In this paper, the authors examine various slip effects on the magnetic field and thermal radiative impacts on the flow, mass and heat transfer of a Jeffrey nanofluid over a 2-dimensional inclined stretching sheet by a porous media. The offered work is modelled to be in the form of a combination of coupled highly nonlinear partial differential equations in dimensional contexts. Governing equations were obtained, dimensionless parameters were defined in terms of similarity parameters, and the solutions were obtained by the Homotopy Analysis Method (HAM). The analysis is significant as the effects of viscosity are identified and the important parameters are to be determined that could eventually control a type of flow behaviour, especially in promoting the flow and inhibiting flow of velocity, temperature, and concentrations. The findings show that such an increase in the magnetic parameter decreases the velocity profile by approximately 15% due to more Lorentz forces, and thermal radiation increases the temperature profile by up to 25%, therefore, enhancing the rate of heat transfer. The process of Brownian motion and thermophoresis increases the depth of the thermal boundary layer by 10–20 percent and reduces in concentration profiles by 12 percent when the Brownian motion parameter increases. A velocity slip parameter lowers the velocity field by about 18 percent, and a parameter of permeability lowers the momentum of flow by another 10 percent. The HAM solutions show very high accuracy levels, having an order of convergence at level 15 and error margins are well below 0.01 percent compared to the earlier studies. All these findings can provide profound knowledge in improving heat transmission in non-Newtonian fluid systems and can be used in biomedical engineering, thermal insulation, and industrial processes such as polymer extrusion and cooling technology. Principles of heat and mass transfer give us the crucial foundation on which to study the behavior of heat and material flows in other engineering and scientific disciplines. Such principles apply to various fields of study, including the following engineering fields: mechanical, chemical, aerospace, civil, and environmental.

A wide range of technological and industrial domains, including heating processors, electrical systems, mechanical systems, and others, are facing issues as a result of the recent developments in heat transmission. Nanofluids are a novel type of heat transfer fluid that has the potential to provide solutions that will improve energy transfer. The current study investigates the effect of a magnetic field on the two-dimensional flow of Williamson nanofluid over an exponentially inclined stretched sheet. This investigation takes into account the presence of multi-slip effects. We also consider the influence of viscous dissipation, thermal radiation, chemical reactions, and suction on the fluid’s velocity. We convert the nonlinear governing partial differential equations (PDEs) of the fluid flow problem into dimensionless ordinary differential equations (ODEs) through the utilization of similarity variables. We then use the homotopy analysis method (HAM) to numerically solve the resulting ordinary differential equations (ODEs). We demonstrate the effects of numerous elements on a variety of profiles through graphical and tabular representations. We observe a drop in the velocity profile whenever we increase either the magnetic number or the suction parameter. Higher values of the Williamson parameter lead to an increase in the thermal profile, while the momentum of the flow displays a trend in the opposite direction. The potential applications of this unique model include chemical and biomolecule detection, environmental cleansing, and the initiation of radiation-induced chemical processes like polymerization, sterilization, and chemical synthesis.

The present study investigates the non-isothermal flow and energy distribution through a loosely bent rectangular duct using a spectral-based numerical approach over a wide range of the Dean number $0<Dn\le 3000$. Unlike previous research, this work offers novel insights by conducting a grid-point-specific velocity analysis and identifying new bifurcation structures. The study reveals how centrifugal and buoyancy forces interact to produce steady, periodic, and chaotic flow regimes significantly influencing heat transfer performance. The Newton-Raphson method is employed to explore four asymmetric steady branches, with vortex solutions ranging from 2- to 12 vortices. Unsteady flow characteristics are analyzed exquisitely by performing time-advancement of the solutions and the flow regimes are shown as a percentage of total flow with longitudinal vortex generation. Axial flow, secondary flow, and temperature profiles have been depicted in accordance with Dn to wander the flow pattern, and it is predicted that the time-dependent flow (TDF) consists of asymmetric 2- to 10-vortex solutions. The significant findings of this study include the axial displacement of the circulations due to the influence of the time-varying temperature dispersal applied along the wall. Chaotic flows, which dominate the higher Dean number range, are shown to enhance heat convection due to increased fluid mixing. A detailed comparison with prior research demonstrates the advantages of this approach, particularly in capturing complex non-linear behaviors. The findings of this study provide practical guidelines for optimizing duct designs to maximize heat transfer and suggest future research directions, such as using nanofluids or studying Magneto-hydrodynamics in the same configuration.