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The increasing number of ways in which carbon nanotubes (CNTs) may be used in business and technology has led to an explosion of interest in these tiny tubes. As a result, the Yamada–Ota model is used to investigate the unsteady, non-axisymmetric MHD Homann stagnation point of carbon nanotubes passing over a convective surface with nonlinear radiation. Consisting of single-walled and multi-walled carbon nanotubes that are suspended in water (H2O). The length of the nanomaterial is between 3 μ m ≤ L ≤ 7 0 μ m nanometers, while its radius is between 1 0 nm ≤ R ≤ 4 0 nm. The method of similarity transformation is altered so that it may be used to get the dimensionless system of differential equations from the mathematical model that is envisioned for PDEs. After that, approximate solutions are obtained using MATHEMATICA and the Shooting with RK-IV technique. In this paper, we provide a graphical discussion and a physical interpretation of the results of measures of practical significance as a function of key factors. The results indicated that an increase in the volume fraction led to a corresponding rise in the heat transfer rate. However, it is reduced by the magnetic energy that is supplied to it. Carbon nanoliquids with a single wall have a greater melting point than nanoliquids with multiple walls. Industrial and technological uses of the issue under examination span several fields, including aviation and health. The results of the interface velocity and heat transfer rate at the surface, as well as the solution of each profile, are shown graphically, along with an analysis of the effects of MHD on the flow and heat transfer characteristics of the fluid under the influence of radiation. [ABSTRACT FROM AUTHOR]

Here, a study of steady, magnetohydrodynamic flow of incompressible, cold fluid around a moving plate with a non‐Darcian porous medium in existence of heat source and nth‐order chemical reaction incorporating Soret and Dufour effects is considered. MATLAB bvp4c technique is used to solve the prevailing equations. Variations in velocity, temperature and concentration are analysed. It is observed that the applicable parameters such as non‐Darcy, Soret, Dufour, chemical reaction play a significant role in controlling the flow. Chemical reaction parameter reduces skin friction, heat transfer, and mass transfer while Eckert number enhances the mass transfer and skin friction. [ABSTRACT FROM AUTHOR]

The stretched surface's convective heat transfer capability can be improved by using nanoparticles. There is a significant role of the Prandtl number in determining the thermal and momentum stretching layer surfaces. It is proposed in this study that an effective Prandtl number model be used to explore the two-dimensional oblique stagnation point flow of γAl2O3−H2O and γAl2O3−C2H6O2 nanofluids moving over a convective stretching surface. The fluid in question is subjected to a thorough investigation. It is necessary to apply non-linear ordinary differential equations in order to connect the controlling partial differential equations with the boundary conditions. To solve these equations, an efficient and reliable numerical technique is used. Shooting Method with Runge Kutta-IV in Mathematica software. Visual representations of normal and tangential velocity and temperature as well as streamlines as a function of many physical parameters are shown. The results show that as the volume fraction of nanoparticles increases, the fluid flow f(y), h(y) and velocity f′(y), h′(y) all increase, whereas the flow f(y) and velocity f′(y) both increase against the stretching ratio parameter, while the flow h(y) and velocity h′(y) both decrease. When the volume percentage of nanoparticles and the Biot number are both increased, the temperature rises. However, when the stretching ratio parameter is increased, the temperature falls. Physical attributes like the local skin friction coefficient and the heat flow may be characterized in many ways. A nanofluid comprised of γAl2O3−C2H6O2 outperformed a γAl2O3−H2O nanofluid in terms of heat transfer rate. The source of zero skin friction may be observed to move to the left or right depending on the balance of obliqueness and straining motion at point xs. The computed numerical results of the current research correspond well with those accessible in the literature for the limiting scenario.

In this research work, we consider the two-dimensional time-dependent laminar hydromagnetic boundary-layer flow of a bio-magnetic fluid over a wedge using a micropolar fluid model with convective boundary conditions and taking into account the action of a transversely magnetic field. The partial differential equations that govern velocity, temperature and micro-rotation are transformed into nonlinear ordinary differential equations with similarity transformations. The findings are analytically analyzed afterward through the Adomian decomposition method (ADM) and numerically through the shooting technique based on Runge–Kutta–Fehlberg. In this study, we have considered the effect of the unsteadiness parameter K , wedge angle parameter β , Reynolds number Re, magnetic field parameter M and induced magnetic field h on the evolution of dimensionless velocity, temperature and micro-rotation of the bio-magnetic flow throughout the boundary layer. It is found that the flow separation may occur with the increase in unsteadiness parameter K and is prevented as the wedge angle parameter β rises. Also, results indicate that in the vicinity of the wedge surface, increasing K parameter leads to a reduction in fluid temperature and grows the micro-rotation of the blood corpuscles. Finally, comparisons between analytical and numerical data clearly show the effectiveness of the adopted analytical ADM technique. [ABSTRACT FROM AUTHOR]

The significance of viscosity and thermal conductivity variation parameters on the dynamics of Newtonian fluid conveying tiny particles over a convectively heated surface is examined. The dimensional partial differential equations controlling the flow are remodeled to ordinary differential equations via suitable similarity variables in conjunction with the rescaled Nusselt, Sherwood and density number of motile microorganisms. The resulting nonlinear coupled ordinary differential equations are consequently scaled down to a system of first order ordinary differential equations. The system of equations are evaluated arithmetically via shooting technique along with fourth order Runge–Kutta integration scheme for different boundary conditions. The result was found to be in excellent agreement when compared with available records in the literature. The major highlights of the problem are analyzed and discussed thoroughly. It is seen that increase in viscosity variation parameter is capable to cause a decline in the local skin friction coefficients at the rate of −0.04985and the Nusselt number is an increasing function of the thermal conductivity variation parameter.

A numerical study is performed to discuss the nonaligned stagnation of a rate type fluid over a convective surface. The rheology of the fluid is presented by the constitutive equation of the Maxwell fluid model. Buongiorno's model is used to elaborate on the effects of Brownian motion and thermophoresis and motile microorganisms are introduced for the stability of the nanoparticles. The governing equations were solved by the implicit finite difference method. Graphical illustrations for velocity, temperature, nanoparticle concentration and motile microorganism profiles for various involved parameters are presented for both convective and nonconvective surfaces. It is depicted that the temperature, nanoparticle, and microorganism concentration profiles decease while both axial and tangential velocities increase with the velocity ratio parameter for both Newtonian and Maxwellian fluids. The magnitude of temperature, nanoparticle, and microorganism concentration profiles is large for the nonconvective surface as compared to the convective surface. The Nusselt number, Sherwood number, and motile organism number decrease as we move from Newtonian fluid to non‐Newtonian fluid. Furthermore, the increase in the Brownian motion parameter and thermophoresis parameter decreases the density of the motile organism over the convective as well as nonconvective surface. [ABSTRACT FROM AUTHOR]

The purpose of present study is to identify the effects of viscous dissipation and suction/injection on MHD flow of a nanofluid past a wedge with convective surface in the appearance of slip flow and porous medium. The basic non-linear PDEs of flow and energy are altered into a set of non-linear ODEs using auxiliary similarity transformations. The system of equations together with coupled boundary conditions have been solved numerically by applying Runge-Kutta-Fehlberg procedure via shooting scheme. The influence of relevant parameters on non-dimensional velocity and temperature profiles are depicted graphically and investigated in detail. The results elucidate that as enhance in the Eckert number, the skin friction coefficient increases, while heat transfer rate decreases. The outcomes also specify that thermal boundary layer thickness declines with an increase in suction parameter. Moreover, it is accelerated with augment in injection parameter. The results are analogized with the study published earlier and it creates a fine concord.

We aimed at examining the magnetohydrodynamic (MHD) radiative non-aligned stagnation point motion of non-Newtonian liquid over a stretched surface. The heat transfer mechanism is investigated in the presence of variable heat sink/source, non-linear Rosseland approximation and Biot number. Appropriate transmutations are exploited to metamorphose the flow equations into ODEs. The acquired non-linear ODEs are highly coupled. These are tackled with the consecutive implication of fourth-order Runge--Kutta and shooting techniques. The variations of flow governing parameters on the dimensionless velocity, microrotation and temperature plus the measure of heat transport, couple stress coefficient and friction factor are thoroughly explained using plots and tables. Outcomes stipulate that increasing the values of the stretching ratio parameter causes the thermal field to decline and the velocity field to inflate. Also, an upsurge in the micropolar parameter produces an increase in the rate of heat transport but an opposite outcome is detected with the couple stress coefficient. To the best of our knowledge the non-orthogonal stagnated motion of micropolar liquid with radiation as non-linear and variable heat source/sink has never before been scrutinized. [ABSTRACT FROM AUTHOR]

Heat transfer characteristics of the traditional wall jet flows subject to various thermal boundary conditions including isothermal surface, prescribed temperature, constant heat flux, prescribed heat flux, adiabatic surface and thermally convective surface are documented in analytic closed forms. Heat dissipation has been also included where the similarity energy equation could structurally adjust to this specific term (for the adiabatic case, this term has been necessarily included). In all the studied cases, both the transpiration velocity and moving wall conditions are allowed to exist (where applicable) in such a way, being consistent with the Glauert integral constraint and subject to the context of exponentially decaying wall jet flows. In particular, it is analytically proved (even without having the closed form solutions) that for the Glauert original case, a surface with a prescribed temperature in the form of T w ( x ) = m x − 1 4 + T ∞ serves zero contribution to heat transfer at the wall (the Induced Heat Shield). More precisely, the value − 1 4 as the prescribing parameter is the Surface Heat Transfer Stopping Point and below this point, heat transfer phenomenon falls from a usual physical interpretation, expressing spectrums of thermal instabilities through a hyper geometric function. Furthermore, it is argued that a normalized similarity temperature in the form of θ ( η ) = T − T ∞ m x n < − 1 4 results in the appearance of an uninterruptable singularity within the heat transfer phenomenon for the Glauert case subject to a rigorous physical ground; and as an immediate practical consequence, there is no physically-valid similarity solution for an adiabatic surface or more precisely, for energy equation with heat dissipation consideration. It should be mentioned that the concept of Induced Heat Shield is discussed in here for the first time (to our knowledge) which may inspire a concealed fact regarding the restrictions of the thermal similarity solutions. Therefore, it is hopeful that heat transfer phenomenon in the Glauert type wall jet flows and the associated physical representations can be better understood by the present research. [ABSTRACT FROM AUTHOR]

The purpose of present study is to identify the effects of viscous dissipation and suction/injection on MHD flow of a nanofluid past a wedge with convective surface in the appearance of slip flow and porous medium. The basic non-linear PDEs of flow and energy are altered into a set of non-linear ODEs using auxiliary similarity transformations. The system of equations together with coupled boundary conditions have been solved numerically by applying Runge-Kutta-Fehlberg procedure via shooting scheme. The influence of relevant parameters on non-dimensional velocity and temperature profiles are depicted graphically and investigated in detail. The results elucidate that as enhance in the Eckert number, the skin friction coefficient increases, while heat transfer rate decreases. The outcomes also specify that thermal boundary layer thickness declines with an increase in suction parameter. Moreover, it is accelerated with augment in injection parameter. The results are analogized with the study published earlier and it creates a fine concord. [ABSTRACT FROM AUTHOR]

The stretched surface's convective heat transfer capability can be improved by using nanoparticles. There is a significant role of the Prandtl number in determining the thermal and momentum stretching layer surfaces. It is proposed in this study that an effective Prandtl number model be used to explore the two-dimensional oblique stagnation point flow of γ A l 2 O 3 - H 2 O and γ A l 2 O 3 - C 2 H 6 O 2 nanofluids moving over a convective stretching surface. The fluid in question is subjected to a thorough investigation. It is necessary to apply non-linear ordinary differential equations in order to connect the controlling partial differential equations with the boundary conditions. To solve these equations, an efficient and reliable numerical technique is used. Shooting Method with Runge Kutta-IV in Mathematica software. Visual representations of normal and tangential velocity and temperature as well as streamlines as a function of many physical parameters are shown. The results show that as the volume fraction of nanoparticles increases, the fluid flow f ( y ) , h ( y ) and velocity f ' ( y ) , h ' ( y ) all increase, whereas the flow f ( y ) and velocity f ' ( y ) both increase against the stretching ratio parameter, while the flow h ( y ) and velocity h ' ( y ) both decrease. When the volume percentage of nanoparticles and the Biot number are both increased, the temperature rises. However, when the stretching ratio parameter is increased, the temperature falls. Physical attributes like the local skin friction coefficient and the heat flow may be characterized in many ways. A nanofluid comprised of γ A l 2 O 3 - C 2 H 6 O 2 outperformed a γ A l 2 O 3 - H 2 O nanofluid in terms of heat transfer rate. The source of zero skin friction may be observed to move to the left or right depending on the balance of obliqueness and straining motion at point x s . The computed numerical results of the current research correspond well with those accessible in the literature for the limiting scenario., Competing Interests: The authors declare no conflict of interest., (© 2023 The Authors.)

In this paper we analyze unsteady two dimensional hydromagnetic forced convective heat transfer flow of a viscous incompressible micropolar fluid along a permeable wedge with convective surface boundary condition. The potential flow velocity has been taken as a function of the distance a- and time t. The governing time dependent non-linear partial differential equations have been reduced to a set of non-linear ordinary differential equations by introducing a new class of similarity transformations. Comparisons with previously published work are performed, and the results are found to be in excellent agreement. The resulting local similarity equations for unsteady flow have been solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Numerical results in the form of non-dimensional velocity, microrotation and temperature profiles are presented graphically and discussed for different material parameters entering into the analysis. The effects of the pertinent parameters on the local skin- friction coefficient, plate couple-stress and the rate of heat transfer are also displayed in tabulated form and discussed them from the physical point of view. The obtained numerical results show that the rate of heat transfer increases with the increase of the unsteadiness parameter and decreases with the increase of the surface convection parameter. [ABSTRACT FROM AUTHOR]

The present study numerically investigates the oblique flow of a Walter-B type nano fluid over a convective surface. Effects of transversely applied magnetic field are also taken into account. The governing system is presented in the form of coupled differential equations by means of suitable similarity transformations which are then solved by using Spectral Quasilinearisation Method (QLM) and the Spectral Local Linearization Method (LLM). The results for velocities temperature as well as nano particle concentration are plotted against pertinent flow parameters. It is found that applied magnetic field M has opposite influence on normal and tangential components of local shear stress and it decays the local heat flux and mass flux rate at the stretching convective surface. Thermophoresis and Brownian diffusion effects on the local heat and mass flux rate are found to be non-similar in a quantitative sense. In order to signify the validity of current numerical scheme, a remarkable agreement is presented with the previous literature for some limiting cases. [ABSTRACT FROM AUTHOR]

Present model examines the 2-D boundary layer flow of natural convective micropolar nanofluid along a vertically stretching sheet. Moreover, we have considered the simultaneous effects of radiation and convective boundary surface. Influences of nanoparticles are also analyzed for both assisting and opposing flow. Similarity transformations are used to transform the governing nonlinear partial differential equation to ordinary differential equations. The condensed boundary layer equations for nanomicropolar fluid model are solved numerically. The effects of emerging parameters on velocity, temperature, and nanoparticle volumetric expansion profiles are discussed. Stimulating results are presented graphically and explained physically. The heat transfer rate and concentration rate are also displayed graphically for different flow control parameters. [ABSTRACT FROM PUBLISHER]

Abstract: Heat transfer characteristics of a two-dimensional steady hydromagnetic slip flow of water based nanofluids (TiO2–water, Al2O3–water, and Cu–water) over a wedge with convective surface taking into account the effects of heat generation (or absorption) has been investigated numerically. The local similarity solutions are obtained by using very robust computer algebra software MATLAB and presented graphically as well as in a tabular form. The results show that nanofluid velocity is lower than the velocity of the base fluid and the existence of the nanofluid leads to the thinning of the hydrodynamic boundary layer. The rate of shear stress is significantly influenced by the surface convection parameter and the slip parameter. It is higher for nanofluids than the base fluid. The results also show that within the boundary layer the temperature of the nanofluid is higher than the temperature of the base fluid. The rate of heat transfer is found to increase with the increase of the surface convection and the slip parameters. Addition of nanoparticles to the base fluid induces the rate of heat transfer. The rate of heat transfer in the Cu–water nanofluid is found to be higher than the rate of heat transfer in the TiO2–water and Al2O3–water nanofluids. [Copyright &y& Elsevier]

The paper presents a numerical study to explore the possible similarity solutions as well as dual branch solutions to study the performance evaluation of various nanoparticles associated water as the base fluid in the case of steady two-dimensional forced convection boundary layer flow through a moving flat porous plate under external magnetic fields. We considered water as a base fluid embedded with the three different types of nanoparticles namely copper (Cu), alumina (Al 2 O 3) and titania (TiO 2). The governing equations are simplified by similarity approach. The resulting equations are solved numerically and the numerical results are explored through graphs and tables and discussed in detail. The influences of problem parameters are discussed for the steady solution. The paper extends results of previous works by others authors contributing to increase the scientific knowledge on the subject. The skin friction coefficient and local Nusselt number on the plane are studied as functions of the problem parameters. The study reveals that the problem considered admits of upper and lower branch solutions for moving parameter λ , magnetic parameter M , the power law parameter n , convection heat transfer b and nanoparticle volume fraction parameter ϕ. [ABSTRACT FROM AUTHOR]