MHD natural convection flow enclosure in a corrugated cavity filled with a porous medium

Haq, Rizwan Ul; Soomro, Feroz Ahmed; Mekkaoui, Toufik; Al‐Mdallal, Qasem M.

doi:10.1016/j.ijheatmasstransfer.2018.01.063

Cited by 97 publications

(25 citation statements)

References 36 publications

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“…To transform the above equation in dimensionless form, we introduce the dimensionless variables as suggested by Labropulu et al 9

\begin{matrix} x = \overset{x}{true} \sqrt{\frac{c}{ν}}, y = \overset{y}{true} \sqrt{\frac{c}{ν}}, u = \frac{\overset{̅}{u}}{\sqrt{ν c}}, v = \frac{v}{\sqrt{ν c}}, p = \frac{1}{ρ c ν} \overset{p,}{true} θ (y) = \frac{\overset{T}{true} - T_{\infty}}{T_{w} - T_{\infty}}, \\ ϕ (y) = \frac{\overset{C}{true} - C_{\infty}}{C_{w} - C_{\infty}}, normalχ (y) = \frac{\overset{N}{true} - N_{\infty}}{N_{w} - N_{\infty}} \end{matrix}},

we get

u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = - \frac{\partial p}{\partial x} + ν (\frac{\partial^{2} u}{\partial y^{2}}) + λ_{1} c (- \frac{\partial u}{\partial y} \frac{\partial p}{\partial y}) - λ_{1} c (v^{2} \frac{\partial^{2} u}{\partial y^{2}} + 2 italicuv \frac{\partial^{2} u}{\partial x \partial y} + u^{2} \frac{\partial^{2} u}{\partial x^{2}}),

and the boundary conditions satisfied by the velocity components in the dimensionless form are

\begin{matrix} true \\ u = x, v = \end{matrix}

…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…A study was carried out by Yian et al 8 to investigate the effects of mixed convection near the oblique stagnation point flow of a viscous fluid towards a stretching sheet. The effects of a magnetic field on the natural convection flow have been investigated by Haq et al 9 in a corrugated cavity. Labropulu et al 10 studied the 2D oblique stagnation point flow of a viscoelastic fluid obeying the constitutive equation of second grade over a stretching sheet with heat transfer.…”

Section: Introductionmentioning

confidence: 99%

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Stagnation point flow of Maxwell nanofluid containing gyrotactic micro‐organism impinging obliquely on a convective surface

2020

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A numerical study is performed to discuss the nonaligned stagnation of a rate type fluid over a convective surface. The rheology of the fluid is presented by the constitutive equation of the Maxwell fluid model. Buongiorno's model is used to elaborate on the effects of Brownian motion and thermophoresis and motile microorganisms are introduced for the stability of the nanoparticles. The governing equations were solved by the implicit finite difference method. Graphical illustrations for velocity, temperature, nanoparticle concentration and motile microorganism profiles for various involved parameters are presented for both convective and nonconvective surfaces. It is depicted that the temperature, nanoparticle, and microorganism concentration profiles decease while both axial and tangential velocities increase with the velocity ratio parameter for both Newtonian and Maxwellian fluids. The magnitude of temperature, nanoparticle, and microorganism concentration profiles is large for the nonconvective surface as compared to the convective surface. The Nusselt number, Sherwood number, and motile organism number decrease as we move from Newtonian fluid to non‐Newtonian fluid. Furthermore, the increase in the Brownian motion parameter and thermophoresis parameter decreases the density of the motile organism over the convective as well as nonconvective surface.

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“…To transform the above equation in dimensionless form, we introduce the dimensionless variables as suggested by Labropulu et al 9

\begin{matrix} x = \overset{x}{true} \sqrt{\frac{c}{ν}}, y = \overset{y}{true} \sqrt{\frac{c}{ν}}, u = \frac{\overset{̅}{u}}{\sqrt{ν c}}, v = \frac{v}{\sqrt{ν c}}, p = \frac{1}{ρ c ν} \overset{p,}{true} θ (y) = \frac{\overset{T}{true} - T_{\infty}}{T_{w} - T_{\infty}}, \\ ϕ (y) = \frac{\overset{C}{true} - C_{\infty}}{C_{w} - C_{\infty}}, normalχ (y) = \frac{\overset{N}{true} - N_{\infty}}{N_{w} - N_{\infty}} \end{matrix}},

we get

u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = - \frac{\partial p}{\partial x} + ν (\frac{\partial^{2} u}{\partial y^{2}}) + λ_{1} c (- \frac{\partial u}{\partial y} \frac{\partial p}{\partial y}) - λ_{1} c (v^{2} \frac{\partial^{2} u}{\partial y^{2}} + 2 italicuv \frac{\partial^{2} u}{\partial x \partial y} + u^{2} \frac{\partial^{2} u}{\partial x^{2}}),

and the boundary conditions satisfied by the velocity components in the dimensionless form are

\begin{matrix} true \\ u = x, v = \end{matrix}

…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stagnation point flow of Maxwell nanofluid containing gyrotactic micro‐organism impinging obliquely on a convective surface

2020

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“…Sheikholeslami [11] put forward a new method on magneto-hydro-dynamics (MHD) Al2O3-water nanofluid transportation inside a permeable medium through Control Volume Finite Element Method (CVFEM) and Darcy model, the shape factor and Brownian motion effect were included in nanofluid modeling for the first time. Haq et al [12] studied on a natural convection phenomenon in a porous cavity under the Lorentz forces with curved boundary domain which showed that Darcy and Hartmann number t have insignificant effects on the temperature distribution. Some of the recent studies are focused on the optimization of the nanofluid heat transfer Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Mixed Convection Heat Transfer of Sio2-Water and Alumina-Pao Nano-Lubricants Used in a Mechanical Ball Bearing

Hatami¹,

Ali²,

Alsabery³

et al. 2021

Journal of Thermal Engineering

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In this study, the mixed convection heat transfer in a mechanical ball bearing filled with nano-lubricants were investigated theoretically. In our case, the bearing including eight balls revolving in counter clockwise while the inner shaft rotates in clockwise direction and the inner and outer walls of bearing were kept at constant hot and cold temperatures, respectively. Two kinds of nano-lubricants SiO2-water and Alumina-Polyalphaolefin (PAO) with different shapes of nanoparticles were considered. The governing equations including velocity, pressure, and temperature formulation were solved based on the Galerkin finite element method. The governing parameters such as nanoparticle volume fraction, Reynolds and Rayleigh numbers, etc., were discussed. It turns out that the average Nusselt number increases by increasing the nanoparticle volume fraction (averagely 15% for each 0.02 increase) and the oil-based nano-lubricant has greater Nusselt number than the water based one. More importantly, the Nono-rod Alumina was found to show much greater heat transfer performance (averagely 5%) than the spherical alumina nanoparticles and nano-rod Alumina-PAO has the best performance and maximum Nusselt numbers for the heat transfer.

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“…ey mentioned that the oscillation period, the magnitude of the magnetic field, and adding nanoparticles have an important effect on heat transfer, temperature field, and flow structure. Haq et al [20][21][22] analyzed the heat transfer with a presence of the Magnetohydrodynamic (MHD) water-based Single-Wall Carbon Nanotubes (SWCNTs), the water-based copper oxide (CuO) nanofluid, and uniform magnetic field. ey, respectively, concluded that the increase of the Rayleigh number enhances the stream flow and isotherms behaviors.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of the Natural Convection with Presence of the Nanofluids in Cubical Cavity

Sannad

Abourida

Belarche

2020

Mathematical Problems in Engineering

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This article consists of a numerical study of natural convection heat transfer in three-dimensional cavity filled with nanofluids. This configuration is heated by a partition maintained at a hot constant and uniform temperature TH. The right and left vertical walls are kept at a cold temperature TC while the rest is adiabatic. The fluid flow and heat transfer in the cavity are studied for different sets of the governing parameters, namely, the nanofluid type, the Rayleigh number Ra = 103, 104, 105, and 106, and the volume fraction Ф varying between Ф = 0 and 0.1. The obtained results show a positive effect of the volume fraction and the Rayleigh number on the heat transfer improvement. The analysis of the results related to the heat transfer shows that the copper-based nanofluid guarantees the best thermal transfer. In addition, the increase of the heating section size and Ra leads to an increased amount of heat. Similarly, increasing the volume fraction improves the intensification of the flow and increases the heat exchange.

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MHD natural convection flow enclosure in a corrugated cavity filled with a porous medium

Cited by 97 publications

References 36 publications

Stagnation point flow of Maxwell nanofluid containing gyrotactic micro‐organism impinging obliquely on a convective surface

Stagnation point flow of Maxwell nanofluid containing gyrotactic micro‐organism impinging obliquely on a convective surface

Mixed Convection Heat Transfer of Sio2-Water and Alumina-Pao Nano-Lubricants Used in a Mechanical Ball Bearing

Numerical Simulation of the Natural Convection with Presence of the Nanofluids in Cubical Cavity

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