Evaluating the unsteady Casson nanofluid over a stretching sheet with solar thermal radiation: An optimal case study

Jamshed, Wasim; S, Suriya Uma Devi; Goodarzi, Marjan; Prakash, M.; Nisar, Kottakkaran Sooppy; Zakarya, Mohammed; Abdel‐Aty, Abdel‐Haleem

doi:10.1016/j.csite.2021.101160

Cited by 154 publications

(43 citation statements)

References 47 publications

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“…Recall that the iteration (9) was constructed so that its fixed points are steady solutions of (8), so this convergence of the scheme gives existence of solutions. We state this result as a theorem: Theorem 1 (Convergence of Steady Solutions to the Stream Function-Vorticity Form of the Boussinesq Navier-Stokes equations).…”

Section: Existence Proofmentioning

confidence: 99%

“…In a similar analysis, Flores-Flores [6] considers microparticle transport driven by laser-induced convective currents in gas at microscale velocities. In nanofluids, Mourad et al [7] and Jamshed et al [8] consider the thermal characteristics of fluid flow undergoing natural convection. At larger fluid velocities, Masoomi [9] considered steady-state convective heat transfer from lasers in the context of additive manufacturing, and Rennie [10] has discussed the impact laser-induced convection can have on material heating times in directed energy applications.…”

Section: Introductionmentioning

confidence: 99%

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Two-Dimensional Steady Boussinesq Convection: Existence, Computation and Scaling

Lane

Akers

2021

Fluids

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This research investigates laser-induced convection through a stream function-vorticity formulation. Specifically, this paper considers a solution to the steady Boussinesq Navier–Stokes equations in two dimensions with a slip boundary condition on a finite box. A fixed-point algorithm is introduced in stream function-vorticity variables, followed by a proof of the existence of steady solutions for small laser amplitudes. From this analysis, an asymptotic relationship is demonstrated between the nondimensional fluid parameters and least upper bounds for laser amplitudes that guarantee existence, which accords with numerical results implementing the algorithm in a finite difference scheme. The findings indicate that the upper bound for laser amplitude scales by O(Re−2Pe−1Ri−1) when Re≫Pe, and by O(Re−1Pe−2Ri−1) when Pe≫Re. These results suggest that the existence of steady solutions is heavily dependent on the size of the Reynolds (Re) and Peclet (Pe) numbers, as noted in previous studies. The simulations of steady solutions indicate the presence of symmetric vortex rings, which agrees with experimental results described in the literature. From these results, relevant implications to thermal blooming in laser propagation simulations are discussed.

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Section: Existence Proofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Steady Boussinesq Convection: Existence, Computation and Scaling

Lane

Akers

2021

Fluids

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“…Kumar et al [9] scrutinized the consequence of particle deposition on heat and mass transmission in Casson fluid motion over a moving thin needle. Jamshed et al [10] deliberated the unsteady Casson nanoliquid flow on a stretching sheet in the presence of solar thermal radiation.…”

Section: Introductionmentioning

confidence: 99%

Influence of Thermophoretic Particle Deposition on the 3D Flow of Sodium Alginate-Based Casson Nanofluid over a Stretching Sheet

et al. 2021

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The wide range of industrial applications of flow across moving or static solid surfaces has aroused the curiosity of researchers. In order to generate a more exact estimate of flow and heat transfer properties, three-dimensional modelling must be addressed. This plays a vital role in metalworking operations, producing plastic and rubber films, and the continuous cooling of fibre. In view of the above scope, an incompressible, laminar three-dimensional flow of a Casson nanoliquid in the occurrence of thermophoretic particle deposition over a non-linearly extending sheet is examined. To convert the collection of partial differential equations into ordinary differential equations, the governing equations are framed with sufficient assumptions, and appropriate similarity transformations are employed. The reduced equations are solved by implementing Runge Kutta Fehlberg 4th 5th order technique with the aid of a shooting scheme. The numerical results are obtained for linear and non-linear cases, and graphs are drawn for various dimensionless constraints. The present study shows that improvement in the Casson parameter values will diminish the axial velocities, but improvement is seen in thermal distribution. The escalation in the thermophoretic parameter will decline the concentration profiles. The rate of mass transfer, surface drag force will reduce with the improved values of the power law index. The non-linear stretching case shows greater impact in all of the profiles compared to the linear stretching case.

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“…To simplify the situation, the majority of researchers have applied the Rosseland approximation to study the effects of linear radiation [30]. Jamshed et al [31] studied the impacts of solar radiation transport and slip condition on the convective thermal features of an unsteady flow of Casson nanofluid. Sheikholeslami [32] investigated the effects of linear thermal radiations on nanofluid flow through an elliptic cylinder.…”

Section: Introductionmentioning

confidence: 99%

A Magnetite–Water-Based Nanofluid Three-Dimensional Thin Film Flow on an Inclined Rotating Surface with Non-Linear Thermal Radiations and Couple Stress Effects

Ullah¹,

Ikramullah

Selim

et al. 2021

Energies

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This study is related to the heat energy transfer during 3D nanofluid (water-based) motion over a rotating surface by incorporating the combined impacts of thermal radiations and couple stress. The flow is modeled by a set of non-linear coupled PDEs, which is converted to a set of coupled non-linear ODEs by using suitable similarity transformations. The transformed equations are solved with the built-in NDSolve command. The effects of relevant interesting parameters on the nanofluid velocity components and temperature distribution are explained through various graphs. It is found that the velocity component f(η) is increased with higher values of γ and A0 while it drops with an increasing rotation parameter and nanoparticle volume fraction. The fluid temperature increases with higher αnf, Rd, ϵ2, ϵ3, A1 and drops with increasing Pr, ϵ1 and couple stress parameter (A0). The Nusselt number remains constant at a fixed Pr and Rd, whereas it increases with increasing Pr and is reduced with rising Rd. A comparison between the achieved results is carried out with the analytical results through different tables. An excellent agreement is observed between these results.

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Evaluating the unsteady Casson nanofluid over a stretching sheet with solar thermal radiation: An optimal case study

Cited by 154 publications

References 47 publications

Two-Dimensional Steady Boussinesq Convection: Existence, Computation and Scaling

Two-Dimensional Steady Boussinesq Convection: Existence, Computation and Scaling

Influence of Thermophoretic Particle Deposition on the 3D Flow of Sodium Alginate-Based Casson Nanofluid over a Stretching Sheet

A Magnetite–Water-Based Nanofluid Three-Dimensional Thin Film Flow on an Inclined Rotating Surface with Non-Linear Thermal Radiations and Couple Stress Effects

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