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The purpose of this paper is to present a numerical and an analytical study of the fluid flow and heat transfer in the unsteady, laminar boundary layer resulting from the forced convection flow along a semi‐infinite wedge, where the transients are initiated at time t¯ = 0 when the wedge is impulsively started from rest with a uniform velocity and a constant heat flux at the walls of the wedge is suddenly imposed.

The velocity of the main free stream is written in non‐dimensional form for t > 0 as u_e(x) = x^m, where x is the non‐dimensional distance along the surface from the leading edge (apex) of the wedge and the constant m is related to the included angle of the wedge πβ by m = β / (2 − β) (0 ≤ m ≤ 1 for physical applications). The wedge and the fluid are assumed to be initially (t¯ = 0) at the same uniform temperature T_∞, so that there is zero heat flux at the surface. A time‐dependent thermal boundary layer is then produced at t¯ = 0 as the zero heat flux at the surface is suddenly changed, and a constant heat flux q_w is imposed as the wedge is set into motion. Analytical solutions for the simultaneous development of the momentum and thermal boundary layers are obtained for both small (initial unsteady flow) and large (steady‐state flow) times for several wedge angles (several values of m) and several values of the Prandtl number Pr. These two asymptotic solutions are matched using two specialised numerical procedures.

The numerical results obtained for the transient fluid velocity and temperature fields concentrate mainly on the case when the Prandtl number Pr = 1 and m = 1 / 5, namely a wedge angle of 60^○. Required alterations to these parameters are then discussed with reference to variations in Pr and m separately. Further, an engineering empirical expression is presented for the skin friction C_f (τ) Re_x^1/2 that is valid for all times. The comparison between the empirical formula and the full numerical solution demonstrates that this matching solution can be used with confidence over the whole range of values of the non‐dimensional time τ for each of the values of m presented, and may therefore be used with confidence in engineering applications.

The results of the present work, which have been obtained through many computations, are very important for the advancement of knowledge on this classical problem of fluid mechanics and heat transfer. It is believed that such very detailed solutions have not previously been presented.

Several graphs, streamlines, isotherms and 3D plots are illustrated to enlighten the noteworthy fallouts of the investigation. Embedding flow factors for velocity, induced magnetic field and temperature have been determined using parametric analysis.

Ternary hybrid nanofluids has outstanding hydrothermal performance compared to classical mono nanofluids and hybrid nanofluids owing to the presence of triple tiny metallic particles. Ternary hybrid nanofluids are considered as most promising candidates in solar energy, heat exchangers, electronics cooling, automotive cooling, nuclear reactors, automobile, aerospace, biomedical devices, food processing etc. In this work, a ternary hybrid nanofluid flow that contains metallic nanoparticles over a wedge under the prevalence of solar radiating heat, induced magnetic field and the shape factor of nanoparticles is considered. A ternary hybrid nanofluid is synthesized by dispersing iron oxide (Fe3O4), silver (Ag) and magnesium oxide (MgO) nanoparticles in a water (H₂O) base fluid. By employing similarity transformations, we can convert the governing equations into ordinary differential equations and then solve numerically by using the Runge–Kutta–Fehlberg approach.

There is no fund for the research work.

This kind of study may be used to improve the performance of solar collectors, solar energy and solar cells.

This investigation unfolds the hydrothermal changes of radiative water-based Fe₃O₄-Ag-MgO-H₂O ternary hybrid nanofluidic transport past a static and moving wedge in the presence of solar radiating heating and induced magnetic fields. The shape factor of nanoparticles has been considered in this study.

The purpose of this paper is to assess the flow of a nanofluid over a porous moving wedge. The passive control model along with the magnetohydrodynamic (MHD) effects is used to formulate the problem. Furthermore, in energy equation, the non-linear thermal radiation has also been incorporated. The equations governing the flow are transformed into a set of ordinary differential equations by using suitable similarity transforms. The reduced system of equations is then solved numerically using a well-known Runge–Kutta–Fehlberg method coupled with a shooting technique. The influence of parameters involved on velocity, temperature and concentration profiles is highlighted with the help of a graphical aid. Expressions for skin-friction coefficient, local Nusselt number and Sherwood number are obtained and presented graphically.

Numerical solution of the problem is obtained using the well-known Runge–Kutta–Fehlberg method.

The analysis provided gives a clear description that the increase in m and magnetic parameter M results in an increased velocity profile. Both these parameters normalize the velocity field. Radiation parameter, Rd, increases the temperature and concentration of the system so does the temperature ratio θ_ω reduces the heat transfer rate at the wall for both stretching and shrinking wedge.

In the study presented, the flow of nanofluid over a moving permeable wedge is considered. The solution of the equations governing the flow is presented numerically. For the validity of results obtained, a comparison is also presented with already existing results. To the best of the authors’ knowledge, this investigation is the first of its kind on the said topic.

The purpose of this study is to analyze the impact of chemical reaction and thermal radiation on mixed convection flow, heat and mass transfer characteristics of nanofluid through a wedge occupied with water–TiO₂ and water–Al₂O₃ made nanofluid by considering velocity, temperature and concentration slip conditions in present investigation.

Using acceptable similarity transformations, the prevailing partial differential equations have been altered into non-linear ordinary differential equations and are demonstrated by the diverse thermophysical parameters. The mathematical model is solved numerically by implementing Galarkin finite element method and the outcomes are shown in tables and graphs.

The temperature and concentration fields impede as magnetic field parameter improves in both water–Al₂O₃ and water–TiO₂ nanofluid. While there is contradiction in the velocity field as the values of magnetic field parameter rises in both nanofluids. The non-dimensional velocity rate, rate of temperature and rate of concentration rise with improved values of Weissenberg number.

Nanofluid flows past wedge-shaped geometries have gained much consideration because of their extensive range of applications in engineering and science, such as, magnetohydrodynamics, crude oil extraction, heat exchangers, aerodynamics and geothermal systems. Virtually, these types of nanofluid flows happen in ground water pollution, aerodynamics, retrieval of oil, packed bed reactors and geothermal industries.

IN the first of these articles it was pointed out that normal supersonic flow can be described theoretically, to a first approximation, by the linearized equation of motion. This has the form of the wave equation and governs first order disturbances to fields of uniform flow; for example, flow past thin wings or slender bodies at small angles of incidence, and flow through ducts of varying cross‐section. In the same way small disturbances in a purely subsonic stream can be described by a linearized equation of motion, which can be reduced to Laplace's equation by contracting the co‐ordinate normal to the direction of flow. Transonic flow, in which regions of both supersonic and subsonic flow occur, is not so easily represented.

The analysis of boundary layers is needed to reflect the behaviour of fluid flows in current industrial processes and to improve the efficacy of products. Hence, this study aims to analyse the flow and heat transfer performance of hybrid alumina-copper/water (Al₂O₃-Cu/H₂O) nanofluid with the inclusion of activation energy and binary chemical reaction effect towards a moving wedge.

The multivariable differential equations with partial derivatives are converted into a specific type of ordinary differential equations by using valid similarity transformations. The reduced mathematical model is elucidated in the MATLAB system by using the bvp4c procedure. This solution method is competent in delivering multiple solutions once appropriate assumptions are supplied.

The results of multiple control parameters have been studied, and the findings are verified to provide more than one solution. The coefficient of skin friction was discovered to be increased by adding nanoparticles volume fraction from 0% to 0.5% and 1%, by almost 1.6% and 3.2%. Besides, increasing the nanoparticles volume fraction improves heat transfer efficiency gradually. The inclusion of the activation energy factor displays a downward trend in the mass transfer rates, consequently reducing the concentration profile. In contrast, the increment of the binary reaction rate greatly facilitates the augmentation of mass transfer rates. There is a significant enhancement in the heat transfer rate, approximately 13.2%, when the suction effect dominates about 10% in the boundary layer flow. Additionally, the results revealed that as the activation energy rises, the temperature and concentration profiles rise as well. It is proved that the activation energy parameter boosts the concentration of chemical species in the boundary layer. A similar pattern emerges as the wedge angle parameter increases. The current effort aims to improve the thermal analysis process, particularly in real-world applications such as geothermal reservoirs, chemical engineering and food processing, which often encountered mass transfer phenomenon followed by chemical reactions with activation energy.

The present results are original and new for the study of flow and heat transfer over a permeable moving wedge in a hybrid nanofluid with activation energy and binary chemical reaction.

This study aims to model the important flow response quantities over a shrinking wedge with the help of response surface methodology (RSM) and an artificial neural network (ANN). An ANN simulation for optimal thermal transport of incompressible viscous fluid under the impact of the magnetic effect (MHD) over a shrinking wedge with sensitivity analysis and optimization with RSM has yet not been investigated. This effort is devoted to filling the gap in existing literature.

A statistical experimental design is a setup with RSM using a central composite design (CCD). This setup involves the combination of values of input parameters such as porosity, shrinking and magnetic effect. The responses of skin friction coefficient and Nusselt number are required against each parameter combination of the experimental design, which is computed by solving the simplified form of the governing equations using bvp4c (a built-in technique in MATLAB). An empirical model for Cf_x and Nu_x using RSM and ANN adopting the Levenberg–Marquardt algorithm based on trained neural networks (LMA-TNN) is attained. The empirical model for skin friction coefficient and Nusselt number using RSM has 99.96% and 99.99% coefficients of determination, respectively.

The values of these matrices show the goodness of fit for these quantities. The authors compared the results obtained from bvp4c, RSM and ANN and found them all to be in good agreement. A sensitivity analysis is performed, which shows that Cf_x as well as Nu_x are most affected by porosity. However, they are least affected by magnetic parameters.

This study aims to simulate ANN and sensitivity analysis for optimal thermal transport of magnetic viscous fluid over shrinking wedge.

This paper aims to present the effect of entropy generation on the unsteady flow of upper-convected Maxwell nanofluid past a wedge embedded in a porous medium in view of buoyancy force. Cattaneo-Christov double diffusion theory simulates the processes of energy phenomenon and mass transfer. Meanwhile, Brownian motion, thermophoresis and convective boundary conditions are discussed to further visualize the heat and mass transfer properties.

Coupled ordinary differential equations are gained by appropriate similar transformations and these equations are manipulated by the Homotopy analysis method.

The result is viewed that velocity distribution is a diminishing function with boosting the value of unsteadiness parameter. Moreover, fluid friction irreversibility is dominant as the enlargement in Brinkman number. Then controlling the temperature and concentration difference parameters can effectively regulate entropy generation.

This paper aims to address the effect of entropy generation on unsteady flow, heat and mass transfer of upper-convected Maxwell nanofluid over a stretched wedge with Cattaneo-Christov double diffusion, which provides a theoretical basis for manufacturing production.

The purpose of this study is to analyze a new idea for external flow over a cylinder to increase the heat transfer and reduce pressure drop. Using wedge-shaped porous media in the front and wake regions of the cylinder can improve its hydrodynamic, and the rotating flow in the wake region can enhance the heat transfer with increased porous–liquid contact. Permeability plays a vital role, as a high-permeable medium improves heat transfer, whereas a low-permeable region improves the hydrodynamic.

Therefore, in the current research, external forced convection of nanofluid laminar flow over a bundle of cylinders is simulated using a two-phase mixture model. Four cases with different porous blocks around the cylinder are assessed: rectangular porous; wedge shape in trailing edge (TEP); wedge shape in leading and trailing edges (LTEP); and no porous block case. Also, three different lengths of wedge-shaped regions are considered for TEP and LTEP cases.

Results are presented in terms of Nusselt (Nu), Euler (Eu) and the performance evaluation criterion (PEC) numbers for various Reynolds (Re) and Darcy (Da) numbers.

It was found that in most situations, LTEP case provides the highest Nu and PEC values. Also, optimal Re and porous medium length exist to maximize PEC, depending on the values of Da and nanofluid volume fraction.

The effect of non-linear thermal radiation and variable thermo-physical properties are investigated in the Falkner-Skan flow of a Casson nanofluid in the presence of magnetic field. The paper aims to discuss this issue.

Selected bunch of similarity transformations are used to reduce the governing partial differential equations into a set of non-linear ordinary differential equations. The resultant equations are numerically solved using Runge-Kutta-Fehlberg fourth-fifth-order method along with shooting technique.

The velocity, temperature and concentration profiles are evaluated for several emerging physical parameters and are analyzed through graphs and tables in detail.

This study only begins to reveal the research potential and pitfalls of research and publishing on boundary-layer flow, heat and mass transfer of Casson nanofluid past and the moving and static wedge-shaped bodies.

It is found that the presence of non-linear thermal radiation and variable properties has more influence in heat transfer. Furthermore, temperature profile increases as the radiation parameter increases.