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The purpose of this paper is to perform an analytical approximation for the flow of magnetohydrodynamic Carreau fluid with the association of nanoparticles over a rotating disk. The disk is moving with a constant uniform speed. Governing equations are obtained by using these assumptions in the form of partial differential equations with boundary conditions. These coupled, highly nonlinear equations are transformed into a coupled system of ordinary differential equations by engaging similarity transformation in the rotating frame of reference.

An efficient and reliable scheme, namely optimal homotopy asymptotic method, is used to obtain the solutions of the arising physical problem, which is further analyzed graphically. After computing the solutions of the arising problem, plots of velocities, temperature and concentration are discussed briefly.

It has been observed that dimensionless velocity reduced due to magnetic effect between the boundary layer and escalating values of the magnetic parameter upsurges the temperature and concentration profiles. Contour plots and numerical results are given for local numbers like skin friction coefficient, Nusselt number and Sherwood number.

The work presented in this manuscript is neither published nor submitted anywhere for the consideration/publications. It is a novel work.

A novel type of heat transfer fluid known as hybrid nanofluids is used to improve the efficiency of heat exchangers. It is observed from literature evidence that hybrid nanofluids outperform single nanofluids in terms of thermal performance. This study aims to address the stagnation point flow induced by Williamson hybrid nanofluids across a vertical plate. This fluid is drenched under the influence of mixed convection in a Darcy–Forchheimer porous medium with heat source/sink and entropy generation.

By applying the proper similarity transformation, the partial differential equations that represent the leading model of the flow problem are reduced to ordinary differential equations. For the boundary value problem of the fourth-order code (bvp4c), a built-in MATLAB finite difference code is used to tackle the flow problem and carry out the dual numerical solutions.

The shear stress decreases, but the rate of heat transfer increases because of their greater influence on the permeability parameter and Weissenberg number for both solutions. The ability of hybrid nanofluids to strengthen heat transfer with the incorporation of a porous medium is demonstrated in this study.

The findings may be highly beneficial in raising the energy efficiency of thermal systems.

The originality of the research lies in the investigation of the Darcy–Forchheimer stagnation point flow of a Williamson hybrid nanofluid across a vertical plate, considering buoyancy forces, which introduces another layer of complexity to the flow problem. This aspect has not been extensively studied before. The results are verified and offer a very favorable balance with the acknowledged papers.

In heat transfer, fluids and nanoparticles can provide new innovative technologies with potential to adapt the heat transfer fluid’s thermal properties through control over particle size, shape and others. This paper aims to examine the effects of spherical and non-spherical (cylinder, disk, platelets, etc.) shapes of silver (Ag) nanoparticles on heat transfer enhancement and inherent irreversibility in hydromagnetic water base nanoliquid flow over a convectively heated stretching sheet with heat generation/absorption.

Applying suitable similarity constraints, the model partial differential equations are transformed into a set of nonlinear ordinary differential equations. Solutions are obtained analytically via optimal homotopy asymptotic method (OHAM) and numerically via shooting technique coupled with the Runge-Kutta-Fehlberg (RK-F) method.

The impact of Ag nanoparticle’s shape along with other germane factors, such as Biot number, magnetic field, solid volume fraction and heat source/sink on velocity and thermal profiles, Nusselt number, skin friction coefficient, heat transfer enhancement, rate of entropy generation and irreversibility ratio, are scrutinized via graphical simulations and discussed. This study revealed that cylindrical shape Ag nanoparticles generate high entropy and fluid friction irreversibility, whereas disk shape Ag nanoparticles exhibit high transfer enhancement rate. Moreover, a boost in magnetic field intensity, volume-fraction parameter and Biot number enhances the thermal boundary layer thickness.

The main objective of this work is to examine the different Ag nanoparticles shape effects on the heat transfer enhancement and inherent irreversibility owing to hydromagnetic nanoliquid flow past a convectively heated stretching sheet with heat source/sink, which has not been yet studied. It is hope that this study will bridge the gap in the present literature and serve as impetus to scholars, engineers and industries for more exploration in this direction. The intrinsic nonlinearity of the model equations precludes its exact solution; hence, OHAM and shooting technique coupled with the RK-F method have been used to numerically tackle the problem. Pertinent results are discussed quantitatively and displayed graphically and in tabular form.

The purpose of this paper is to study the steady laminar magnetohydrodynamics (MHD) flow of a magnesium oxide-silver/water hybrid nanofluid along a horizontal slim needle with thermal radiation by considering dual solutions.

It is assumed that the needle can move in the same or opposite direction of the free stream. Also the solid phase and fluid phase are in thermal equilibrium. The basic partial differential equations become dimensionless using a similarity transformation method. Moreover, problem coding is accomplished using the finite difference method. The emerging parameters are nanoparticles mass (0–40 gr), base fluid mass (100 gr), needle’s size (0.001–0.2), magnetic field parameter, velocity ratio parameter, radiation parameter and Prandtl number (6.2).

With help of the stability analysis, it is shown that always the first solutions are physically stable. Results indicate that the magnetic parameter and the second nanoparticle’s mass limit the range of the velocity ratio parameter for which the solution exists. Besides, the magnetic parameter leads to decrease of quantities of engineering interest, i.e. skin friction coefficient and local Nusselt number.

To the best of the authors’ knowledge, no one has ever attempted to study the present problem through a mass-based model for hybrid nanofluid. Moreover, the dual solutions for the problem are new. Indeed, the results of this paper are purely original and the numerical achievements were never published up to now. Finally, the authors expect that the present investigation would be useful in hot-wire anemometer or shielded thermocouple for measuring the velocity of the wind, etc.

The purpose of this study is to numerically analyze the mixed convection and entropy generation in an annulus with a rotating heated inner cylinder for single-wall carbon nanotube (SWCNT)–water nanofluid flow using local thermal nonequilibrium (LTNE) model. An examination of the system behavior is presented considering the heat-generating solid phase inside the porous layer partly filled at the inner surface of the outer cylinder.

The discretized governing equations for nanofluid and porous layer by means of the finite volume method are solved by using the SIMPLE algorithm.

It is found that the buoyancy force and rotational effect have an important impact on the change of the strength of streamlines and isotherms for nanofluid flow. The minimum average Nusselt number on the inner cylinder is obtained at Ra$_E$ = 10$^4$, and the minimum total entropy generation is found at Re = 400 for given parameters. The entropy generation minimization is determined in case of different nanoparticle volume fractions. It is observed that at the same external Rayleigh numbers, the LTNE condition obtained with internal heat generation is very different from that without heat generation.

To the best of the authors’ knowledge, there is no previous paper presenting mixed convection and entropy generation of SWCNT–water nanofluid in a porous annulus under LTNE condition. The addition of nanoparticles to based fluid leads to a decrease in the value of minimum total entropy generation. Thus, using nanofluid has a significant role in the thermal design and optimization of heat transfer applications.

The purpose of this paper is to study entropy generation in magneto-Jeffrey nanomaterial flow by impermeable moving boundary. Adopted nanomaterial model accounts Brownian and thermophoretic diffusions. Modeling is arranged for thermal radiation, nonlinear convection and viscous dissipation. In addition, the concept of Arrhenius activation energy associated with chemical reaction are introduced for description of mass transportation.

Homotopy algorithms are used to compute the system of ordinary differential equations.

The afore-stated analysis clearly notes that simultaneous aspects of activation energy and entropy generation are not yet investigated. Therefore, the intention here is to consider such effects to formulate and investigate the magneto-Jeffrey nanoliquid flow by impermeable moving surface.

As per the authors’ knowledge, no such work has yet been published in the literature.

The purpose of this paper is to address the impact of induced magnetic field in mixed convective stagnation flow of TiO₂-Cu-water hybrid nanofluid towards a stretchable sheet. Non-linear thermal radiation and heat source/sink are accounted. Flow of hybrid nanofluid is discussed. Non-linear partial differential expressions are converted to ordinary ones through appropriate transformations.

The obtained systems are solved for convergence solutions via homotopy analysis method. Graphical results are discussed for different physical variables on the velocity, induced magnetic field and temperature fields for both Cu water nanofluid and TiO₂-Cu-water hybrid nanofluid. Finally, the effect of different physical variables on skin friction coefficient (C_fx) and Nusselt number Nu_x in the presence of water nanofluid and TiO₂-Cu-water hybrid nanofluid are discussed.

Velocities and induced magnetic field are increasing functions of mixed convection parameter and nanoparticle volume fraction. Temperature rises for higher radiation parameter. Skin friction is greater in case of Cu-water nanoliquid, while Nusselt number is less for Cu-water nanofluid when they are compared with hybrid nanoliquid TiO₂-Cu-water.

No such work is not yet present in the literature.

This paper aims to focus on the steady state flow of nanoliquid through microchannel with the aid of internal heat source and different shapes of nanoparticle. The influence of MoS₂ and TiO₂ particles of nano size on flow and thermal fields is examined. The governing equations are modelled and then solved numerically. The obtained physical model is nondimensionalized using dimensionless quantities. The nondimensional equations are treated with numerical scheme. The outcome of the current work is presented graphically. Diverse substantial quantities such as entropy generation, Bejan number and Nusselt number for distinct parameters are depicted through graphs. The result established that nanoparticle of blade shape acquires larger thermal conductivity. Entropy analysis is carried out to explore the impact of various parameters such as nanoparticle volume fraction, magnetic parameter, radiation parameter and heat source parameter.

The resultant boundary value problem is converted into initial value problem using shooting scheme. Then the flow model is resolved using Runge-Kutta-Fehlberg-Fourth-Fifth order technique.

It is emphasized that entropy generation for the fluid satisfies N(ζ)_{(TiO2−water)} > N(ζ)_{(MoS2−water)}. In addition to this, it is emphasized that N(ζ)_sphere > N(ζ)_brick > N(ζ)_cylinder > N(ζ)_platelet > N(ζ)_blade. Also, it is obtained that blade-shaped nanoparticle has higher thermal conductivity for both MoS₂ and TiO₂.

Shape effects on Molybdenum disulphide and TiO₂ nanoparticle in a microchannel with heat source is examined. The analysis of entropy shows that N(ζ)_{(TiO2−water)} > N(ζ)_{(MoS2−water)}.

This paper aims to examine the three-dimensional (3D) flow of carbon nanotubes (CNTs) due to bidirectional nonlinearly stretching surface by considering porous medium. Characteristics of both single-walled CNTs and multi-walled CNTs are discussed by considering Xue model. Darcy–Forchheimer model is used for flow saturating porous medium.

Optimal homotopy analysis method is used for the development of series solutions.

The authors deal with 3D Darcy–Forchheimer flow of CNTs over a nonlinearly stretching surface. Heat transport mechanism is discussed in the presence of Xue model. The homogeneous and heterogeneous effects are also accounted. The mathematical modeling is computed using boundary-layer approximations.

No such work has been done yet in the literature.

The novel mechanical, chemical and thermodynamics characteristics of both single- and multi-wall carbon nanotubes (CNTs) make them a subject of much attention for the scientists and engineers from all domains. Fluid flows subject to CNTs are significant in biomedical engineering, energy storage systems, domestic and industrial cooling, automobile industries and solar energy collectors, etc. Keeping such effectiveness of CNTs in mind, this paper aims to examine peristaltic flow subject to CNTs in an asymmetric tapered channel. Both single and multiple walls CNTs are considered. The viscosity of nanomaterial depends on nanoparticles volume fraction and temperature. Total entropy rate through second law of thermodynamics is calculated. Heat source/sink and nonlinear heat flux are accounted.

The complicated flow expressions are simplified through lubrication approach. The velocity, temperature and entropy expressions are numerically solved by the built-in-shooting method.

The solutions for entropy generation, temperature and velocity are plotted, and the influences of pertinent variables are examined. The authors noticed that entropy generation is an increasing function of the Brinkman number.

The originality of this work is to communicate peristaltic CNTs-based nanomaterial peristaltic flow of viscous fluid in an asymmetric channel. No such consideration is yet published in the literature.