The effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer of upper-convected Maxwell fluid in the presence of nanoparticle past a stretching sheet

Ibrahim, Wubshet

doi:10.1016/j.jppr.2016.05.003

Cited by 56 publications

(30 citation statements)

References 44 publications

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“…The convective heat transfer is considered, and effects of higher order chemical reactions are included in the concentration of nanoparticles as well. Through the boundary layer theory, the ultimate governing equations yielded as

\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0,

u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = \frac{A}{ρ} \frac{\partial^{2} u}{\partial y^{2}} + \frac{A}{2 ρ C^{3}} {(\frac{\partial u}{\partial y})}^{2} \frac{\partial^{2} u}{\partial y^{2}} - \frac{σ B^{2}}{ρ} u,

u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} = α \frac{\partial^{2} T}{\partial y^{2}} + τ D_{B} ((), \frac{\partial C}{\partial y} . \frac{\partial T}{\partial y}) + \frac{τ D_{T}}{T_{\infty}} {(\frac{\partial T}{\partial y})}^{2},

u \frac{\partial C}{\partial x} + v \frac{\partial C}{\partial y} = D_{B} \frac{\partial^{2} T}{\partial y^{2}} + \frac{D_{T}}{T_{\infty}} \frac{\partial^{2} T}{\partial y^{2}} - K {(C - C_{\infty})}^{n};

the Navier slip conditions, convective conditions, and Nield boundary conditions are assumed

\begin{matrix} ... \end{matrix}

…”

Section: Mathematical Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Mathematical analysis on MHD Prandtl‐Eyring nanofluid new mass flux conditions

Rehman

Awais

Hussain

et al. 2018

Math Methods in App Sciences

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A speculative investigation has been presented to explore the salient features of magnetohydrodynamic (MHD) Prandtl-Eyring nanofluid over stretching surface. Effects of Navier slip and convective boundary conditions are included in flow configuration. The effects of higher order chemical reactions along with Nield conditions are assumed in the concentration of nanoparticles. The mathematical modelling of the said flow problem accomplished the nonlinear partial differential equations along with appropriate boundary conditions. The nondimensional form of governing problem is yielded with the aid of similarity variables. The pivotal physical quantities, ie, velocity, temperature, and concentration (in nondimensional form), within boundary layer region are computed with shooting technique. The physical significance of flow controlling parameters on velocity, temperature, and concentration is illustrated through graphs. Additionally, thermophysical aspects of fluid near stretching surface (wall friction factor, wall heat flux, and wall mass flux) are instantiated graphically. A comparison of the current solution with reported data is established to validate the accuracy of adapted procedure. It is observed that the current findings agree with existing data. This led to confidence on adapted numerical procedure.

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\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0,

u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = \frac{A}{ρ} \frac{\partial^{2} u}{\partial y^{2}} + \frac{A}{2 ρ C^{3}} {(\frac{\partial u}{\partial y})}^{2} \frac{\partial^{2} u}{\partial y^{2}} - \frac{σ B^{2}}{ρ} u,

u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} = α \frac{\partial^{2} T}{\partial y^{2}} + τ D_{B} ((), \frac{\partial C}{\partial y} . \frac{\partial T}{\partial y}) + \frac{τ D_{T}}{T_{\infty}} {(\frac{\partial T}{\partial y})}^{2},

u \frac{\partial C}{\partial x} + v \frac{\partial C}{\partial y} = D_{B} \frac{\partial^{2} T}{\partial y^{2}} + \frac{D_{T}}{T_{\infty}} \frac{\partial^{2} T}{\partial y^{2}} - K {(C - C_{\infty})}^{n};

the Navier slip conditions, convective conditions, and Nield boundary conditions are assumed

\begin{matrix} ... \end{matrix}

…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Ram Reddy et al described the Soret effects on mixed convective flow of viscous nanofluid through stretched sheet under the convective boundary conditions effects. Recently, the convective heat transfer gained a serious attention of researchers; for instance, see previous literatures …”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis on MHD Prandtl‐Eyring nanofluid new mass flux conditions

Rehman

Awais

Hussain

et al. 2018

Math Methods in App Sciences

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“…They solved the problem numerically using the Keller box method. The MHD stagnation point flow of a Maxwell fluid with the effects of an induced magnetic field and convective boundary condition were studied by Ibrahim [22]. The results showed that the skin friction coefficient, the local Sherwood number and the local Nusselt number were inversely proportional to the Maxwell and magnetic parameters.…”

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic Flow and Heat Transfer Induced by a Shrinking Sheet

2020

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The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of MATLAB software. The numerical results obtained are for different values of the magnetic parameter M, heat generation parameter Q, Prandtl number Pr and reciprocal of magnetic Prandtl number ε. The influences of these parameters on the flow and heat transfer characteristics are investigated and shown in tables and graphs. Two solutions are found for a certain rate of the shrinking strength. The stability of the solutions in the long run is determined, and shows that only one of them is stable. It is found that the skin friction coefficient f ″ ( 0 ) and the local Nusselt number − θ ′ ( 0 ) decrease as the magnetic parameter M increases. Further, the local Nusselt number increases as the heat generation increases.

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“…Convective heat transfer and MHD viscoelastic nanofluid flow has been actuated by Shit et al [27]. In contemporary epoch, MHD has become a great fact-finding argument of computational fluid dynamics (CFD) which contrived by multitudinous scientists commensurate as Ibrahim [28]; Rani and Kim [29]; Animasaun and Oyem [30] and Lavanya and Ratnam [31].…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation with Stability Convergence Analysis of Chemically Hydromagnetic Casson Nanofluid Flow in the Effects of Thermophoresis and Brownian Motion

Mondal¹,

Biswas²,

Shanchia³

et al. 2019

IJHT

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In this evaluation, a numerical exploration is inscribed on MHD unsteady heat and mass transfer of Casson nanofluid flow where variable thermal conductivity, radiation and heat absorption are counterfeited. The model is implemented for the nanofluid which annexes the impression of thermophoresis and Brownian motion. The governing models are metamorphosed as a dimensionless silhouette by the renovation rule of mathematics and the procured dimensionless couple of partial differential equations (PDEs) are elucidated by utilizing explicit finite difference method (EFDM). The numerical aggregates are enumerated for the miscellaneous dimensionless parameters on velocity, temperature and concentration profiles along with the skin friction, Nusselt number and Sherwood number with distinct time interims. ForTran programing language is manipulated as the predominated software for executing the numerical values. Also, by wielding the initial boundary conditions U=T=C=0, X=0.83 and Y=0.50 for =0.0005, convergence criteria are exhibited with Sc 0.18 and Le0.20. At the end, the prevailed culminations are illustrated and perused after the stability convergence test (SCT) by manoeuvring graphics software tecplot-9 and streamlines and isotherms are delineated.

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The effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer of upper-convected Maxwell fluid in the presence of nanoparticle past a stretching sheet

Cited by 56 publications

References 44 publications

Mathematical analysis on MHD Prandtl‐Eyring nanofluid new mass flux conditions

Mathematical analysis on MHD Prandtl‐Eyring nanofluid new mass flux conditions

Magnetohydrodynamic Flow and Heat Transfer Induced by a Shrinking Sheet

Numerical Investigation with Stability Convergence Analysis of Chemically Hydromagnetic Casson Nanofluid Flow in the Effects of Thermophoresis and Brownian Motion

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