Heat and mass diffusions for Casson nanofluid flow over a stretching surface with variable viscosity and convective boundary conditions

Khan, Mair; Shahid, Amna; Salahuddin, T.; Malik, M.Y.; Mushtaq, Muhammad

doi:10.1007/s40430-018-1415-y

Cited by 36 publications

(22 citation statements)

References 29 publications

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“…to produce quick results. As an example, in boundary layer problems, we know that scaling, translation and spiral group of transformations are the most common ones yielding physical solutions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Hence, for a new boundary layer problem, the initial attempt might be to try these special transformations before applying the general Lie group analysis.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, for a new boundary layer problem, the initial attempt might be to try these special transformations before applying the general Lie group analysis. Motivated by the previous work on boundary layers of non-Newtonian fluids [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], we propose here a transformation which includes scaling, translation and spiral group of transformations as its special cases. Like the other special transformations, this transformation would be useful especially for an applied oriented researcher who is seeking a physical solution of his problem without involving deeply into the theory.…”

Section: Introductionmentioning

confidence: 99%

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Investigation of Velocity Profile in Time Dependent Boundary Layer Flow of a Modified Power-Law Fluid of Fourth Grade

Yürüsoy

2020

International Journal of Applied Mechanics and Engineering

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This paper deals with the investigation of time dependent boundary layer flow of a modified power-law fluid of fourth grade on a stretched surface with an injection or suction boundary condition. The fluid model is a mixture of fourth grade and power-law fluids in which the fluid may display shear thickening, shear thinning or normal stress textures. By using the scaling and translation transformations which is a type of Lie Group transformation, time dependent boundary layer equations are reduced into two alternative ordinary differential equations systems (ODEs) with boundary conditions. During this reduction, special Lie Group transformations are used for translation, scaling and combined transformation. Numerical solutions have been carried out for the ordinary differential equations for various fluids and boundary condition parameters. As a result of numerical analysis, it is observed that the boundary layer thickness decreases as the power-law index value increases. It was also observed that for the fourth-grade fluid parameter, as the parameter increases, the boundary layer thickness decreases while the velocity in the y direction increases.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Investigation of Velocity Profile in Time Dependent Boundary Layer Flow of a Modified Power-Law Fluid of Fourth Grade

Yürüsoy

2020

International Journal of Applied Mechanics and Engineering

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“…Common heat transfer fluids, such as water, all kinds of glycols, and mineral oil possess low thermal conductivity, which is insufficient to satisfy requirements in the rate of the cooling that are then used as other options to increase the rate of heat transfer in such fluids. Recently, much work related to the nanofluid has been reported . It is worth mentioning that all above researchers considered the MHD effect in nanofluids.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, much work related to the nanofluid has been reported. 23,24 It is worth mentioning that all above researchers considered the MHD effect in nanofluids. One of the objectives of this study is to consider nanofluids without the effect of MHD and suction.…”

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confidence: 99%

Stefan Blowing and Slip Effects on Unsteady Nanofluid Transport Past a Shrinking Sheet: Multiple Solutions

Dero

Uddin

Rohni

2019

Heat Trans. Asian Res.

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The aim of a present article is to investigate the laminar unsteady two‐dimensional boundary layer flow of a nanofluid with Stefan blowing and slip effect. First, governing boundary layer equations are converted in the ordinary form of the differential equations (ODEs) from partial differential equations using appropriate coordinate transformations. The obtained ODEs are then solved by applying a shooting method with the Runge‐Kutta fourth order method by implementation of the Maple software. The influences of different controlling dimensionless parameters over the dimensionless velocity, temperature, concentration, friction factor, local heat as well as mass transfer have been discussed and represented by plots. It is found that there exist dual solutions for the different applied nanofluid parameters along with the blowing parameter. The results reveal that by increasing the values of the Brownian motion (Nb), thermophoresis (Nt) and blowing parameters (fw), the skin friction increases (decreases) in the first (second) solution.

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“…Nadeem et al (2013) investigated the two-dimensional boundary layer equations for Williamson liquid induced by a stretching surface. Kumaran and Sandeep (2017) (Farooq et al, 2018;Hayat et al, 2016a;Hayat et al, 2015;Khan et al, 2018d;Khan et al, 2018e;Hayat et al, 2016b).…”

Section: Introductionmentioning

confidence: 99%

Variable diffusion and conductivity change in 3D rotating Williamson fluid flow along with magnetic field and activation energy

Khan

Salahuddin

Yousaf

et al. 2019

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Purpose The purpose of the current flow configurations is to bring to attention the thermophysical aspects of magnetohydrodynamics (MHD) Williamson nanofluid flow under the effects of Joule heating, nonlinear thermal radiation, variable thermal coefficient and activation energy past a rotating stretchable surface. Design/methodology/approach A mathematical model is examined to study the heat and mass transport analysis of steady MHD Williamson fluid flow past a rotating stretchable surface. Impact of activation energy with newly introduced variable diffusion coefficient at the mass equation is considered. The transport phenomenon is modeled by using highly nonlinear PDEs which are then reduced into dimensionless form by using similarity transformation. The resulting equations are then solved with the aid of fifth-order Fehlberg method. Findings The rotating fluid, heat and mass transport effects are analyzed for different values of parameters on velocity, energy and diffusion distributions. Parameters like the rotation parameter, Hartmann number and Weissenberg number control the flow field. In addition, the solar radiation, Joule heating, Prandtl number, thermal conductivity, concentration diffusion coefficient and activation energy control the temperature and concentration profiles inside the stretching surface. It can be analyzed that for higher values of thermal conductivity, Eckret number and solar radiation parameter the temperature profile increases, whereas opposite behavior is noticed for Prandtl number. Moreover, for increasing values of temperature difference parameter and thermal diffusion coefficient, the concentration profile shows reducing behavior. Originality/value This paper is useful for researchers working in mathematical and theoretical physics. Moreover, numerical results are very useful in industry and daily-use processes.

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Heat and mass diffusions for Casson nanofluid flow over a stretching surface with variable viscosity and convective boundary conditions

Cited by 36 publications

References 29 publications

Investigation of Velocity Profile in Time Dependent Boundary Layer Flow of a Modified Power-Law Fluid of Fourth Grade

Investigation of Velocity Profile in Time Dependent Boundary Layer Flow of a Modified Power-Law Fluid of Fourth Grade

Stefan Blowing and Slip Effects on Unsteady Nanofluid Transport Past a Shrinking Sheet: Multiple Solutions

Variable diffusion and conductivity change in 3D rotating Williamson fluid flow along with magnetic field and activation energy

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