Kuppalapalle Vajravelu

Building upon the theoretical investigation of fully developed porous-channel flow by Nield et al. ( J. Fluid Mech. vol. 322, 1996, 201–214), the present study examines hydrodynamically developing flow in anisotropic porous channels to better characterise realistic transport behaviour. A variational formulation for the steady incompressible Darcy–Brinkman–Forchheimer (DBF) equations is derived, where the Darcy, Brinkman and Forchheimer terms represent porous drag, viscous shear effects and nonlinear inertial resistance, respectively. The existence and uniqueness of solution are established using the Browder–Minty theorem together with the inf-sup condition to ensure the uniqueness of the pressure field. The porous medium is represented through a spatially varying anisotropic permeability tensor to account for directional resistance effects. A physics-informed neural network (PINN) framework using feed-forward deep neural networks (DNNs) is employed to solve the coupled nonlinear DBF equations solely from the governing equations and boundary conditions, without the need for external simulation or experimental data. Results indicate that lower anisotropic permeability ratios enhance both axial and transverse velocity components, whereas increasing the Darcy number substantially reduces pressure drop due to weakened porous resistance. The proposed framework provides an effective approach for modelling anisotropic porous-medium flows relevant to subsurface transport, filtration, biomedical devices and energy-storage systems.

Pharmaceutical delivery, microelectronics, fuel cell membranes, water purification, crackresistant coatings, thermal energy plants, catalysts, micro-capacitors, and car cooling systems all benefit from developments in nanotechnology. In each of these applications, ethylene glycol performs exceptionally well. The effects of a ternary hybrid nanofluid (C₂H₆O₂/CuO, TiO₂, Ag) on a rotating stretching sheet, including Darcy-Forchheimer, stagnation, radiation, and Soret-Dufour (Cross-Diffusion), were analysed using the Williamson fluid model. Using appropriate similarity transformations, the set of partial differential equations (PDEs) governing the model is first transformed into a set of ordinary differential equations (ODEs). The “bvp4c” boundary-value problem solver in MATLAB is then used to numerically solve the equations. Additionally, tables and visuals are used to display the results of parameters affecting the flow. The variations in the temperature, concentration, and velocity fields arising from radiation, cross-diffusion, and Darcy-Forchheimer processes are succinctly described in this paper. As the Darcy-Forchheimer and magnetic parameters increase with temperature, the primary velocity decreases while the secondary velocity increases. In the current investigation, the fluid's thermal efficiency increases by 8.92% with the inclusion of these nanoparticles.

This paper presents the theoretical modelling of the microfluidic transport of immiscible, non-Newtonian fluids (specifically, Jeffrey and Casson fluids) through a vertical porous medium by considering magnetohydrodynamic, Hall current, electroosmotic, buoyancy, thermal radiation, and internal heat generation effects all simultaneously. Current literature in this area has primarily focused on Newtonian or single non-Newtonian fluid flows and has not addressed two distinct non-Newtonian fluid flow models in multiphase porous systems with Hall effects and electroosmosis. To accomplish this goal, governing continuity, momentum, and energy equations were formulated for each of the two fluids, the equations were reduced to non-dimensional form through appropriate scaling and analytical solutions for velocity and temperature distributions were obtained. The key findings of this study include that the velocity profile of both fluids is enhanced at high permeability and at high electroosmotic flow parameters and is reduced by the Lorentz force associated with a high magnetic field strength. Theoretical modelling at this level can provide important information on the dynamics of immiscible fluids that can be applied to the design and operation of microfluidic systems and technological applications associated with energy transport and thermal management for cooling systems.