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This study investigates the two-dimensional magnetohydrodynamic (MHD) boundary-layer flow over a stretching sheet embedded in a porous medium, focusing on the innovative use of hybrid nanofluids. The research has practical applications in heat exchangers, nanofluid technology, porous media, and MHD systems. Key governing parameters, including internal heat sources/sinks, multiple slips, and thermal radiation, are analyzed for their impact on the flow. The nanofluid consists of hybridized nanoparticles (Alumina-Magnetite) dispersed in a water and ethylene glycol mixture (WEG-50:50). Assuming steady-state, incompressible, and laminar flow with small boundary layer thickness and constant nanofluid properties, the governing equations for continuity, momentum, energy, and species concentration are formulated. The fluid is modeled as a non-Newtonian (Maxwell) fluid. The resulting nonlinear ordinary differential equations system, with specified boundary conditions, is solved using the Runge-Kutta integration scheme implemented in MAPLE 23. Numerical results of heat transfer rates are validated against existing data, showing a 12 % increase in the Nusselt number for the WEG-Al2O3 nanofluid and a 20 % increase for the hybrid WEG- Al2O3–Fe3O4 nanofluid. It is demonstrated that skin friction decreases by up to 15 % with increased thermal Grashof number and that the Nusselt number can be reduced by up to 10 % due to magnetic effects. Overall, hybrid nanofluids generally demonstrate higher Nusselt and Sherwood numbers, enhancing heat transfer efficiency.

Magnetohydrodynamic (MHD) flows have several applications in a wide area of engineering such as industrialized processes, including generating MHD electrical power, processing of magnetic materials, etc. The present examination focuses on incorporating the induced magnetic field (IMF) and multiple slips on the convective MHD Casson nanofluid flow over an elongating sheet with Brownian motion and thermophoresis effects. Heat source/sink, non-linear radiation, and suction/injection impacts are added to strengthen the study. The governing equations are framed with the above assumptions and converted from PDE to ODE using a suitable transformation. The MATLAB solver “bvp5c” is engaged to solve the governing equations and the results are depicted through graphs and tables. Moreover, a good agreement is found while comparing these results with pre-existing results. It is established that an increase in the Casson fluid parameter diminishes the fluid's velocity. Also, the induced magnetic field plays a vital role in decreasing the speed of the fluid. Further, with an increase in the double-diffusive parameters, the temperature rises. As the chemical process and Schmidt number parameter elevate, the concentration drops. The convective parameter and the velocity slip parameter both enhance skin friction. The Nusselt number rises when the Prandtl number gets larger. This investigation makes major contributions to reactor safety devices, crystal growth in liquids, chemical-catalyzed reactors, geophysics, solar technology, etc.

A viscous, incompressible, micropolar bio-nanofluid flowing across a stretching sheet in three dimensions while being driven to convect several slip boundaries in the presence of a magnetic field was studied. With the assistance of the relevant transformations, a mathematical model is presented. The finite difference method numerically solves the converted non-linear ordinary differential equations. A comprehensive assessment was conducted to examine the impact of governing parameters on dimensionless velocity, micro-rotation, temperature, nanoparticle volume fraction, microorganisms, and heat transfer rate. The findings of this investigation showed a strong correlation when compared to previous studies, indicating a high level of agreement and consistency between the results. The study's conclusions indicate that the velocity profile increases with higher values of λ and δ, while it decreases with higher values of A, δv, and M. The micro-rotation profile F(η) drops as the spin gradient viscosity parameter rises, but G(η) increases. The temperature profile decreases with higher Prandtl numbers but increases with higher thermophoresis parameters. The concentration profile decreases with higher Schmidt numbers and Brownian motion parameters. The microorganism profile increases with higher Peclet numbers and microorganism slip parameters but decreases with higher bio-convection Schmidt numbers. Lastly, the local Nusselt number grows with increasing values of the stretching parameter λ.

Stoke's problems significantly impact several domains, including industrial manufacturing, geophysical flows, chemical engineering, and heat conduction. Stoke's second problem deals with the movement of a semi-infinite viscous incompressible fluid caused by an oscillating flat plate. Thus, this work examines Stoke's second problem for an unsteady hydromagnetic surface-driven flow along an infinite flat plate in the presence of thermal radiation and heat dissipation. The governing momentum and energy equations form an emerging nonlinear system of partial differential equations through dimensionless proxies. MAPLE 2022 is employed to solve the resulting system of nonlinear partial differential equations that control the flow both analytically and numerically in specific situations. The analytical solutions are displayed graphically, along with variations of skin friction and Nusselt number at the plate. It has been observed that momentum and thermal slips significantly diminished the flow characteristics to cause damping flow rate and temperature distributions. Rising the values of Magnetic and velocity slip parameters, an oscillatory motion is observed in skin friction. This is due to the periodic and wavy nature of the boundary wall. Furthermore, a rise in the Prandtl number and radiation value correspondingly boosted the wall heat gradient profiles. Finally, this study will assist industry and engineering in understanding the sensitivity of their working fluids to parameter variations and for the exact prediction of their base fluids.

The present manuscript deals with bioconvective induced magnetohydrodynamic (MHD) flow of non-Newtonian fluids with simultaneous effects of multiple slips, heat source/sink, and nonlinear thermal radiation. Flows of Maxwell and Casson fluids are considered separately, but a single governing momentum conservation equation is constructed by combining these two flow models. Transformed governing equations are solved by MATLAB solver ‘bvp4c’. The objective of the current study is to check the comparative behaviour of two non-Newtonian fluids viz., Maxwell and Casson in presence of induced MHD effect with the bioconvective phenomenon and slip effect. The main findings reveal the growth of velocity and fall of microorganisms’ motile density with induced magnetic number. With higher values of Peclet number and microorganism concentration difference parameter, the microbe's motile density significantly reduces. The temperature hike is witnessed with heat generation/absorption, thermal radiation, and temperature ratio parameters. Also, for a fixed set of values of parameters the Casson fluid velocity is more prominent than the Maxwell fluid velocity and the scenario is the opposite for the motile density of microorganisms. Velocity increases, whereas motile density decreases with raising the amount of magnetic Prandtl number. Casson fluids have more velocity than Maxwell fluids, whereas the movement of the motile density of microorganisms is showing prominency for Maxwell fluids. The magnitude of surface drag and surface cooling rate are at a higher level for Casson fluid in comparison with Maxwell fluid. The motile density number enhances with the microorganism concentration difference parameter and Peclet number.