This paper analyzes the combined effects of buoyancy force, convective heating, Brownian motion, thermophoresis and magnetic field on stagnation point flow and heat transfer due to nanofluid flow ...towards a stretching sheet. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then tackled numerically using the Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for dimensionless velocity, temperature, nanoparticle volume fraction, as well as the skin friction, local Nusselt and Sherwood numbers. The results indicate that dual solutions exist for shrinking case. The effects of various controlling parameters on these quantities are investigated. It is found that both the skin friction coefficient and the local Sherwood number decrease while the local Nusselt number increases with increasing intensity of buoyancy force.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
•Non-aligned MHD stagnation point flow of nanofluids with radiation is examined.•The nonlinear model is solved using similarity transformation and shooting method.•Pertinent results with respect to ...spray cooling applications are displayed graphically.•Skin friction, Nusselt number and Sherwood number are determined.
This paper investigates the problem of oblique hydromagnetic stagnation point flow of a variable viscosity electrically conducting optically dense viscous incompressible nanofluid over a convectively heated stretching sheet in the presence of thermal radiation. The nanofluid model employed in this study incorporates the effects of Brownian motion and thermophoresis. The governing nonlinear partial differential equations for momentum, energy and nanoparticles concentration are reduced into a set of non-linear ordinary differential equations with the aid of suitable similarity transformations. The transformed equations are numerically integrated using fourth–fifth order Runge–Kutta–Fehlberg method. The effects of various controlling parameters on the dimensionless velocity, temperature, nanoparticles concentration, skin friction, Nusselt and Sherwood numbers are analysed and presented graphically. Obtained numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. It is found that non-alignment of the re-attachment point on the sheet surface decreases with an increase in magnetic field intensity.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
•Magnetohydrodynamic flow of Casson fluid over a stretched surface is considered.•Homogeneous-heterogeneous reaction effect is taken into account.•Concentration profile enhances with an increase in ...heterogeneous parameter.•Numerical simulation is developed for solution of nonlinear partial differential equations.
Our objective here is to introduce the new chemical reaction model in MHD stagnation point flow. Mathematical modeling is based for the rheological relations of Casson liquid. Flow induced is due to sheet moving with nonlinear velocity. The velocity of external flow is also nonlinear. Effects of magnetohydrodynamics (MHD), viscous dissipation and Joule heating are also accounted. Nonlinear differential systems via implementation of appropriate transformations are computed through built in shooting method. Graphical and tabular behaviors of various pertinent parameters on velocity, temperature, concentration, skin friction and Nusselt and Sherwood numbers are analyzed. Our computed results interpret that velocity distribution decays for higher estimation of magnetic parameter while temperature distribution shows increasing behavior for larger homogeneous heat parameter.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
The major focus of this work is to examine the results of steady mixed convection flow of SiO2−Al2O3/water hybrid nanofluid near the stagnation point with the curved surface of radius R and mass ...suction S. Hybrid nanofluid is taken into consideration by suspending a couple of distinct nanoparticles (SiO2 and Al2O3) into pure water. Depending on similarity variables, the governing equations with associated boundary conditions are modified to formulate a normalized boundary value problem of coupled differential equations and the MATLAB problem solver bvp4c is efficient to resolve the resulting problem. From this study it is determined that the skin friction coefficient and local Nusselt number of hybrid nanofluid improves with high values of mass suction and nanoparticles concentration while increasing curvature K declines the skin friction coefficient and gives rise to a poor performance of heat transfer. Moreover, the improvement of thermal boundary layer and velocity boundary layer take place with powerful concentration of SiO2 and Al2O3 and greater values of curvature K. Some interesting results for the flat sheet (K→∞) were also computed.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
An analysis on the subject of “induced magnetic field effect on stagnation flow of a TiO2-Cu/water hybrid nanofluid over a stretching sheet” has been carried out in this paper. It should be noted ...that hybrid nanofluid consists of two or more types of nanoparticles along with a base fluid and it is used to increase the heat transfer. Furthermore, the non-linear differential equations modeling this issue are included in this article. In order to solve these equations numerically, Runge-Kutta Fehlberg method is used as a numerical method in this problem. The main objective of this paper is to investigate the effects of change in parameters of stretching ratio parameter (A∗), nanoparticles volumetric fractions (∅2), magnetic parameter (β) and reciprocal magnetic Prandtl number (λ) on the functions including velocity, induced magnetic field and temperature for both Cu-water nanofluid and TiO2-Cu/water hybrid nanofluid. Also Lorentz force which is derived from magnetic field is mentioned in this section. In addition, the impacts of (∅2), (β) and (λ) on the profiles of nanofluid and hybrid nanofluid temperature for three categories of nanoparticle shapes named brick, cylinders, and platelets are analyzed. At the end, the influences of (∅2), (β) and (λ) on skin friction coefficient (Cf) and Nusselt number (Nux) for Cu-water nanofluid and TiO2-Cu/water hybrid fluid for different nanoparticles shapes are discussed. In all of these studies it can be seen that applying platelets shaped nanoparticles is more effective.
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•TiO2‐Cu/H2O hybrid nanofluid is incorporated.•Analysis of thermal conductivity of hybrid nanofluid is highlighted.•Different shape factors for nanoparticles are addressed.•Nonlinear differential equations are solved numerically.
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Magnetohydrodynamic (MHD) stagnation point flow of Casson fluid towards a stretching sheet is addressed. Homogeneous-heterogeneous reactions together with homogeneous heat effect ...subject to a resistive force of electromagnetic origin is discussed. It is assumed that the homogeneous process in the ambient fluid is governed by first order kinetics and the heterogeneous process on the wall surface is given by isothermal cubic autocatalator kinetics. Ordinary differential systems have been considered. Solutions of the problems are presented via a numerical technique namely built in shooting method. Graphical behaviors of velocity, temperature and concentration are analyzed comprehensively. Velocity is noticed a decreasing function of Hartman number.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
In this article, we have examined the steady 2D magnetohydrodynamic (MHD) stagnation point flow of an incompressible viscous nanofluid over a curved surface based on mass suction. Alumina ( A l 2 O 3 ...) is taken to be a nanoparticle while ethylene glycol is considered a base fluid. The developed flow and heat equations are changed into coupled ordinary differential equations through dimensionless variables, which are resolved numerically via the bvp4c scheme in MATLAB. The graphical results for temperature, velocity, Nusselt number and skin friction have been obtained under the effect of various parameters, such as suction parameter S , Hartmann number M , curvature parameter K and nanoparticle volume fraction . From these results, it is noticed that S , M and act directly on the skin friction and heat transfer rate, although the reverse effect has been shown by K . Furthermore, increasing K leads to lower fluid velocity and higher temperature field.
•A hybrid nanofluid near stagnation-point on a vertical plate is considered.•A novel analytic model of hybrid nanofluid is presented.•Conjugate effects of SiO2andAl2O3 on heat transfer rate are ...studied.•Heat transfer rate of hybrid nanofluid is higher respect to regular nanofluid.•Dual solutions for assisting and opposing flows of hybrid nanofluid are observed.
Hybrid nanofluid as an extension of nanofluid is obtained by dispersing composite nano-powder or several different nanoparticles in the base fluid. 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. Here, a kind of hybrid nanofluid including silicon dioxide (SiO2) and aluminum oxide (Al2O3) nano-size particles with water as base fluid is analytically modeled to develop the problem of the steady laminar MHD mixed convection boundary layer flow of a SiO2–Al2O3/water hybrid nanofluid near the stagnation-point on a vertical permeable flat plate. The flow of nanofluids near the stagnation point has recently attracted the attention of many investigators because of its wide applications in the local cooling/heating processes, especially in industries of electronic devices and nuclear reactors. In first, analytic modeling of hybrid nanofluid is presented and using appropriate similarity variables, the governing PDEs are transformed into nonlinear ODEs in the dimensionless stream function, which is solved numerically applying the function bvp4c from MATLAB. Our results demonstrate that the developed model can be used with great confidence to study the flow and heat transfer of hybrid nanofluids. Moreover, dual solutions of hybrid nanofluid flow for both assisting and opposing regimes are observed, where the range of the mixed convection parameter for which the solution exists, increases with the volume fraction of second nanoparticle and magnetic field. Finally, the heat transfer rate of nanofluids and hybrid nanofluids with different values of nanoparticles volume fraction have been compared that HNF3 (ϕSiO2=ϕAl2O3=0.1) has the largest heat transfer rate between all cases.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
This article is motivated to find the impact of various flow controlling parameters such as viscous dissipation, negative and positive values of activation energy on MHD stagnation point micropolar ...nanofluid flow over a surface. However, negative activation energy is scarce in practice, but the impact of negative values of activation energy could not be neglected as seen in chemical processes. The present mathematical model is solved with successive linearization method (a spectral technique). The velocity, angular velocity, temperature and concentration profiles are drawn by varying flow controlling parameters. The bar diagrams for skin friction, Nusselt number, Sherwood number and couple stress are also displayed. Results indicate that the activation energy boosts the concentration profile up. The negative values of activation energy have higher impact on concentration curves compared to positive values. Arrhenius function decays as activation energy enlarges. This eventually promotes the generative chemical reaction due to which concentration rises. By varying thermophoretic parameter from 0.1 to 0.3, 88.65% and 8.34% enhancement is captured in heat transfer and mass transfer respectively.
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BFBNIB, GIS, IJS, KISLJ, NUK, PNG, UL, UM, UPUK
