardt algorithm. This soft computing approach minimizes discrepancies between target numerical evaluations and artificial neural network predictions, generating an adaptive computational proxy capable of forecasting complex velocity, concentration, and multi-phase temperature fields in real time without sacrificing physical precision.

Model training and validation confirmed high predictive fidelity across multiple test cases, evaluated through regression analysis, error histograms, and mean squared error metrics. In Case I, the neural network attained an optimal training performance value of 6.16 multiplied by 10 to the negative ninth power at epoch 532, exhibiting near-perfect alignment between target and predicted curves. In Case II, the framework reached an optimal validation performance of 3.61 multiplied by 10 to the negative ninth power at epoch 951, with prediction errors clustering tightly around zero. For Case III, testing evaluations recorded an optimal performance value of 1.57 multiplied by 10 to the negative eighth power at epoch 924, accompanied by a regression coefficient of unity indicating complete statistical agreement.

Parametric analysis of fluid mechanics revealed that increasing the volume fraction of suspended nanoparticles systematically diminishes the flow velocity field. The authors attribute this velocity reduction to enhanced internal flow resistance and higher effective fluid viscosity introduced by the dispersed solid phase. Conversely, raising the nanoparticle volume fraction enhances the Nusselt number, demonstrating that denser nanoparticle concentrations actively improve heat transmission rates despite the corresponding hydrodynamic drag within the boundary layer.

Thermal and concentration behaviors responded strongly to cross-diffusion driving potentials governed by the Dufour and Soret numbers. The Dufour effect, which describes energy transport stimulated by concentration gradients, was shown to thicken the thermal boundary layer and elevate local fluid temperature profiles as its value rose. Higher Dufour values correspondingly accelerated the overall rate of heat transfer. Simultaneously, increasing the Soret parameter amplified both the concentration profiles and molar mass diffusivity, resulting in elevated Sherwood numbers and enhanced mass transmission rates throughout the moving fluid layer.

The study also examined the transitional behavior governed by the interphase heat transfer parameter and the porosity-modified conductivity ratio. As the interphase heat transfer coefficient increased, the liquid phase temperature expanded while the solid phase temperature declined, reflecting rapid thermal exchange across phases. At intermediate coefficient values, clear thermal gaps persisted, highlighting the necessity of non-equilibrium modeling. When the parameter reached sufficiently large values, the thermal difference between phases diminished toward equality, shifting system dynamics back toward local thermal equilibrium control. Validation against published integer-case benchmarks confirmed complete consistency with established literature.

The authors conclude that their integrated machine learning and non-equilibrium thermal transport model provides a practical foundation for designing advanced automotive cooling circuits, predictive maintenance strategies, and high-performance lubricants. While the mathematical architecture demonstrates robust noise tolerance and high computational efficiency under simulated boundary conditions, the findings remain based on numerical and soft computing models rather than physical engine dynamometer testing or clinical trials.

By capturing the interplay between thermo-diffusion effects, magnetic resistance, and solid-liquid thermal disparities, the study provides valuable computational insights into hybrid nanofluid engineering. The research establishes that artificial neural networks trained with Levenberg-Marquardt optimization can reliably bridge the gap between computational cost and physical accuracy, assisting engineers in tailoring 10W40 engine oil formulations for enhanced thermal dissipation and fuel efficiency under extreme convective conditions.

In contextualizing the broader technological utility of their work, the investigators note that nanofluids incorporate nanoparticles smaller than 100 nanometers to elevate basic heat conductivity across diverse operational environments. Such colloidal materials have expanded beyond conventional engineering operations into chemical reactors, solar collectors, refrigeration chillers, heat exchangers, aggregate manufacturing, and industrial coolant loops. Beyond these traditional settings, the paper highlights emerging uses in specialized fields including geothermal engineering, petroleum extraction, safe industrial cooling procedures, and precision biomedical therapies such as cancer treatments and brain tumor procedures. Fluid dynamics within permeable media form an essential operational component across many of these engineering applications.

Permeable structures consist of solid structural matrices with organized pore spaces that permit internal fluid motion. As detailed in the study, these systems encompass engineered media such as porous metal foams, ceramics, and composite materials, alongside natural porous configurations like sand formations, wood grain structures, and biological human lung tissue. Within industrial processing, permeable media serve crucial roles in microchemical reactors, steel and iron production, electrochemical energy platforms, and renewable fuel manufacturing systems. The researchers point out that previous fluid dynamics investigations regularly examined related dynamics, evaluating how variations in Darcy-Forchheimer porous configurations, Hall currents, chemical radiation, and diffusion absorption influence magnetohydrodynamic flows across expanding surfaces.

The authors explain that cross-diffusion mechanisms emerge when combined heat and mass transfer occur simultaneously during fluid motion, introducing complex couplings between driving potentials and transport fluxes. In physical systems, Soret and Dufour phenomena become significant whenever appreciable density variations appear across the flow domain, or when solutal concentrations of participating chemical species diverge substantially. In binary fluid systems involving gases or liquids with transitional atomic weights, these cross-diffusion forces govern the coupled migration of mass and thermal energy. Such interdependent transport behaviors govern real-world operational challenges in underground nuclear waste repositories, catalytic processing reactors, commercial drying units, thermal insulation arrays, and subterranean energy storage sites.

To capture the internal material characteristics of their working medium, the mathematical framework incorporates the porosity-modified conductivity ratio, denoted as gamma, which represents the direct ratio between fluid thermal conductivity and solid matrix conductivity. The authors observed that increasing this conductivity parameter directly elevates the thermal profiles within both the circulating liquid phase and the stationary solid phase.

The research emphasizes that machine learning methodologies, including artificial neural networks and regression frameworks, provide a computationally efficient alternative to traditional computational fluid dynamics simulations. Conventional numerical approximations often face intense computing overhead when resolving complex multi-phase velocity and temperature distributions, whereas supervised neural architectures decrease processing expenses while maintaining high physical fidelity. By leveraging high-fidelity training data, these intelligent computational networks can reliably forecast real-time fluid velocity, pressure fields, and thermal gradients across varied geometrical boundaries, effectively closing the historical gap between simulation precision and practical engineering turnaround times.

Subject of Research: Machine learning prediction of thermo-diffusion and heat transfer in engine oil hybrid nanofluids

Article Title: Machine learning algorithm of thermo-diffusion effects on 10W40 engine oil hybrid nanomaterial for automotive engine cooling

Article References: Altherwi, A. A., Anja, M. I. A., Yildirim, Y., Shano, L., & Abdulakimov, G. (2026). Machine learning algorithm of thermo-diffusion effects on 10W40 engine oil hybrid nanomaterial for automotive engine cooling. Discover Nano, 21(1), Article 540. https://doi.org/10.1186/s11671-026-05024-4

Image Credits: AI Generated

DOI: 10.1186/s11671-026-05024-4

Keywords: 10W40 engine oil, hybrid nanofluid, thermo-diffusion, Dufour effect, Soret effect, local thermal non-equilibrium, artificial neural network, Levenberg-Marquardt algorithm, automotive cooling, porous media, heat transfer, mass transfer, Nusselt number, Sherwood number, thermal conductivity, computational fluid dynamics