Flows with Slip of Oldroyd-B Fluids over a Moving Plate

Shakeel, Abdul; Ahmad, Sohail; Khan, Hamid; Haq, Sami Ul

doi:10.1155/2016/8619634

Cited by 12 publications

(9 citation statements)

References 22 publications

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“…• By taking magnetic field M = 0, we get identical results obtained by Shakeel et al (Eq. (15) in [22]).…”

Section: 1mentioning

confidence: 98%

“…Moreover, if (λ r = 0) and (M = 0) the resultant result becomes identity to Riaz et al (Eqs. (22) and (29)in [20]).…”

Section: Atangana-baleanu Fractional Time Derivativementioning

confidence: 99%

“…Siddiqui et al [23] discussed an unsteady flow of an Oldroyd-B fluid with the effect of slip condition. Oldroyd-B fluid with slip effect over moving plate analyzed by Shakeel et al [22]. In industry, there are many applications to the effect of the slip parameter.…”

mentioning

confidence: 99%

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Comprehensive analysis of integer-order, Caputo-Fabrizio (CF) and Atangana-Baleanu (ABC) fractional time derivative for MHD Oldroyd-B fluid with slip effect and time dependent boundary condition

Riaz¹,

Saeed²

2021

DCDS-S

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This article is focused on the slip effect in the unsteady flow of MHD Oldroyd-B fluid over a moving vertical plate with velocity Uof (t). The Laplace transformation and inversion algorithm are used to evaluate the expression for fluid velocity and shear stress. Fractional time derivatives are used to analyze the impact of fractional parameters (memory effect) on the dynamics of the fluid. While making a comparison, it is observed that the fractional-order model is best to explain the memory effect as compared to the classical model. The behavior of slip condition as well as no-slip condition is discussed with all physical quantities. The influence of dimensionless physical parameters like magnetic force M , retardation time λr, fractional parameter α, and relaxation time λ on fluid velocity has been discussed through graphical illustration. Our results suggest that the velocity field decreases by increasing the value of the magnetic field. In the absence of a slip parameter, the strength of the magnetic field is maximum. Furthermore, it is noted that the Atangana-Baleanu derivative in Caputo sense (ABC) is the best to highlight the dynamics of the fluid.

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“…• By taking magnetic field M = 0, we get identical results obtained by Shakeel et al (Eq. (15) in [22]).…”

Section: 1mentioning

confidence: 98%

“…Moreover, if (λ r = 0) and (M = 0) the resultant result becomes identity to Riaz et al (Eqs. (22) and (29)in [20]).…”

Section: Atangana-baleanu Fractional Time Derivativementioning

confidence: 99%

See 1 more Smart Citation

Comprehensive analysis of integer-order, Caputo-Fabrizio (CF) and Atangana-Baleanu (ABC) fractional time derivative for MHD Oldroyd-B fluid with slip effect and time dependent boundary condition

Riaz¹,

Saeed²

2021

DCDS-S

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“…Khan et al [8] analytically probed the role of porosity in magnetohydrodynamic (MHD) motion of Oldroyd-B model. Shakeel et al [9] studied the role of slip condition in flow of Oldroyd-B model and drawn a comparison with zero-slip condition at boundary. Khan et al [10] examined the porosity effects on Oldroyd-B model by calculating the exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Heat Transfer Analysis of Unsteady Natural Convection Flow of Oldroyd-B Model in the Presence of Newtonian Heating and Radiation Heat flux

et al. 2020

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The main focus of this theoretical inspection is to explore the control of Newtonian heating on heat transfer for an unsteady natural convection flow of Oldroyd-B fluid confined to an infinitely long, vertically static plate. Partial differential equations are constructed effectively to describe the fluid flow and heat transfer. Some appropriate dimensionless quantities and Laplace transformation are employed as basic tools to evaluate the solutions of these differential equations. However, due to the complex nature of velocity field, solution is approximated by using Durbin's numerical Laplace inverse algorithm. This solution is further validated by obtaining the velocity solution through algorithms proposed by Stehfest and Zakian. The temperature and velocity gradient are also determined to anticipate the heat transfer rate and skin friction at wall. Some well known results in literature are also deduced from the considered model. Conclusively, to have a deep understanding of the physical mechanism of considered model, and influence of implanted parameters, some outcomes are elucidated with the assistance of tables and graphs. As a result, it is found that under the effect of Newtonian heating, freely convective viscous fluid has greater velocity than Oldroyd-B fluid, Maxwell fluid and second grade fluid. INDEX TERMS Free convection, Laplace transform, Newtonian heating, Oldroyd-B model, thermal radiation. NOMENCLATURE ρ Fluid density (kgm −3) g Acceleration due to gravity (ms −2) β Coefficient of thermal expansion (K −1) T Fluid temperature (K) x, y, z Spatial variables (m) u, v, w Velocity components (ms −1) The associate editor coordinating the review of this manuscript and approving it for publication was Hamid Mohammad-Sedighi. µ Dynamic viscosity (kgms −1) λ Relaxation time (s) λ r Retardation time (s) S Shear stress (Nm −2) ν Kinematic viscosity (m 2 s −1) k Thermal conductivity (Wm −1 K −1) c p Specific heat (Jkg −1 K −1) σ 1 Stefan-Boltzmann coefficient (Wm −2 K −4) K 1 Rosseland absorption constant (m −1) T ∞ Ambient temperature (K)

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“…Akbar and Khan 16 given the numerical study of carbon nanotubes postponed magnetohydrodynamics (MHD) stagnation point flow over a stretching sheet with convective slip. Shakeel et al 17 studied the flows of an Oldroyd-B fluid under the consideration of slip condition at the boundary, the fluid motion is generated by the flat plate which has a translational motion in its plane with a time-dependent velocity. Hayat et al 18 find out the unstable flow of magnetohydrodynamics (MHD) over stretching sheet with velocity and thermal slip boundary conditions, and many different boundaries were find out on to calculate velocity and temperature.…”

mentioning

confidence: 99%

Heat transfer flow of Maxwell hybrid nanofluids due to pressure gradient into rectangular region

Chu

Ali

Asjad

et al. 2020

Sci Rep

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In this work, influence of hybrid nanofluids (Cu and $$\mathrm{Al}_{2}\mathrm{O}_{3}$$ Al 2 O 3 ) on MHD Maxwell fluid due to pressure gradient are discussed. By introducing dimensionless variables the governing equations with all levied initial and boundary conditions are converted into dimensionless form. Fractional model for Maxwell fluid is established by Caputo time fractional differential operator. The dimensionless expression for concentration, temperature and velocity are found using Laplace transform. As a result, it is found that fluid properties show dual behavior for small and large time and by increasing volumetric fraction temperature increases and velocity decreases respectively. Further, we compared the Maxwell, Casson and Newtonian fluids and found that Newtonian fluid has greater velocity due to less viscosity. Draw the graphs of temperature and velocity by Mathcad software and discuss the behavior of flow parameters and the effect of fractional parameters.

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Flows with Slip of Oldroyd-B Fluids over a Moving Plate

Cited by 12 publications

References 22 publications

Comprehensive analysis of integer-order, Caputo-Fabrizio (CF) and Atangana-Baleanu (ABC) fractional time derivative for MHD Oldroyd-B fluid with slip effect and time dependent boundary condition

Comprehensive analysis of integer-order, Caputo-Fabrizio (CF) and Atangana-Baleanu (ABC) fractional time derivative for MHD Oldroyd-B fluid with slip effect and time dependent boundary condition

Heat Transfer Analysis of Unsteady Natural Convection Flow of Oldroyd-B Model in the Presence of Newtonian Heating and Radiation Heat flux

Heat transfer flow of Maxwell hybrid nanofluids due to pressure gradient into rectangular region

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