The current article aims to present a numerical analysis of MHD Williamson nanofluid flow maintained to flow through porous medium bounded by a non-linearly stretching flat surface. The second law of thermodynamics was applied to analyze the fluid flow, heat and mass transport as well as the aspects of entropy generation using Buongiorno model. Thermophoresis and Brownian diffusion is considered which appears due to the concentration and random motion of nanoparticles in base fluid, respectively. Uniform magnetic effect is induced but the assumption of tiny magnetic Reynolds number results in zero magnetic induction. The governing equations (PDEs) are transformed into ordinary differential equations (ODEs) using appropriately adjusted transformations. The numerical method is used for solving the so-formulated highly nonlinear problem. The graphical presentation of results highlights that the heat flux receives enhancement for augmented Brownian diffusion. The Bejan number is found to be increasing with a larger Weissenberg number. The tabulated results for skin-friction, Nusselt number and Sherwood number are given. A decent agreement is noted in the results when compared with previously published literature on Williamson nanofluids.

This paper presents an analysis of the features of magnetohydrodynamic Darcy–Forchheimer nanofluid flow over a nonlinear stretching sheet. A viscous incompressible nanofluid saturates the porous medium via the Darcy–Forchheimer relation. Heat and mass transfer is analyzed through the Brownian motion factor and thermophoresis. A non-uniform magnetic field is induced to enhance the electric conductivity of the nanofluid. The model emphasizes a small magnetic Reynolds number and boundary layer formulation. The governing partial differential equations are converted into nonlinear ordinary differential equations using similarity transformations and thereafter solved utilizing the homotopy analysis method. Graphs are sketched for different values of various fluid parameters. Drag force, heat flux, and mass flux are interpreted numerically. The porosity factor results in increasing the skin friction due to the high resistance offered by the porous medium. The heat and mass flux are reduced for a stronger porosity factor, which is an important finding for industrial applications of nanofluids. The temperature profile shows increasing values of both Brownian diffusion and thermophoresis.

This article presents the implementation of a numerical solution of bioconvective nanofluid flow. The boundary layer flow (BLF) towards a vertical exponentially stretching plate with combination of heat and mass transfer rate in tangent hyperbolic nanofluid containing microorganisms. We have introduced zero mass flux condition to achieve physically realistic outcomes. Analysis is conducted with magnetic field phenomenon. By using similarity variables, the partial differential equation which governs the said model was converted into a nonlinear ordinary differential equation, and numerical results are achieved by applying the shooting technique. The paper describes and addresses all numerical outcomes, such as for the Skin friction coefficients (SFC), local density of motile microorganisams (LDMM) and the local number Nusselt (LNN). Furthermore, the effects of the buoyancy force number, bioconvection Lewis parameter, bioconvection Rayleigh number, bioconvection Pecelt parameter, thermophoresis and Brownian motion are discussed. The outcomes of the study ensure that the stretched surface has a unique solution: as Nr (Lb) and Rb (Pe) increase, the drag force (mass transfer rate) increases respectively. Furthermore, for least values of Nb and all the values of Nt under consideration the rate of heat transfer upsurges. The data of SFC, LNN, and LDMM have been tested utilizing various statistical models, and it is noted that data sets for SFC and LDMM fit the Weibull model for different values of Nr and Lb respectively. On the other hand, Frechet distribution fits well for LNN data set for various values of Nt.

Nanofluids, an advanced class of heat transfer fluids, have gained significant attention due to their superior thermophysical properties, making them highly effective for various engineering applications. This review explores the impact of nanoparticle integration on the thermal conductivity, viscosity, and overall heat transfer performance of base fluids, highlighting improvements in systems, such as heat exchangers, electronics cooling, PV/T systems, CSP technologies, and geothermal heat recovery. Key mechanisms such as nanolayer formation, Brownian motion, and nanoparticle aggregation are discussed, with a focus on hybrid nanofluids that show enhanced thermal conductivity. The increase in viscosity poses a trade-off, necessitating careful control of the nanoparticle properties to optimize heat transfer while reducing energy consumption. Empirical data show up to a 123% increase in the convective heat transfer coefficients, demonstrating the tangible benefits of nanofluids in energy efficiency and system miniaturization. The review also considers the environmental impacts of nanofluid use, such as potential toxicity and the challenges of sustainable production and disposal. Future research directions include developing hybrid nanofluids with specific properties, integrating nanofluids with phase change materials, and exploring new nanomaterials such as metal chalcogenides to enhance the efficiency and sustainability of thermal management systems.