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Outstanding features such as thermal conductivity and superior electrical conductivity of nanofluids unfold a new window in the context of their extensive applications in engineering and industrial domains. The purpose of this study to simulate numerically the magneto-nanofluid flow and heat transfer over a curved stretching surface. Heat transport is explored in the presence of viscous dissipation. At the curved surface, the convective boundary condition is adopted. Three different nanoparticles, namely, copper, aluminium oxide and titanium dioxide are taken into consideration because of easily available in nature.

The basic flow equations are framed in terms of curvilinear coordinates. The modelled partial differential equations are transformed into a system of non-linear ordinary differential equations by means of appropriate similarity transformation. The subsequent non-linear system of equations is then solved numerically by using the Runge–Kutta–Felhberg method with the shooting scheme via bvp4c MATLAB built-in function. Impacts of various physical parameters on velocity, pressure and temperature distributions, local skin-friction coefficient, local Nusselt number and wall temperature are portrayed through graphs and tables followed by a comprehensive debate and physical interpretation.

Graphical results divulge that augmenting values of the magnetic parameter cause a decline in velocity profiles and stream function inside the boundary layer. The magnitude of the pressure function inside the boundary layer reduces for higher estimation of curvature parameter, and it is also zero when the curvature parameter goes to infinity. Furthermore, the temperature is observed in a rising trend with growing values of the magnetic parameter and Biot number.

This research study is very pertinent to the expulsion of polymer sheet and photographic films, metallurgical industry, electrically-conducting polymer dynamics, magnetic material processing, rubber and polymer sheet processing, continuous casting of metals, fibre spinning, glass blowing and fibre, wire and fibre covering and sustenance stuff preparing, etc.

Despite the huge amount of literature available, but still, very little attention is given to simulate the flow configuration due to the curved stretching surface with the convective boundary condition. Very few papers have been examined on this topic and found that its essence inside the boundary layer is not any more insignificant than on account of a stretching sheet. A numerical comparison with the published works is conducted to verify the accuracy of the present study.

The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically.

The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined.

Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter.

The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.

The main focus is to provide a non-similar solution for the magnetohydrodynamic (MHD) flow of Casson fluid over a curved stretching surface through the novel technique of the artificial intelligence (AI)-based Lavenberg–Marquardt scheme of an artificial neural network (ANN). The effects of joule heating, viscous dissipation and non-linear thermal radiation are discussed in relation to the thermal behavior of Casson fluid.

The non-linear coupled boundary layer equations are transformed into a non-linear dimensionless Partial Differential Equation (PDE) by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ordinary differential equations (ODEs). The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

The results indicate that the non-linear radiation parameter increases the fluid temperature. The Casson parameter reduces the fluid velocity as well as the temperature. The mean squared error (MSE), regression plot, error histogram, error analysis of skin friction, and local Nusselt number are presented. Furthermore, the regression values of skin friction and local Nusselt number are obtained as 0.99993 and 0.99997, respectively. The ANN predicted values of skin friction and the local Nusselt number show stability and convergence with high accuracy.

AI-based ANNs have not been applied to non-similar solutions of curved stretching surfaces with Casson fluid model, with viscous dissipation. Moreover, the authors of this study employed Levenberg–Marquardt supervised learning to investigate the non-similar solution of the MHD Casson fluid model over a curved stretching surface with non-linear thermal radiation and joule heating. The governing boundary layer equations are transformed into a non-linear, dimensionless PDE by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ODEs. The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

The purpose of this study is to examine how fluid flow and heat transfer are affected by the influence of hybrid nanofluids flowing across a stagnation zone of a stretching curved surface. Stagnation point flow has garnered considerable attention over the past few decades. This is because many technical applications, such as the cooling of nuclear reactors and rotating equipment divisions, rely on stagnation-point flow.

A thorough analysis is conducted of the impacts of several regulating parameters on fluid flow and thermal performance, including the radiation parameter, heat source parameter, mixed convection parameter, porosity parameter curvature and nanoparticle concentration. The laws governing the field of flow equations are transformed by similarity substitutions into two nonlinear ordinary differential equations, which are then solved numerically using Maple. The MR-Solve technique in the built-in Maple package was used. The MR-Solve technique was used to numerically solve highly coupled ordinary differential equation problems. This approach produced highly precise and consistent results. It also provides the best performance while using a minimum amount of CPU and the shortest phrases.

The main conclusions of this study show that axial velocity drops, while radial velocity increases as the mixed convection parameter increases. The rate of heat transmission and skin friction is higher for hybrid nanoparticles with volume fraction percentile (0.01–0.03) than for those with volume fraction percentile (0.1–0.3).

Further research on this topic could examine a broader range of parameter values, suction/injection, entropy, mass equation, micropolar fluid, ternary hybrid nanofluid and Newtonian heating flow on a curved stretching surface.

By investigating a novel physical design that combines the various effect with stagnation flow, this study adds value and offers insights and prospective improvements in the discipline of heat fluid mechanics. Mathematical modeling or experimental studies in a variety of multiphysical contexts can be used to achieve this. Heat exchangers, crystalline procedures, microelectronic machines, systems for conserving energy, integrating operations, food manufacturing, climate control, purification and other engineering domains can all benefit from the geometric configurations investigated in this study. The results of this study greatly aid in optimizing thermal performance in a variety of application domains. This study is novel because it compares several volume fraction percentiles.

A stretching curved surface’s stagnation zone is traversed by hybrid nanofluids, offering insights into how curvature affects heat transfer and fluid flow efficiency. The results aid in the design and improvement of the energy transfer efficiencies for a range of commercial and biological purposes. The results offer possibilities for increased efficiency in a range of applications by developing hybrid nanofluid flow control methods and helping to create ideal thermal systems.

The primary purpose of this research is to investigate the flow and heat transfer characteristics of non-Newtonian nanofluids, specifically Reiner–Philippoff (R-Ph) fluids, across a radially magnetized, curved, stretched surface. By considering factors such as Brownian motion, thermophoresis and viscous dissipation, the study aims to enhance the understanding of heat transfer mechanisms in various engineering and industrial applications, thereby contributing to improved thermal management strategies.

This study employs the local non-similarity method to analyze the flow and thermal behavior of R-Ph nanofluids over a radially magnetized, curved, stretched surface. The governing system is simplified using suitable transformations, and a local non-similarity approach is applied to treat non-dimensional partial differential equations as ordinary differential equations. The resulting system is numerically solved by employing the Bvp4c algorithm via MATLAB. Various dimensionless parameters, such as thermophoresis and magnetic numbers, are systematically varied to evaluate their impact on the velocity, concentration and temperature profiles of the nanofluid.

The results indicate that the concentration profile of the nanofluid improves with increasing thermophoresis and magnetic numbers, while it decreases with higher Schmidt and Bingham numbers. The velocity of the nanofluid decreases with larger magnetic numbers and curvature parameters but increases with the R-Ph fluid and Bingham numbers. Additionally, the temperature profile shows a decreasing trend for higher curvature and Bingham numbers while rising with higher Brinkman and magnetic numbers. The Sherwood number increases with Schmidt number, thermophoresis and Brownian motion parameters.

This study provides a novel analysis of R-Ph nanofluids in the context of curved stretching surfaces under magnetic fields, contributing to the understanding of non-Newtonian fluid dynamics. The use of the local non-similarity method to transform and solve the governing equations offers a fresh perspective on heat transfer phenomena. The findings have significant implications for various fields, including engineering, electronics and biomedical applications, by enhancing thermal efficiency and performance in systems utilizing nanofluids.

The purpose of this article is to analyze the magnetohydrodynamic viscous liquid flow with heat absorption/generation. Flow is induced by an unsteady stretching curved surface. A time-dependent magnetic field is utilized.

The resulting nonlinear system is solved through shooting method.

An increment in the values of curvature A and unsteadiness parameters correspond to higher velocity, temperature and concentration fields. There is a reduction in the temperature and related layer via Prandtl number. Skin friction is increasing factor of magnetic number. Local Nusselt and Sherwood numbers are lower for greater magnetic number.

To the best of author's knowledge, no such consideration has been given in the literature yet.

Investigation for convective flow of water-based nanofluid (composed of ferric oxide asnanoparticles) by curved stretching sheet of variable thickness is made. Bejan number andentropy generation analysis is presented in presence of viscous dissipation, mixed convectionand porous medium.

In this paper, by using NDSolve of MATHEMATICA, the nonlinear system of equations is solved. Velocity, temperature, Bejan number and entropy generation for involved dimensionless variables are discussed.

Increase in velocity is depicted for larger curvature parameter, and opposite trend is witnessed for higher nanoparticle volume concentration. Enhancement in temperature is seen for higher Eckert number while reverse behavior is noticed for larger curvature parameter. Entropy rate increases for variation of curvature parameter, Brinkman number and nanoparticle volume fraction. Bejan number decays for mixed convection and curvature parameters.

To the authors’ knowledge, there exists no study yet which describes flow by curved sheet of variable thickness. Such consideration with nanoparticles seems important task. Thus, the main objective here is to determine entropy generation in ferromagnetic nanofluid flow due to variable thickened curved stretching surface. Additionally, effects of Joule heating, porous medium, mixed convection and viscous dissipation are taken into account.

This paper aims to discuss the salient aspects of the Darcy–Forchheimer flow of viscous liquid in carbon nanotubes (CNTs). CNTs are considered as nanofluid, and water is taken as the continuous phase liquid. The flow features are discussed via curved surface. Water is taken as the base liquid. Flow is generated via nonlinear stretching. Energy expression is modeled subject to heat generation/absorption. Furthermore, convective conditions are considered at the boundary. The Xue model is used in the mathematical modeling which describes the features of nanomaterials. Both types of CNTs are considered, i.e. single-walled CNTs and multi-walled CNTs.

Appropriate transformations are used to convert the flow expressions into dimensionless differential equations. The bvp4c method is used for solution development.

Velocity enhances via higher estimations of nanoparticles volume fraction while decays for higher Forchheimer number, curvature parameter, behavior index and porosity parameter. Furthermore, thermal field is an increasing function of nanoparticle volume fraction, behavior index, Forchheimer number and porosity parameter.

Here, the authors have discussed two-dimensional CNTs-based nanomaterial Darcy–Forchheimer flow of viscous fluid over a curved surface. The authors believe that all the outcomes and numerical techniques are original and have not been published elsewhere.

The purpose of present communication is to analyze Darcy–Forchheimer flow of viscous nanofluid by curved stretchable surface. Flow in porous medium is characterized by Darcy–Forchheimer relation. Brownian diffusion and thermophoresis are considered. Convective heat and mass boundary conditions are also used at the curved stretchable surface.

The resulting nonlinear system is solved through shooting technique.

Skin friction coefficient is enhanced for larger porosity parameter and inertia coefficient while reverse trend is noticed for curvature parameter. Local Nusselt number is enhanced for higher Prandtl number and thermal Biot number, whereas the opposite trend is seen via curvature parameter, porosity parameter, inertia coefficient, thermophoresis parameter and Brownian motion parameter. Local Sherwood number is enhanced for Schmidt number, Brownian motion parameter and concentration Biot number, while reverse trend is noticed for curvature parameter, porosity parameter, inertia coefficient and thermophoresis parameter.

To the best of author’s knowledge, no such consideration has been given in the literature yet.

The study aims to determine an efficiency of external magnetic field on the bacteria surrounded by thousands of magnetic magnetite nanoparticles. The interstitial nanoliquid in which an artificial bacteria swims in biological cell is utilized with variable thermal conductivity. Two dimensions unsteady motion of second grade fluid are considered. The stretching wall is taken as a curved surface pattern.

The mathematical results have been obtained by Chebyshev pseudospectral method.

The impact of the various governing parameters is described by numerical tables and diagrams. It is proven that the pure blood velocity curves are higher when compared with the magnetite/blood. It is demonstrated from clinical disease that dangerous tumors show diminished blood flow. This study concludes that the blood velocity profile increases by increasing the values of fluid parameters. This implies that the medication conveyance therapy lessens the tumor volume and helps in annihilating malignancy cells. The blood temperature distribution raises as the magnetite nanoparticles concentration increases. Consequently, the physical properties of the blood can be enhanced by immersing the magnetite nanoparticles. Further, the present outcomes cleared the thermal conductivity as, a variable function of the temperature, has an important role to enhance the heat transfer rate.

To the best of authors’ knowledge, this study is reported for the first time.