Effects of aligned magnetic field and CNTs in two different base fluids over a moving slip surface

Haq, Rizwan Ul; Rashid, Irfan; Khan, Zafar Hayat

doi:10.1016/j.molliq.2017.08.084

Cited by 64 publications

(23 citation statements)

References 22 publications

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“…where velocity components are ( ) The boundary layer equations for the aforementioned problem (see, for example, the works of [49][50][51][52]) are as follows:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…where velocity components are (u, v) along the xand y-axes, respectively; T denotes the temperature; ν n f , α n f denotes the effective kinematic viscosity and thermal diffusivity of nanoliquid, respectively; (U w , U e ) are defined as the stretching surface and free stream velocity, respectively; q r defines the radiative heat flux; and C p defines the specific heat. The fruitful characteristics of nanoliquids may be defined using the properties of base liquid and carbon nanotubes and the solid volume fraction of CNTs in the base liquids (see, for example, the works of [49][50][51][52]) as follows:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Sharma and Singh [46] investigated stagnation point flow past a linearly stretching sheet with additional effects of variable thermal conductivity, heat source/sink, and MHD. Some other important studies with some interesting experimental findings are given in the works of [47][48][49][50][51][52][53][54][55][56][57][58][59][60] and cross references cited therein.…”

Section: Introductionmentioning

confidence: 99%

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Influence of Single- and Multi-Wall Carbon Nanotubes on Magnetohydrodynamic Stagnation Point Nanofluid Flow over Variable Thicker Surface with Concave and Convex Effects

et al. 2020

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This paper reports a theoretical study on the magnetohydrodynamic flow and heat exchange of carbon nanotubes (CNTs)-based nanoliquid over a variable thicker surface. Two types of carbon nanotubes (CNTs) are accounted for saturation in base fluid. Particularly, the single-walled and multi-walled carbon nanotubes, best known as SWCNTs and MWCNTs, are used. Kerosene oil is taken as the base fluid for the suspension of nanoparticles. The model involves the impact of the thermal radiation and induced magnetic field. However, a tiny Reynolds number is assumed to ignore the magnetic induction. The system of nonlinear equations is obtained by reasonably adjusted transformations. The analytic solution is obtained by utilizing a notable procedure called optimal homotopy analysis technique (O-HAM). The impact of prominent parameters, such as the magnetic field parameter, Brownian diffusion, Thermophoresis, and others, on the dimensionless velocity field and thermal distribution is reported graphically. A comprehensive discussion is given after each graph that summarizes the influence of the respective parameters on the flow profiles. The behavior of the friction coefficient and the rate of heat transfer (Nusselt number) at the surface (y = 0) are given at the end of the text in tabular form. Some existing solutions of the specific cases have been checked as the special case of the solution acquired here. The results indicate that MWCNTs cause enhancement in the velocity field compared with SWCNTs when there is an increment in nanoparticle volume fraction. Furthermore, the temperature profile rises with an increment in radiation estimator for both SWCNT and MWCNT and, finally, the heat transfer rate lessens for increments in the magnetic parameter for both types of nanotubes.

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“…where velocity components are ( ) The boundary layer equations for the aforementioned problem (see, for example, the works of [49][50][51][52]) are as follows:…”

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Influence of Single- and Multi-Wall Carbon Nanotubes on Magnetohydrodynamic Stagnation Point Nanofluid Flow over Variable Thicker Surface with Concave and Convex Effects

et al. 2020

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“…Electric and magnetic fields are induced in a fluid, which is electrically conducting by involving a magnetic field. Several authors examined the MHD effects over a stretching sheet in various types of fluids in different situations.…”

Section: Introductionmentioning

confidence: 99%

Homogeneous‐heterogeneous chemical action and non‐Fourier flux theory effects in a flow with carbon nanotubes

Suneetha

Subbarayudu

Wahidunnisa

et al. 2019

Heat Trans. Asian Res.

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A theoretical outline is sketched to figure out the stream of polyvinyl alcohol (PVA)-based CNTs along a moving surface with multiple slip effects on homogeneous and heterogeneous chemical reactions. The nonlinear radiant, heat, and nonuniform heat source/sink is incorporated in the energy equation to discuss the heat transport phenomenon. The novel theory of non-Fourier flux model of heat diffusion is also merged in the energy equation. Two kinds of nanoparticles are considered, namely, single wall carbon nanotubes and multiple wall carbon nanotubes, and are suspended in the working PVA to illustrate the flow behavior. Due to a large variety of applications, PVA is used in papermaking, textiles, and a variety of coatings. The principal structure of mathematical model is based upon the system of differential equations, which has been tackled through Runge-Kutta-Fehlberg method in MATLAB software. Graphical images are made vs different physical parameters which emerged in the model. The heat transfer of the fluid enhances with the increase of nonuniform thermal radiation. The homogeneous and heterogeneous chemical reactions slow down the concentration rate. K E Y W O R D S C-CHFM, CNTs, homogeneous/heterogeneous, nonlinear radiation, nonuniform heat source/sink 1 | INTRODUCTIONIn physical systems, transportation of thermal energy is accredited by heat transfer, which has abundant utilization in fields like engineering, and in modern processes of industries, contemporary industrial process that absorb heat transmission in tissues, effectiveness of fuel cell, knowledge in food manufacturing, removing heat from electronic devices, targeting of tumors, and several others. Bicentenary before the most excellent model in heat conduction was proposed by Fourier, 1 which became a benchmark to examine the heat transfer facets in different conditions. But it has a pessimistic phase, that is, a parabolic equation in thermal field is created, which was cited as "Paradox of heat conduction" in literature. To overcome this, in 1948, Cattaneo 2 remodeled this by sticking the term thermal relaxation time with the movement of heat by the proliferation of hot waves with a firm velocity. Soon after, Christov 3 further reshaped the Cattaneo model by restoring the ordinary derivative with Oldroyd's upper-convected derivatives in order to attain the material-invariant formulation. This recovered replica is eminent as Cattaneo-Christov heat flux model (C-CHFM). The outcomes of C-CHFM for flow problems, which are not compressible, are depicted by Tibulle and Zampoli. 4 Bala Anki Reddy and Suneetha 5 contemplated the cause of C-CHF over a stretching surface in the Casson fluid flow. In recent times, many researchers 6-11 reported on various C-CHF models.Nanotechnology plays startling applications in various domains of engineering. Nanofluid is one of the important sectors of nanotechnology. Choi 12 introduced the idea of nanofluid by dropping solid nano-sized particles in a host fluid: ethylene glycol, oil, water, and so on. Hayat et al 13...

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“…The fluid is suspended with the nanoparticles bounded by a stretchable heated surface. In addition to all above mentioned studies by various researchers with their adopted approaches, several investigations relevant to this presented endeavor have been listed in [15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Models of Electro-Magnetohydrodynamic Multiphase Flows Synthesis with Nano-Sized Hafnium Particles

2018

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Featured Application: This model can be used to design and engineer for nozzle or diffuser type of injectors in the latest models of automobiles to improve their performance and reduce the consumption of fuel. Abstract:The multiphase fluid flow under the influence of electro-magnetohydrodynamics (EHD) is investigated in this study. The base fluid contains hafnium particles. Two illustrative models namely fluid phase and particulate phase are considered for three different geometries having great importance in both industrial and mechanical usage. The impact of pertinent parameters from different aspects is illustrated graphically with requisite discussion keeping in view their physical aspects. The stream lines are also erected to highlight their physical importance regarding the flow patterns. In addition, the paper is terminated by making a comparison with the existing literature as a limiting case of considered problem to confirm the validations of achieved results and hence found in excellent agreement. This model can be used to design and engineer for nozzle or diffuser type of injectors in the latest models of automobiles to improve their performance and reduce the consumption of fuel.

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Effects of aligned magnetic field and CNTs in two different base fluids over a moving slip surface

Cited by 64 publications

References 22 publications

Influence of Single- and Multi-Wall Carbon Nanotubes on Magnetohydrodynamic Stagnation Point Nanofluid Flow over Variable Thicker Surface with Concave and Convex Effects

Influence of Single- and Multi-Wall Carbon Nanotubes on Magnetohydrodynamic Stagnation Point Nanofluid Flow over Variable Thicker Surface with Concave and Convex Effects

Homogeneous‐heterogeneous chemical action and non‐Fourier flux theory effects in a flow with carbon nanotubes

Mathematical Models of Electro-Magnetohydrodynamic Multiphase Flows Synthesis with Nano-Sized Hafnium Particles

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