Explicit solutions of wall jet flow subject to a convective boundary condition

Raees, Ammarah; Xu, Hang; Raees-ul-Haq, Muhammad

doi:10.1186/1687-2770-2014-163

Cited by 19 publications

(5 citation statements)

References 27 publications

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“…velocity as in Raees et al,[31]. It should be noticed that for the regular fluid case ( )  ==, Eq.…”

mentioning

confidence: 86%

“…with the magnetic field strength 0 B [34,35]. Thus, the governing equations are (see Glauert [25], Raees et al, [31], Zaidi et al, [33])…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Later, Merkin and Needham [28] reported the effect of suction or injection on the wall jet flow by considering the moving wall. Since that, just to name a few, there are several studies on the wall jet flow has been reported by the researchers, for examples, Cohen et al, [29], Magyari and Keller [30], Raees et al, [31], Turkyilmazoglu [32], Zaidi et al, [33], Jafarimoghaddam [34,35], Jafarimoghaddam and Pop [36], and Selimefendigil and Öztop [37].…”

Section: Introductionmentioning

confidence: 99%

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MHD Glauert Flow of a Hybrid Nanofluid with Heat Transfer

Waini

Ishak

Pop

2021

ARFMTS

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This paper examines the wall jet flow and heat transfer of the Glauert problem with the effect of the hybrid nanoparticles. Also, the influence of the magnetic field and the variable surface temperature are taken into consideration. Here, we consider copper (Cu) and alumina (Al2O3) as the hybrid nanoparticles while water is the base fluid. The governing equations are reduced to the similarity equations using similarity transformations. Then, the numerical solutions are obtained by using the bvp4c function in MATLAB software. The findings reveal that hybrid nanofluid provides a higher heat transfer rate compared to regular nanofluid. Besides, the heat transfer rate and the skin friction coefficient increase in the presence of nanoparticles. Moreover, the rise of the temperature index parameter contributes to the enhancement of the heat transfer rate, but it does not affect the skin friction coefficient. The stronger magnetic strength led to the reduction of the heat transfer rate and the skin friction coefficient.

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“…velocity as in Raees et al,[31]. It should be noticed that for the regular fluid case ( )  ==, Eq.…”

mentioning

confidence: 86%

“…with the magnetic field strength 0 B [34,35]. Thus, the governing equations are (see Glauert [25], Raees et al, [31], Zaidi et al, [33])…”

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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MHD Glauert Flow of a Hybrid Nanofluid with Heat Transfer

Waini

Ishak

Pop

2021

ARFMTS

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“…Introducing the following similarity transformations:

\begin{matrix} η = \frac{y}{ν_{f}^{1 / 2} x^{3 / 4}}, ψ = 4 ν_{f}^{1 / 2} x^{1 / 4} f (η), θ (η) = \frac{T - T_{\infty}}{T_{w} - T_{\infty}}, ϕ (η) = \frac{C - C_{\infty}}{C_{w} - C_{\infty}}, \\ W (η) = \frac{S - S_{\infty}}{S_{w} - S_{\infty}}, χ (η) = \frac{n - n_{\infty}}{n_{w} - n_{\infty}} \end{matrix}},

where

u = \frac{\partial ψ}{\partial y}, italicv = - \frac{\partial ψ}{\partial x}

, and

ψ

is the stream function.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Thermal diffusion and diffusion thermo effects of Eyring‐Powell nanofluid flow with gyrotactic microorganisms through the boundary layer

Eldabe

Rizkalla

Abou-zeid

2019

Heat Trans. Asian Res.

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In this article, the effects of thermal diffusion and diffusion thermo on the motion of a non-Newtonian Eyring Powell nanofluid with gyrotactic microorganisms in the boundary layer are investigated. The system is stressed with a uniform external magnetic field. The problem is modulated mathematically by a system of a nonlinear partial differential equation, which governs the equations of motion, temperature, the concentration of solute, nanoparticles, and microorganisms. This system is converted to nonlinear ordinary differential equations by using suitable similarity transformations with the appropriate boundary conditions. These equations are solved numerically by using the Rung-Kutta-Merson method with a shooting technique.The velocity, temperature, concentration of solute, nanoparticles, and microorganisms are obtained as functions of the physical parameters of the problem.The effects of these parameters on these solutions are discussed numerically and illustrated graphically through figures. It is found that the velocity decreases with the increase in the non-Newtonian parameter and the magnetic field, whereas, the velocity increases with a rise in thermophoresis and Brownian motion. Also, the temperature increases with an increase in the non-Newtonian parameter, magnetic field, thermophoresis, and Brownian motion. These parameters play an important role and help in understanding the mechanics of complicated physiological flows. K E Y W O R D SEyring-Powell model, microorganisms, nanofluid, Soret and Dufour effects

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“…To get classified analysis wall jet flow problem, we use the following similarity transforms as defined by Glauert (1956), Raees et al (2014):…”

Section: Problem Formulationmentioning

confidence: 99%

A comparative study of wall jet flow containing carbon nanotubes with convective heat transfer and MHD

Zaidi

Mohyud‐Din

Bin-Mohsen

2017

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Purpose The purpose of this study is to conduct a comparative investigation for incompressible electrically conducting nanofluid fluid through wall jet. Single-walled carbon nanotubes (SWCNTs) and multiple-walled carbon nanotubes (MWCNTs) are considered as the nanoparticles. To record the effect of Lorentz forces, a magnetic field is applied normally with the assumption that the induced magnetic field is negligible. Design/methodology/approach Boundary layer approximation is used to convert governing equations into ordinary differential equations along with appropriate boundary conditions. To obtain the results, used homotopy analysis method (HAM) has been used as an analytical technique and to validate the obtained results a famous numerical Runge–Kutta–Fehlberg method is also exploited. It has been observed that the results obtained through both of the methods are in excellent agreement with exact solution. Findings The Hartmann number is used as controlling parameter for velocity and temperature profile. That can be recorded as its extended values help to normalize the velocity, whereas it controls the rapid increase in temperature. The temperature profile is boosted by increasing the value of the Biot number, a physical parameter. Similarly, it also increases for an increased percentage of volume fraction of particles (SWCNTs/MWCNTs). The Hartmann number plays an important role in decreasing local skin friction coefficient. The influence of the Biot number and volume fraction of nanoparticles caused similar increasing effects on the local Nusselt number. Nanoparticles of the form SWCNT provide better heat transfer as compared to MWCNTs. Influence of the Biot number and volume fraction of nanoparticles caused similar increasing effects on the local Nusselt number. Nanoparticles of the form SWCNT provide better heat transfer as compared to MWCNTs. Originality/value To gain insight into the problem, the effects of various emerging parameters and physical quantities such as Biot number, Nusselt number and skin friction coefficient, have been explored.

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Explicit solutions of wall jet flow subject to a convective boundary condition

Cited by 19 publications

References 27 publications

MHD Glauert Flow of a Hybrid Nanofluid with Heat Transfer

MHD Glauert Flow of a Hybrid Nanofluid with Heat Transfer

Thermal diffusion and diffusion thermo effects of Eyring‐Powell nanofluid flow with gyrotactic microorganisms through the boundary layer

A comparative study of wall jet flow containing carbon nanotubes with convective heat transfer and MHD

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