Two-phase natural convection dusty nanofluid flow

Siddiqa, Sadia; Begum, Naheed; Hossain, Md. Anwar; Gorla, Rama Subba Reddy; Al‐Rashed, Abdullah A.A.A.

doi:10.1016/j.ijheatmasstransfer.2017.10.067

Cited by 38 publications

(17 citation statements)

References 20 publications

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“…The physical model that incorporating the above assumptions into the dimensional governing equations of the dusty nanofluid are as follows:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The wall shear stress between irregular wall and the dusty nanofluid can be analyzed using the friction factor. Coefficient of skin friction provides the surface drag and is calculated by:

C_{f} = \frac{τ_{w}}{ρ_{nf} U^{2}},

where

τ_{w} = μ_{nf} {true(\frac{\partial \bar{u}}{\partial \bar{y}} + \frac{\partial \bar{v}}{\partial \bar{x}} true)}_{\overset{y}{true} = {\bar{y}}_{w}}

is the shearing stress and

U = L / ν_{italicnf} G r^{1 / 2}

. Upon using the nondimensional variables, the surface drag of the dusty nanofluid reduced to:

C_{fx} = C_{f} G r^{1 / 4} = (1 - σ_{x}^{2}) {true(\frac{\partial u}{\partial y} true)}_{y = 0} .

…”

Section: Numerical Solutionmentioning

confidence: 99%

“…The heat transfer rate is the ratio of heat flux

{\bar{q}}_{w}

per unit area to the excess temperature

T_{w} - T_{\infty}

. The dimensional heat transfer coefficient is:

italicNu = \frac{\overset{x}{true} {\bar{q}}_{w}}{k_{nf} (T_{w} - T_{\infty})},

where

{\bar{q}}_{w} = - {false(k_{italicnf} n \cdot \nabla \bar{T} false)}_{\overset{y}{true} = {\bar{y}}_{w}}

is the heat flux at the wall. Here,

n = (- \frac{σ_{x}}{\sqrt{1 + σ_{x}^{2}}}, \frac{1}{\sqrt{1 + σ_{x}^{2}}})

is the unit normal vector transverse to the wavy surface.…”

Section: Numerical Solutionmentioning

confidence: 99%

“…The effectiveness of mass convection of the dusty nanofluid at the surface can be represented by nanoparticle Sherwood number, which is the ratio of mass convection to the mass diffusion. The mass transfer rate of nanoparticle is given by:

S h_{p} = \frac{\overset{x}{true} {\bar{j}}_{w}}{D_{B} (C_{w} - C_{\infty})},

where

{\bar{j}}_{w} = - {false(D_{B} n \cdot \nabla \overset{C}{true} false)}_{\overset{y}{true} = {\bar{y}}_{w}}

is mass flux at the wall.…”

Section: Numerical Solutionmentioning

confidence: 99%

“…Natural convection in nanofluids along an inclined sinusoidal surface embedded in permeable medium was reported by Srinivasacharya and it was found that the amplitude of wavy surface leads to velocity expansion near the plate and to declination in temperature. The numerical computation on two‐phase natural convective flow of water‐based dusty nanofluid over a wavy vertical surface is discussed by Siddiqa et al…”

Section: Introductionmentioning

confidence: 99%

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Numerical computation on Marangoni convective flow of two‐phase MHD dusty nanofluids under Brownian motion and thermophoresis effects

Kalpana¹,

Madhura

Iyengar

2019

Heat Trans. Asian Res.

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dusty nanofluids, Marangoni convection, space-dependent heat source, two-phase flow, wavy surface | INTRODUCTIONThe Marangoni convection is a phenomenon, which is induced by thermocapillarity or solutocapillarity, that is, the variation of surface tension of the fluid with temperature or concentration. Surface tension is one of the fluid characteristics, which remain stable basically. However, the primary conditions affecting the surface tension of the fluid are variation in temperature and addition of chemicals in it. When temperature rises, the molecules in the fluid become more active, which results into the reduction in the surface tension of the fluid. Also, it changes according to the chemical reactions that occur when the chemicals are added to the fluid. Further, the surface tension of the fluid also gets affected by impurities present in it. For instance, the salt which is a highly solvable substance, increases the surface tension of water, whereas the soap, which is a sparingly soluble substance, decreases it. Hence, it is worthy to investigate the Marangoni effect on dusty nanofluid flow. The study on Marangoni convection is essential in view of numerous industrial applications including crystal growth, thin liquid films, semiconductor processing, coating flow technology, microfluidics, etc. After a promising research, this mechanism has been adopted in the field of nanotechnology to get an artificial rain by a process called cloud seeding. Here, substances like dry ice (silver iodide aerosol is commonly used, which acts as a cloud condenser) is dispersed into the upper parts of clouds, which alters the surface tension and then causes microphysical changes within the clouds. Therefore, condensation of water vapor in the atmosphere occurs. One of the widely practiced applications using this effect is suppressing the fog in airports during harsh weather. The concept of Marangoni boundary layer was introduced by Napolitano, 1 and, later, several authors 2-7 studied the flow under the Marangoni effect. It is evident from Mahanthesh et al 8 that Marangoni effect enhances the temperature and concentration fields of Casson liquid flow due to an infinite disk. The buoyancy and thermocapillary effect on convective fluid flow and transfer of heat inside a vertical cylindrical cavity under the impact of evaporation was evaluated numerically by Kozhevnikov and Sheremet. 9 Siddiqa et al 10 have assessed the effect of thermal radiation on Marangoni boundary layer flow along a vertical irregular surface and their mathematical results disclosed that water-particle mixture, that is, dusty fluid, reduces the heat transfer rate.The mechanism of heat transfer plays a significant role in hypersonic, space vehicles, gas turbines, etc. In those applications, the thermal performance of commonly employed traditional fluids like water, oils, glycol, etc, is deficient. With the intention of boosting the thermal conductivity of these base fluids, several processes, such as adding surfactant, salts, alcohol to the base fluids, inc...

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“…The physical model that incorporating the above assumptions into the dimensional governing equations of the dusty nanofluid are as follows:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The wall shear stress between irregular wall and the dusty nanofluid can be analyzed using the friction factor. Coefficient of skin friction provides the surface drag and is calculated by:

C_{f} = \frac{τ_{w}}{ρ_{nf} U^{2}},

where

τ_{w} = μ_{nf} {true(\frac{\partial \bar{u}}{\partial \bar{y}} + \frac{\partial \bar{v}}{\partial \bar{x}} true)}_{\overset{y}{true} = {\bar{y}}_{w}}

is the shearing stress and

U = L / ν_{italicnf} G r^{1 / 2}

. Upon using the nondimensional variables, the surface drag of the dusty nanofluid reduced to:

C_{fx} = C_{f} G r^{1 / 4} = (1 - σ_{x}^{2}) {true(\frac{\partial u}{\partial y} true)}_{y = 0} .

…”

Section: Numerical Solutionmentioning

confidence: 99%

“…The heat transfer rate is the ratio of heat flux

{\bar{q}}_{w}

per unit area to the excess temperature

T_{w} - T_{\infty}

. The dimensional heat transfer coefficient is:

italicNu = \frac{\overset{x}{true} {\bar{q}}_{w}}{k_{nf} (T_{w} - T_{\infty})},

where

{\bar{q}}_{w} = - {false(k_{italicnf} n \cdot \nabla \bar{T} false)}_{\overset{y}{true} = {\bar{y}}_{w}}

is the heat flux at the wall. Here,

n = (- \frac{σ_{x}}{\sqrt{1 + σ_{x}^{2}}}, \frac{1}{\sqrt{1 + σ_{x}^{2}}})

is the unit normal vector transverse to the wavy surface.…”

Section: Numerical Solutionmentioning

confidence: 99%

S h_{p} = \frac{\overset{x}{true} {\bar{j}}_{w}}{D_{B} (C_{w} - C_{\infty})},

where

{\bar{j}}_{w} = - {false(D_{B} n \cdot \nabla \overset{C}{true} false)}_{\overset{y}{true} = {\bar{y}}_{w}}

is mass flux at the wall.…”

Section: Numerical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical computation on Marangoni convective flow of two‐phase MHD dusty nanofluids under Brownian motion and thermophoresis effects

Kalpana¹,

Madhura

Iyengar

2019

Heat Trans. Asian Res.

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Activation energy effectiveness in dusty Carreau fluid flow along a stretched cylinder due to nonuniform thermal conductivity property and temperature‐dependent heat source/sink

et al. 2021

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This article studies the boundary layer flow analysis and heat and mass transfer of magnetohydrodynamic (MHD) Carreau fluid around a stretchable circular cylinder, comprehensively studying the suspended dust particles' impact. Here, the viscous fluid is theorized to be incompressible and loaded with spherical dust particles of the same size. Additionally, heat and sink sources are examined in the thermal boundary layer in the existence of both chemical reaction and activation energy influences. A compatible similarity set of transformations are utilized to mutate the system of partial differential equation formed in momentum and temperature equations of the fluid and dust phases as well the concentration equation into a set of ordinary differential equations. Therefore, the mathematical analysis of the problem facilitates and the numerical estimates of the problem are obtained using MATLAB bvp4c function. Computations are iterated for various values of emerging physical parameters from dimensionless boundary layer conservation equations in terms of temperature and non‐Newtonian Carreau velocity of fluid and dust phases and concentration distribution. Moreover, the terminology of skin friction and Nusselt and Sherwood numbers have been obtained and studied numerically. Some interesting findings in this study are the heat transfer rate dwindles due to the increase of mass concentration of the dust particle. Also, there is a strengthening of the flow with variance in values of the curvature parameter while a weakening has been observed in the thickness of the thermal boundary layer and this hence improves the heat transfer rate. Therefore, the fluid flow around a stretched cylinder would be better, due to its multiple applications in various progressing industrial technologies such as the cement processing industry, plastic foam processing, watering system channels, and so forth. Also, activation energy plays a significant role in various areas such as the oil storage industry, geothermal, and hydrodynamics. The dusty fluid flow is very important in the field of fluid dynamics and can be found in many natural phenomena such as blood flow, the flow of mud in rivers, and atmospheric flow during mist. Moreover, MHD applications are numerous including power generation, plasma, and liquid metals, and so forth. A perfect agreement between our results and other studies available in the literature is obtained through carrying out a comparison with treating the problem in special circumstances.

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Unsteady natural convection flow of a dusty non-Newtonian Casson fluid along a vertical wavy plate: numerical approach

Hady

Mahdy

Mohamed

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

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The present contribution provides a numerical treatment for the flow of unsteady natural convection of non-Newtonian Casson fluid model loaded with dusty particles over a vertical wavy plate. It is assumed that the fluid is incompressible and the dusty particles are considered to be spheres with the same size. Via the help of primitive variable formulation, the dimensionless boundary layer governing equations are reduced into a convenient coordinate system. The transformed resulting system of governing equations is tackled numerically employing the fully implicit finite difference method. The impact of various controlling physical parameters such as the amplitude of the wavy plate, the dimensionless time and fluid-particle interaction parameters on the velocity and temperature of both fluid and particle phase is analyzed. It is found that the magnitude of the velocity of both fluid and particle phase diminishes with increasing amplitude of the wavy plate parameter, while an opposite behavior is observed on temperature distributions as the amplitude of the wavy plate parameter rises. A significant impact is noticed for the heat transfer rate with enhancement values of fluid-particle interaction parameter. The numerical solutions are compared with the available data in the literature. Quantitative comparison illustrates good compatibility between the current and previous results. Keywords Dusty fluid • Wavy plate • Non-Newtonian Casson fluid • Natural convection • Finite difference List of symbolŝ a Amplitude of the wavy surface a Dimensionless amplitude of the wavy surface C Concentration of fluid C fx Local skin-friction coefficient c p Specific heat at constant pressure c s Specific heat of particle phase D Mass diffusivity of fluid D Mass concentration of the dust particle Ec Eckert number

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Two-phase natural convection dusty nanofluid flow

Cited by 38 publications

References 20 publications

Numerical computation on Marangoni convective flow of two‐phase MHD dusty nanofluids under Brownian motion and thermophoresis effects

Numerical computation on Marangoni convective flow of two‐phase MHD dusty nanofluids under Brownian motion and thermophoresis effects

Activation energy effectiveness in dusty Carreau fluid flow along a stretched cylinder due to nonuniform thermal conductivity property and temperature‐dependent heat source/sink

Unsteady natural convection flow of a dusty non-Newtonian Casson fluid along a vertical wavy plate: numerical approach

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