This study investigates the complex interaction between Rayleigh–Bénard and Marangoni convection in liquid metal batteries (LMBs), which are essential for efficient large-scale energy storage. The challenge addressed is understanding how temperature gradients and layer thickness influence heat transfer and stability within LMBs, as effective thermal management is critical for improving battery performance and longevity. Using computational simulations, we modeled the fluid dynamics within a three-layer LMB system, observing how temperature-driven convection patterns, driven by buoyancy (Rayleigh–Bénard) and surface tension (Marangoni) forces, affect heat transfer. Key findings include that thinner middle layers enhance Marangoni effects, leading to a more efficient convective heat transfer, while thicker layers reduce this effect, impacting overall battery efficiency. This study also identifies critical conditions where these convection modes interact or destabilize, impacting the battery's thermal performance. This study introduces a novel approach by quantitatively demonstrating the joint influence of layer thickness and temperature gradients on heat transfer efficiency in liquid metal batteries, optimizing thermal management strategies beyond previous models.

Ultrasound imaging, often known as sonography, employs high-frequency sound waves to generate images of inside structures of human body. Its non-aggressive nature and real-time capabilities make it commonly used in medical diagnostics. Ultrasound waves are projected into the body and their echoes are recorded to produce intricate images of organs, tissues, and fetuses in utero, among other things. An essential aspect of enhancing image quality and safety involves the examination of how sound waves interact with biological tissues, including the phenomena of propagation, reflection, and absorption of ultrasound. It is commonly employed to monitor the well-being and growth of the fetus throughout pregnancy. Various organs, such as liver, kidneys, heart, and blood arteries, are also examined to detect abnormalities, tumors, and other disorders. This work investigates the behavior of gas bubbles with a spherical shape in non-Newtonian fluid when subjected to an external sonic field. Artificial intelligence has greatly impacted fluid dynamics by enhancing mesh efficiency, reducing manual intervention, offering dependable predictions, aiding in data analytics, and allowing for machine automation. This research investigates the behavior of bubbles in the flow of a tangent hyperbolic fluid model (THFM) through the application of artificial intelligence methods. The system employs Nonlinear Autoregressive with Exogenous inputs (NARX) networks trained with the Levenberg–Marquardt technique (LMT), known as NARX. The NARX-LMT model was applied to data produced using the Adams numerical approach for the THFM by systematically adjusting parameters such as Weber number, Weissenberg number, pressure affecting velocity, and bubble radius. The effectiveness of projected THFM is demonstrated comprehensively through mean square error generated iterative learning curves, error histogram plots, analysis of adaptive control factors, regression, and time series response metrics for different versions of nonlinear differential equations of THFM based on bubble dynamics.

In this report, a theoretical study is directed at the cilia motion of the Ellis fluid model due to the propagation of an infinite metachronal wave train traveling along the walls of the channel due to the continuous beating of the cilia. The governing equations of continuity and equation of motion for the well-known Ellis fluid model are carried out by taking long-wavelength approximations. The equations were solved with the help of the computational software Mathematica 13.0, and the results were obtained. The influence of physical parameters on pressure rise ( ∆ p \triangle p ), axial velocity u ( x , y ) u(x\left,y) , and stream function ψ ( x , y ) \psi (x,y) are exhibited graphically and discussed briefly. It is observed from graphical results that the velocity field shows a parabolic nature, achieves its highest magnitudes at the mid of the channel, and then reduces drastically at the walls of the channel. Velocity reduces with increasing material constant α and rises with increasing material constant β . It is also noted that pressure increases with rising α \alpha and β \beta . The present inquiry is also valid in the treatment of different symptomatic problems and different medicament delivery methods in pharmacological and biomedical engineering.