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This research work employs a machine learning approach with Python to analyze the complex relation of thermophoretic deposition and radiation effect on the mass and heat transfer of ternary hybrid nanofluid flow over the wedge. The colloidal comprising ${\mathrm{\text{CoFe}}}_2{\mathrm{\text{O}}}_4$, ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$ and ZnO with Engine Oil and Water in equal proportion as a base fluid, is considered here, due to the potential enhancer of thermal performance in numerous applications. The governing PDEs for flow rate, heat and mass transfer are transformed into a system of ODEs and numerical dataset generated by Python for stochastic evaluation through Matlab Neural Network assisted by Levenberg Marquardt Machine Learning Algorithm to extract intricate patterns and comparison between numerical and stochastic simulations. The impact of influencing parameters such as volume fraction, wedge angles, Eckert ratio and Radiation coefficients are analyzed. The outcomes of this research shed light on the synergetic effects of thermophoretic deposition and radiation on the thermal mass exchange of tri-nanohybrid fluid across the sharp edge of the device. This machine learning artificial intelligence (AI) tool is cost-effective and far better than deterministic numerical outputs as compared with analytical evaluations. A detailed graphical representation is embedded in this paper for comparisons and error analysis. Influencing parameters are analyzed for temperature, velocity and concentration profiles. Moreover, engineering parameters are also evaluated and plotted against the infecting agents. Graphical analysis of Nusselt, Sherwood and Skin friction coefficients added for broad spectrum comparison and comprehensive analysis for the significant implementation of the present discussion at the industrial level, for the benefit of production units, heavy industry and energy management systems in numerous fields.

We simulate the gas flow and heat transfer in micro-Couette flow by the lattice Boltzmann method (LBM). A new boundary treatment is adopted in the numerical experiment in order to capture the velocity slip and the temperature jump of the wall boundary. Velocity and temperature profiles are in good agreement with the analytic results, which exhibits the availability of this model and boundary treatment in describing thermal micro-flow with viscous heat dissipation. We also find the upper boundary's temperature jump is zero at the critical Ec, which is around 3.0 with different Kn.

The roughness effects of the gas flows of nitrogen and helium in microchannels with various relative roughnesses and different geometries are studied and analyzed by a lattice Boltzmann model. The shape of surface roughness is simulated to be square, sinusoidal, triangular, and fractal. Numerical computations compared with theoretical and experimental studies show that the roughness geometry is an important factor besides the relative roughness in the study of the effects of surface roughness. The fractal boundary presents a higher influence on the velocity field and the resistance coefficient than other regular boundaries at the same Knudsen number and relative roughness. In addition, the effects of rarefaction, compressibility, and roughness are strongly coupled, and the roughness effect should not be ignored in studying rarefaction and compressibility of the microchannel as the relative roughness increases.

Considering the velocity slip effect of the gas film at the solid boundary, the performance of a micro gas bearing is given. For the length scale of the micro gas bearing, the gas flow in the bearing is dominated by the slip regime instead of the continuum one. With different slip models, the modified Reynold's equations are obtained. Solving the Reynold's equation with finite difference method, the bearing forces are compared between the different models, and the second order slip model is found to fit the microelectromechanical systems (MEMS) case very well. Adopting the second order slip model, the dynamical coefficients and the stable threshold speed of the system are estimated based on the linear bearing force. And the dynamical response of the micro gas bearing is acquired with fourth-rank Runge–Kutta method. Compared with the results of the second order slip flow, the continuum flow overestimates the dynamical coefficients and underestimates the threshold speed. What is more, the period of the journal oscillation rose for the slip effect.

In this research, thermal radiation, entropy generation and variable thermal conductivity effects on hybrid nanofluids by moving sheet are analyzed. The liquid is placed by stretchable flat wall that is flowing in a nonlinear pattern. Thermal conductivity changes with temperature governed by thermal radiation and MHD is incorporated. Approximations of boundary layer correspond to a set of PDEs which are then changed into ODEs by considering suitable variables. The resulting ODEs are solved using the bvp4c method. The implication with considerable physical characteristics on temperature, entropy generation and velocity profile is graphically represented and numerically discussed. Entropy generation increases for increasing Reynolds number, velocity slip parameter, Brinkman number and magnetic parameter. Scientists have recently established a rising interest in the importance of nanoparticles due to their numerous technical, industrial and commercial uses. The provided insights can be used in extrusion application areas, macromolecules, biomimetic systems, energy production and industrial process improvements.

In the recent decades, the increasing energy demands and its applications have seen the focus shifting to the hybrid nanofluid flows but so much is still left to be investigated. This analysis is executed to explore the hydro-magnetic flow to investigate the incompressible flow and heat transfer towards a stretching surface with velocity and thermal slips. The scaling similarity transformations are created using Lie group analysis and employing these to convert nonlinear partial differential equations to the nonlinear ordinary differential equations. Here, after converting equations from dimensional to non-dimensional, we will use the BVP4C solver (MATLAB) for plotting the graphs to analyze how distinct non-dimensional parameters affect the skin friction and Nusselt number transfer rate, case 1 graphene + CNT + aluminum oxide with base fluid as water and case 2 magnesium oxide + zirconium oxide + copper oxide with water as base fluid, here taking nanoparticles without different shapes. The hybrid nanofluid temperature profile has mixed behavior, and the velocity profile increases when M rises. The hybrid nanofluid temperature profile curvature has composite behavior when $Pr$ rises. The link between several independent or predictor variables and one dependent or criterion variable has been examined using multilinear regression analysis (MLR). When coefficient values for many variables are subject to change, it can forecast a wide range of outcomes.

This paper reports the hydromagnetic mixed convective flow of Carreau nanofluid in the vertical microchannel with slip and convective mechanisms at the boundaries. The main objective of this work is to analyze the conduct of Carreau nanofluid under Buongiorno model as the nano-dimensions of the particle consequently encounters random motion. The novel impression is to retain the outcomes of the flow in regard of Brownian dispersion and thermophoresis. Parameters such as buoyancy ratio, Brownian motion and thermophoresis along with the effect of Weissenberg number are discussed on distribution of flow, temperature and concentration by using graphical demonstration. Surface drag coefficients, transport rates of mass and heat are portrayed by numeric esteems. Boundary layer approximations are made use to tackle nonlinear ordinary differential equations and solved by Runge–Kutta–Fehlberg 4-5th-order method. Results so obtained elaborate that velocity depletes with increased values of buoyancy ratio and viscosity ratio parameter along with power law index. Also, distinct behavior is noticed in the profile of velocity for varying Weissenberg number by boosting and diminishing depending on the power law index. On the other hand, temperature rises by augmentation of thermophoresis and Brownian motion parameter. Elevation in Brownian motion parameter accelerate the concentration panel of the fluid. Skin friction and Nusselt number are in direct proportion with buoyancy ratio parameter and Brownian motion parameter, respectively.

To meet the energy requirement of the world, this work addresses the MHD flow of ternary hybrid nanofluid between two rotating and stretchable disks having porous medium. Thermal radiation effects along with velocity slips at the interface of fluid and disk are considered in this study. Three types of nanoparticles, namely, Al₂O₃ (alumina), CuO (copper oxide) and Cu (copper), have been taken with water as the host fluid. The flow and thermal characteristics of hybrid (Al₂O${}_3+\mathrm{\text{CuO}}$) and ternary (Al₂O${}_3+\mathrm{\text{CuO}}+\mathrm{\text{Cu}}$) nanofluids formed by the combination of nanoparticles have been observed. This combination aids in the breakdown of dangerous compounds, environmental purification and the cooling of other equipment. The corresponding equations are modeled in terms of PDEs, and these PDEs are transformed into ODEs using Von Karman similarity transformations. The resulting equations are solved by using finite difference method based ND solver. The rate of heat transfer increases with the rise in thermal Biot numbers. Moreover, the solution predicts that for variations in radiation parameter from 0.5 to 1.5, heat transfer upsurges 88% for traditional nanoparticles, 92.4% for hybrid nanoparticles while for trihybrid nanoparticles, it grows up from 0% to 95%.

The bioconvective flows are truly connected to real-life and engineering development. So, the models of biomicrosystems and biocells are considered for the technical analysis in this paper. Our intention for the current analysis was to theoretically examine electrical conduction flow into mass and heat transfer by an extensive gyrotactic microorganism into an inclined magnetic field toward a vertical stretching sheet with nonlinear solar radiation with different solar thermal appliances. The effect on velocity slip and Joule heating was again studied in detail. This classical problem on Navier Stokes equations to the current imitation was decreased to ordinary differential equations by applying the comparison method. The numerical solutions were changed by boundary value problem (BVP) to clarify the subject into finite difference numerical scheme by applying MATLAB. The important results show that the density of motile microorganisms reduces to the bioconvection Lewis number and Peclet number, although reverse performance was noticed for the bioconvection Rayleigh number. Further, solar radiation fosters heat transport. In this paper, complete analysis is provided for potential functions of solar thermoelectric cells, solar ponds, solar thermal power fabrication, etc.

The current work investigates the effects of oblique Lorentz force and Navier’s slip boundary condition on unsteady hybrid nanoliquid flow with three different base liquids (H₂O, CH₃OH and H₂O–EG) across a nonlinearly elongating surface set in a porous medium. This research considers the effects of viscous–Ohmic dissipation, nonlinearly variable thermal radiation, internal heat source, the Soret effect, first-order chemical reaction and thermal and solutal jump conditions at the boundary. Proper thermo-physical relationships for the hybrid nanoliquid have been established. Rosseland’s estimate for an optically thick regime is used when calculating the heat flow owing to radiation. The dimensional governing equations are translated into nondimensional forms using appropriate similarity transformations. The velocity, energy and concentration fields are numerically solved using a shooting strategy based on the secant iteration and the Runge–Kutta–Fehlberg method. The physical implications of several essential parameters on the hybrid nanoliquid velocity, temperature and concentration are investigated using graphical and tabular representations of numerical data. Furthermore, the multiple (quadratic) regression analysis reveals that physical parameters strongly influence the local skin friction coefficient, Sherwood and Nusselt numbers. For continuously growing values of the unsteadiness parameter, the velocity, thermal and concentration scattering declined everywhere within the boundary layer region.

It has been demonstrated that there are nanobubbles on hydrophobic surface. Molecular dynamics simulation was adopted to investigate the impacts of the hydrophobic surface nanobubbles on fluid flow in nanochannel. A method for calculating the velocity of nanobubbles is presented. The results show that the bubbles on two plates enhance the velocity slip and disturb the flow. The behavior is attributed to the attractive force between nanobubbles.

The recent applications in industrial products and engineering need high thermal efficiency for the betterment of the shape of the products, the concept of hybrid nanofluid is significant in comparison to nanofluid and pure fluid. Therefore, this analysis focuses on the flow of a micropolar hybrid nanofluid over a vertical permeable plate. The study considers free convection of an electrically conducting fluid, incorporating metal and oxide components with a water-based hybrid nanofluid. Further, the conjunction of dissipative and radiating heat with generative/absorptive heat enhances the thermal properties. The use of standard transformation rules gives rise to converting the nondimensional form of concerned PDEs to ODEs. Moreover to get rid of the solution, for the nondimensional set of equations, a shooting-based numerical technique like Runge–Kutta (RK)-fourth-order is adopted for the standard values of several components within their range. The effectiveness of these parameters is studied and displayed through graphs. The computed result of the rate coefficients at the surface is depicted in tabular form. The comparative analysis with earlier work studied by considering the base liquid shows a good correlation in particular cases. However, the important outcomes are, the magnetized nano as well as hybrid nanoparticles produces a thicker momentum boundary layer thickness whereas it enhances the fluid temperature.

This work theoretically studies the effects of wall velocity slip on the hydraulic resistance and convective heat transfer of laminar flow in a microchannel network with symmetric fractal treelike branching layout. It is found that the slip can reduce the hydraulic resistance and enhance the Nusselt number of laminar flow in the network; furthermore, the slip can also affect the optimal structure of the fractal treelike microchannel network with minimum hydraulic resistance and maximum convective heat transfer. Under the size constraint of constant total channel surface area, the optimal diameter ratio of microchannels at two successive branching levels of the symmetric fractal treelike microchannel network with a minimized hydraulic resistance is only dependent on branching number $N$ in the manner of $N^{-2/5}$ for no slip condition, but decreases with the increasing slip length, the increasing branching number and the increasing length ratio of microchannels at two successive branching levels for slip condition. The convective heat transfer of the treelike microchannel network is independent on the diameter ratio for no slip condition, but displays an increasing after decreasing trend with the increasing diameter ratio for slip condition. The symmetric treelike microchannel network with the worst convective heat transfer performance is the network with diameter ratio equaling one for slip condition.