Thermal stratification of rotational second-grade fluid through fractional differential operators

Abro, Kashif Ali; Siyal, Ambreen; Atangana, Abdon

doi:10.1007/s10973-020-09312-8

Cited by 59 publications

(14 citation statements)

References 41 publications

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“…The heat and mass transfer phenomenon in different fluids with the help of fractional derivatives has also been examined [37]. The researchers discussed viscoelastic fluids with and without fractional derivative operator [38]- [42].…”

Section: Introductionmentioning

confidence: 99%

A scientific report of singular kernel on the rate-type fluid subject to the mixed convection flow

et al. 2022

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The response of inhomogeneous fluids whose material properties are strongly interconnected with mean normal stress and shear rate; such phenomenon undergo to rate constitutive type theories within thermodynamical aspects. In this context, the thermodynamic approach for modeling a class of viscoelastic fluids so-called Oldroyd-B fluid is investigated through a singular kernel. This is because, role of the singular kernel has become imperative due to the wide applications of rate type fluid subject to the mixed convection flow. To have the systematical and molecular dynamics of Oldroyd-B fluid, the temperature distribution, velocity profile and Nusslet numbers have been explored by invoking the Laplace transform on the governing equations. Owing to the strengthening of physical parameters, the enhancement of convective heat transfer is emphasized based on relaxation as well as retardation phenomenon. Additionally, the evaluation of thermal and flow characteristics of Oldroyd-B fluid have resulted in discovering more evolutionary mechanisms of the considered problem of rate type fluid subject to the mixed convection flow.

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Section: Introductionmentioning

confidence: 99%

A scientific report of singular kernel on the rate-type fluid subject to the mixed convection flow

et al. 2022

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“…MHD oblique stagnation point flow of secondgrade fluid with the geometry of oscillatory stretching surface is explained by Abro et al 10 Impact of magnetic effect, heat and mass transfer, effects of thermal dissipation and diffusion and radiative heat flux on a second-grade fluid is explored by several investigators. [11][12][13][14] Recently, the scholars gave full consideration and interest to investigate the convective transport of nanofluids. Thermal conductivity plays an important role in increasing heat transfer in nanofluids.…”

Section: Introductionmentioning

confidence: 99%

Energy transference in time‐dependent Cattaneo–Christov double diffusion of second‐grade fluid with variable thermal conductivity

et al. 2021

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The current investigation communicates the characteristics of upper-convected second grade nanofluid thin film flow over a time-dependent stretching sheet with variable thermal conductivity and Cattaneo-Christov double diffusion theory. The mathematical model generates a system of nonlinear partial differential equations (PDEs) for heat, momentum, and mass transfer phenomena. Similarity variables converted the PDEs into nonlinear ordinary differential equations (ODEs). Furthermore, received ODEs are numerically rescued with the built-in program Bvp4c in MATLAB. The impact of physical parameters like second-grade fluid λ, unsteadiness parameter S, Prandtl number Pr, Schmidt number Sc, variable thermal conductivity ε, variable diffusivity ε 1 , the square of dimensionless film thickness γ, relaxation time δ e , and retardation time δ c are scrutinized. Tables revealed numerical exposure and graphs depict the geometrical aspect of the current study. The velocity field is improved by heightening the λ, magnification in temperature is found for greater conductivity parameter ε. Greater δ e in the temperature profile goes smaller. The rate of mass transfer diminishes by uplifting the estimations in relaxation time parameter δ . c

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“…e applications are numerous, whether in electricity, chemistry, or signal processing [6][7][8][9]. e main problem for the automation researcher is to represent these physical processes with sufficient estimation and a simple structural model.…”

Section: Introductionmentioning

confidence: 99%

A Proposed High-Gain Observer for a Class of Nonlinear Fractional-Order Systems

Etlili

Khedher

Errachdi

2021

Mathematical Problems in Engineering

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This paper proposes a high-gain observer for a class of nonlinear fractional-order systems. Indeed, this approach is based on Caputo derivative to solve the estimation problem for nonlinear systems. The proposed high-gain observer is used to estimate the unknown states of a nonlinear fractional system. The use of Lyapunov convergence functions to establish stability of system is detailed. The influence of different fractional orders on the estimation is presented. Ultimately, numerical simulation examples demonstrate the efficiency of the proposed approach.

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Thermal stratification of rotational second-grade fluid through fractional differential operators

Cited by 59 publications

References 41 publications

A scientific report of singular kernel on the rate-type fluid subject to the mixed convection flow

A scientific report of singular kernel on the rate-type fluid subject to the mixed convection flow

Energy transference in time‐dependent Cattaneo–Christov double diffusion of second‐grade fluid with variable thermal conductivity

A Proposed High-Gain Observer for a Class of Nonlinear Fractional-Order Systems

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