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This paper aims to analyze the steady two-dimensional stagnation-point flow of an electrically conducting Newtonian or micropolar fluid when the obstacle is uniformly heated.

The governing boundary layer equations are transformed into a system of ordinary differential equations using appropriate similarity transformations. Some analytical considerations about existence and uniqueness of the solution are obtained. The system is then solved numerically using the bvp4c function in MATLAB.

If the temperature of the obstacle T_w coincides with the environment temperature T₀, then the motion reduces to the usual orthogonal stagnation-point flow; if T_w = T₀, then it is necessary to include in the similarity function describing the velocity an oblique part due to the temperature. Also, the presence of a uniform external magnetic field orthogonal to the obstacle is examined. In all cases, the motion is reduced to a system of nonlinear ordinary differential equations with boundary conditions, whose solution is discussed numerically when the Prandtl and the Hartmann number varies.

The present results are original and new for the problem of magnetohydrodynamic mixed convection in the plane stagnation-point flow of a Newtonian or a micropolar fluid over a vertical flat plate. At infinity, the motion approaches the orthogonal stagnation-point flow of an inviscid fluid; the effect of an uniform external magnetic field is considered, and the obstacle has a uniform temperature.

The purpose of this paper is to do a comprehensive study on the unsteady general three-dimensional stagnation-point flow and heat transfer of a nanofluid by Buongiorno’s model.

In this study, the convective transport equations include the effects of Brownian motion and thermophoresis. By introducing new similarity transformations for velocity, temperature and nanoparticle volume fraction, the basic equations governing the flow, heat and mass transfer are reduced into highly non-linear ordinary differential equations. The resulting non-linear system has been solved both analytically and numerically.

The analysis shows that velocity, temperature and nanoparticle concentration profiles in the respective boundary layers depend on five parameters, namely unsteadiness parameter A, Brownian motion parameter Nb, thermophoresis parameter Nt, Prandtl number Pr and Lewis number Le. It is found that the thermal boundary layer thickens with a rise in both of the Brownian motion and the thermophoresis effects. Therefore, similar to the earlier reported results, the Nusselt number decreases as the Brownian motion and thermophoresis effects become stronger. A correlation for the Nusselt number has been developed based on a regression analysis of the data. This correlation predicts the numerical results with a maximum error of 9 percent for a usual domain of the physical parameters.

The stagnation point flow toward a wavy cylinder (with nodal and saddle stagnation points) that a little attention has been given to it up to now. The examination of unsteadiness effect on the general three-dimensional stagnation-point flow. The application of an interesting and global model (Boungiorno’s model) for the nanofluid that incorporates the effects of Brownian motion and thermophoresis. The study of the effects of Brownian motion and thermophoresis on the nanofluid flow, heat and mass transfer characteristics. The prediction of correlation for the Nusselt number based on a regression analysis of the data. General speaking, we can tell the problem with this geometry, characteristics, the applied model, and comprehensive results, was Not studied and analyzed in literature up to now.

Asymptotic methods are employed to derive the long wave equations governing the fluid dynamics of thin, time‐dependent, incompressible, vertical, planar liquid sheets at low Reynolds numbers subjected to London‐van der Waals body forces and gravity. Analytical solutions for steady, viscous sheets in gravitational and zero‐gravity environments are obtained for large surface tension. Numerical studies of planar liquid sheets at low Reynolds numbers with no surface tension indicate that, for plane stagnation flows, the deceleration of the sheet as it approaches the solid wall decreases as the London‐van der Waals forces are increased, the effects of these body forces decrease as the Froude number is increased, and, for Reynolds‐to‐Froude numbers greater than one, the thickening of the sheet as it approaches the solid boundary increases as the Hamaker constant is increased. Numerical experiments of film casting processes with three different flow approximations which account for or neglect inertia and/or the gravitational pull have also been performed and indicate that for high take‐up speeds, a boundary layer is formed at the downstream boundary, the thickness of this layer decreases as the London‐van der Waals forces are increased, and, for Reynold‐to‐Froude numbers larger than one, the leading‐order thickness and axial velocity component are very sensitive to the value of the Hamaker constant.

This paper aims to probe the problem of an unsteady mixed convection stagnation point flow and heat transfer past a stationary surface in an incompressible viscous fluid numerically.

The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which is then solved numerically by a Runge – Kutta – Fehlberg method with shooting technique and a collocation method, namely, the bvp4c function.

The effects of the governing parameters on the fluid flow and heat transfer characteristics are illustrated in tables and figures. It is found that dual (upper and lower branch) solutions exist for both the cases of assisting and opposing flow situations. A stability analysis has also been conducted to determine the physical meaning and stability of the dual solutions.

This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans.

The case of suction on unsteady mixed convection flow at a three-dimensional stagnation point has not been studied before; hence, all generated numerical results are claimed to be novel.

The purpose of this paper is to investigate analytically the steady general three-dimensional stagnation-point flow of an aqueous titania-copper hybrid nanofluid past a circular cylinder that has a sinusoidal radius variation.

First, the analytic modeling of hybrid nanofluid is presented, and using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved by the well-known function bvp4c from MATLAB.

The current solution demonstrates good agreement with those of the previously published studies in the special cases of regular fluid and nanofluids. Graphical results are presented to investigate the influences of the titania and copper nanoparticle volume fractions and also the nodal/saddle indicative parameter on flow and heat transfer characteristics. Here, the thermal characteristics of hybrid nanofluid are found to be higher in comparison to the base fluid and fluid containing single nanoparticles. An important point to note is that the developed model can be used with great confidence to study the flow and heat transfer of hybrid nanofluids.

Analytic modeling of hybrid nanofluid is the important originality of present study. Hybrid nanofluids are potential fluids that offer better heat transfer performance and thermophysical properties than convectional heat transfer fluids (oil, water and ethylene glycol) and nanofluids with single nanoparticles. In this investigation, titania (TiO₂, 50 nm), copper (Cu, 20 nm) and the hybrid of these two are separately dispersed into the water as the base fluid and analyzed.

This paper aims to simulate the steady laminar mixed convection incompressible viscous and electrically conducting hybrid nanofluid (CuO-Cu/blood) flow near the plane stagnation-point over a horizontal porous stretching sheet along with an external magnetic field and induced magnetic field effects that can be applicable in the biomedical fields like the flow dynamics of the micro-circulatory system and especially in drug delivery.

The basic partial differential equations (PDEs) are altered to a set of dimensionless ordinary differential equations (ODEs) with the help of suitable similarity variables which are then solved numerically using bvp4c scheme from MATLAB. Inasmuch as validation results have shown a good agreement with previous reports, the present novel mass-based algorithm can be used in this problem with great confidence. Governing parameters are both nanoparticle masses, base fluid mass, empirical shape factor of both nanoparticles, suction/injection parameter, magnetic parameter, reciprocal magnetic Prandtl number, Prandtl number, heat source parameter, mixed convection parameter, permeability parameter and frequency ratio. The effect of these parameters on the flow and heat transfer characteristics of the problem is discussed in detail.

It is shown that the use of CuO and Cu hybrid nanoparticles can reduce the hemodynamics effect of the capillary relative to pure blood case. Moreover, as the imposed magnetic field enhances, the velocity of the blood decreases. Besides, when the blade shapes for both nanoparticles are taken into account, the local heat transfer rate is maximum that is also compatible with experimental observations.

An innovative mass-based model of CuO-Cu/blood hybrid nanofluid has been applied. The novel attitude to one-phase hybrid nanofluid model corresponds to considering nanoparticles mass as well as base fluid mass to computing the solid equivalent volume fraction, the solid equivalent density and also solid equivalent specific heat.

The gas assisted Iaser heating of engineering surfaces finds wide application in industry. Numerical simulation of the heating process may considerably reduce the cost spent on experimentation. In the present study, 2‐dimensional axisymmetric flow and energy equations are solved numerically using a control volume approach for the case of a gas assisted laser heating of steel surfaces. Various turbulence models including standard k‐ε, k‐ε YAP, low Reynolds number k‐ε and RSTM models are tested. The low Reynolds number k‐ε model is selected to account for the turbulence. Variable properties of both solid and gas are taken into account during the simulation. Air is considered as an assisting gas impinging the workpiece surface coaxially with the laser beam. In order to validate the presently considered methodology, the study is extended to include comparison of present predictions with analytical solution for the case available in the literature. It is found that the assisting gas jet has some influence on the temperature profiles. This effect is minimum at the irradiated spot center and it amplifies considerably in the gas side. In addition, account for the variable properties results in lower surface temperatures as compared to the constant properties case.

The purpose of this article is to study the steady laminar magnetohydrodynamics mixed convection stagnation-point flow of an alumina-graphene/water hybrid nanofluid with spherical nanoparticles over a vertical permeable plate with focus on dual similarity solutions.

The single-phase hybrid nanofluid modeling is based on nanoparticles and base fluid masses instead of volume fraction of first and second nanoparticles as inputs. After substituting pertinent similarity variables into the basic partial differential equations governing on the problem, the authors obtain a complicated system of nondimensional ordinary differential equations, which has non-unique solution in a certain range of the buoyancy parameter. It is worth mentioning that, the stability analysis of the solutions is also presented and it is shown that always the first solutions are stable and physically realizable.

It is proved that the magnetic parameter and the wall permeability parameter widen the range of the buoyancy parameter for which the solution exists; however, the opposite trend is valid for second nanoparticle mass. Besides, mass suction at the surface of the plate as well as magnetic parameter leads to reduce both hydrodynamic and thermal boundary layer thicknesses. Moreover, the assisting flow regime always has higher values of similarity skin friction and Nusselt number relative to opposing flow regime.

A novel mass-based model of the hybridity in nanofluids has been used to study the foregoing problem with focus on dual similarity solutions. The results of this paper are completely original and, to the best of the authors’ knowledge, the numerical results of the present paper were never published by any researcher.

The purpose of this paper is to present the results of an analysis performed to study unsteady mixed convection at the stagnation point flow over a plate moving along the direction of flow impingement. The similarity transformations are used to transform the governing nonlinear partial differential equation to a system of an ordinary differential equation.

The transformed equations are then solved numerically by a shooting technique together with bvp4c function.

The numerical results are compared with the corresponding results from previous researchers. The effects of the unsteadiness Parameter A, Prandtl number Pr, mixed convection parameter λ for plane (m = 0) and axisymmetric (m = 1) flow on the shear stress or the skin friction and heat transfer coefficients, as well as the velocity and temperature profiles, are presented and discussed.

Dual solutions for the opposing flow and multiple solutions for the assisting flow are found.

The purpose of this paper is to study theoretically the steady two‐dimensional mixed convection flow of a micropolar fluid impinging obliquely on a stretching vertical sheet. The flow consists of a stagnation‐point flow and a uniform shear flow parallel to the surface of the sheet. The sheet is stretching with a velocity proportional to the distance from the stagnation point while the surface temperature is assumed to vary linearly. The paper attempts also to show that a similarity solution of this problem can be obtained.

Using a similarity transformation, the basic partial differential equations are first reduced to ordinary differential equations which are then solved numerically using the Keller box method for some values of the governing parameters. Both assisting and opposing flows are considered. The results are also obtained for both strong and weak concentration cases.

These results provide information about the effect of a/c (ratio of the stagnation point velocity and the stretching velocity), σ (shear flow parameter) and K (material parameter) on the flow and heat transfer characteristics in mixed convection flow near a non‐orthogonal stagnation‐point on a vertical stretching surface. The results show that the shear stress increases as K increases, while the heat flux from the surface of the sheet decreases with an increase in K.

The results in this paper are valid only in the small region around the stagnation‐point on the vertical sheet. It is found that for smaller Prandtl number, there are difficulties in the numerical computation due to the occurrence of reversed flow for opposing flow. An extension of this work could be performed for the unsteady case.

The present results are original and new for the micropolar fluids. They are important in many practical applications in manufacturing processes in industry.