New mathematical model accelerates the design of industrial lubrication systems

An international team of researchers has developed an advanced computational model based on a neural network that can quickly and accurately predict the behavior of motor oil enriched with nanoparticles under heating and flow in demanding industrial conditions. This makes it possible to significantly speed up calculations required for the development of more efficient technologies.

Researchers from the Czech Republic, Pakistan, Saudi Arabia and China focused on simulating the complex flow of motor oil containing nanoparticles of aluminum oxide and titanium dioxide. Although such a fluid enhances heat more effectively, its behavior is considerably more complex than that of conventional fluids.

„This represents a real challenge. The fluid flow occurs in the presence of a magnetic field, thermal radiation, internal heat generation, and a chemical reaction with activation energy. All these effects had to be incorporated in order to develop a functional model and accurately predict the fluid’s behavior,“ says Mohammad Ayman Mursaleen of the Department of Mathematics, Faculty of Science, University of Ostrava.

Traditional calculations of this type of fluid flow require solving a system of strongly nonlinear equations, which is computationally demanding and must be repeated whenever conditions change. The new model, however, works differently.

„The neural network first learned the system’s behavior from accurate numerical simulations and can then rapidly predict how the fluid will respond to changes in conditions while maintaining a high level of accuracy. The computations can be performed approximately 50 percent faster than with conventional numerical methods,“ Mursaleen concludes.

Faster simulations in practice mean that engineers can test more design variants within the same amount of time, such as different nanoparticle concentrations, magnetic field intensities, or flow conditions, and search for optimal configurations of lubrication and cooling systems.

The study also demonstrates that modern mathematics plays a key role in the design of contemporary technologies. The combination of mathematical modeling and neural networks may find applications in other areas where fast and accurate simulation of complex fluid flow and heat transfer is required, including energy and mechanical engineering as well as other industrial sectors.

Ayman-Mursaleen, M., Saeed, S. T., Almohammadi, S. M., Ali, F., & Alshatwi, S. (2026). A deep neural network model for heat transfer in darcy–forchheimer hybrid nanofluid flow with activation energy. Scientific Reports, 16(1), 3291.

Updated: 20. 03. 2026