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In this study, we are going to investigate semi-analytically the steady laminar incompressible two-dimensional boundary layer flow of a TiO2-CuO/water hybrid nanofluid over a static/moving wedge or corner that is called Falkner-Skan problem. A novel mass-based approach to one-phase hybrid nanofluid model that suggests both first and second nanoparticles as well as base fluid masses as the vital inputs to obtain the effective thermophysical properties of our hybrid nanofluid, has been presented. Other governing parameters are moving wedge/corner parameter (λ), Falkner-Skan power law parameter (m), shape factor parameter (n) and Prandtl number (Pr). The governing partial differential equations become dimensionless with help of similarity transformation method, so that we can solve them numerically using bvp4c built-in function by MATLAB. It is worthwhile to notice that, validation results exhibit an excellent agreement with already existing reports. Besides, it is shown that both hydrodynamic and thermal boundary layer thicknesses decrease with the second nanoparticle mass as well as Falkner-Skan power law parameter. Further, we understand our hybrid nanofluid has better thermal performance relative to its mono-nanofluid and base fluid, respectively. Moreover, a comparison between various values of nanoparticle shape factor and their effect on local heat transfer rate is presented. It is proven that the platelet shape of both particles (n1 = n2 = 5.7) leads to higher local Nusselt number in comparison with other shapes including sphere, brick and cylinder. Consequently, this algorithm can be applied to analyze the thermal performance of hybrid nanofluids in other different researches.

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

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In the present article, we intend to study quasi-analytically the unsteady three-dimensional squeezed flow of the magnetite–graphene oxide/water hybrid nanofluid inside a rotating channel with two horizontal and parallel sheets, in which the lower sheet is stationary, stretchable, and permeable, while the upper sheet is moving and impermeable. Our methodology is based on the single-phase Tiwari–Das hybrid nanofluid model considering nanoparticles and base fluid masses instead volume concentration of first and second nanoparticles. The dimensional partial differential equations are altered to a set of nondimensional ordinary differential equations with the help of similarity transformation method, which is then solved numerically using the bvp4c function from MATLAB. The governing similarity parameters are the empirical shape factor of nanoparticles, the suction parameter, the squeezing parameter, the rotation parameter, the Eckert number, and the Prandtl number. Results indicate that when the upper sheet faster moves toward the lower sheet, the profiles trend is opposite in comparison with when the upper sheet faster moves away from the lower one. On the one hand, the drastic thermal conductivity of the graphene oxide is a major reason to achieve maximum heat transfer rate enhancement of our working fluid. Finally, this study may be applicable in biomechanics, flow through arteries, food processing, polymer processing, lubrication, injection modeling, etc.

Purpose 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. Design/methodology/approach 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). Findings 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. Originality/value 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.

We analyzed the problem of the steady general three-dimensional magnetohydrodynamics stagnation-point boundary layer flow past an impermeable wavy circular cylinder considering aluminium–copper/water hybrid nanofluid as the working fluid and velocity slip as well as temperature jump boundary conditions. The induced magnetic field effect was also taken into account. The analytical procedure is based on the model that implements the nanoparticles and base fluid masses to formulate the equivalent volume fraction, equivalent density, and equivalent specific heat at constant pressure which is then substituted in the chosen single-phase thermophysical properties. Then, the foregoing relations were used in basic governing PDEs (partial differential equations), according to Tiwari–Das nanofluid scheme. It is worth mentioning that the bvp4c code from MATLAB software that is a famous finite-difference method has been exploited for solving the final similarity ODEs (ordinary differential equations). Results demonstrate that the developed mass-based model can be successfully employed with great confidence to study the flow and heat transfer of hybrid nanofluid in other similar problems. Moreover, it is proved that the nodal stagnation points possess higher values of skin friction coefficients and local Nusselt numbers relative to those for the saddle stagnation points. Besides, enhancing the second nanoparticle's mass leads to increase in all parameters of engineering interest including skin friction coefficients along x and y directions as well as local Nusselt number.