Unsteady thermal transport flow of Casson nanofluids with generalized Mittag–Leffler kernel of Prabhakar's type

Wang, Fuzhang; Asjad, Muhammad Imran; Zahid, Muhammad; Iqbal, Azhar; Ahmad, Harith; Alsulami, M. D.

doi:10.1016/j.jmrt.2021.07.029

Cited by 82 publications

(18 citation statements)

References 42 publications

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“…The thermo-physical values of Al O 2 3 and water are shown in Table 1. The thermophysical features of nanomaterial are reported as per Wang et al 40 and Devi and Devi 41 :…”

Section: Mathematical Developmentmentioning

confidence: 99%

“…The thermo‐physical values of

{Al}_{2} O_{3}

and water are shown in Table 1. The thermophysical features of nanomaterial are reported as per Wang et al 40 and Devi and Devi 41 :

k_{n f} = \frac{- 2 ϕ false(- k_{s} + k_{f} false) + 2 k_{f} + k_{s}}{2 ϕ false(- k_{s} + k_{f} false) + 2 k_{f} + k_{s}} k_{f}, {false(ρ C p false)}_{n f} = ()(, - ϕ + 1 + \frac{{(ρ C p)}_{s}}{{(ρ C p)}_{f}} ϕ) {false(ρ C p false)}_{f}, μ_{n f} = \frac{μ_{f}}{{(1 - ϕ)}^{2.5}}, ρ_{n f} = ρ_{f} ()(, 1 - ϕ + ϕ \frac{ρ_{s}}{ρ_{f}}), D_{n f} = D_{f} {false(1 - ϕ false)}^{2.5} .

…”

Section: Mathematical Developmentmentioning

confidence: 99%

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Thermophoretic particle deposition and heat generation analysis of Newtonian nanofluid flow through magnetized Riga plate

et al. 2021

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The Riga surface is composed of an electromagnetic actuator that comprises a span‐wise associated array of discontinuous electrodes and an everlasting magnet mounted over a planer surface. The electro‐magneto‐hydrodynamic has an attractive role in thermal reactors, fluidics network flow, liquid chromatography, and micro coolers. Inspired by these applications, a laminar, two‐dimensional nanofluid flow with uniform heat sink‐source, thermophoretic depositions of the particles, and the Newtonian heating effect are investigated. The equations that describe the fluid motion are reduced into a system of ordinary differential equations with the help of spatial similarity variables. Numeric solutions of ordinary differential equations are executed through the Runge–Kutta–Felhberg 45 order technique via a shooting scheme. The role of various nondimensional factors on physically interesting quantities is elaborated graphically. The velocity profile rises for modified Hartmann number and decreases for porosity parameter. Thermal enhancement is high in the common wall temperature condition comparative to the case of the Newtonian heating conditions. The concentration profile is enhanced with Schmidt number, but the reverse trend is observed for the thermophoretic parameter. The rate of mass transfer is increased with Schmidt number.

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“…The thermo-physical values of Al O 2 3 and water are shown in Table 1. The thermophysical features of nanomaterial are reported as per Wang et al 40 and Devi and Devi 41 :…”

Section: Mathematical Developmentmentioning

confidence: 99%

“…The thermo‐physical values of

{Al}_{2} O_{3}

and water are shown in Table 1. The thermophysical features of nanomaterial are reported as per Wang et al 40 and Devi and Devi 41 :

k_{n f} = \frac{- 2 ϕ false(- k_{s} + k_{f} false) + 2 k_{f} + k_{s}}{2 ϕ false(- k_{s} + k_{f} false) + 2 k_{f} + k_{s}} k_{f}, {false(ρ C p false)}_{n f} = ()(, - ϕ + 1 + \frac{{(ρ C p)}_{s}}{{(ρ C p)}_{f}} ϕ) {false(ρ C p false)}_{f}, μ_{n f} = \frac{μ_{f}}{{(1 - ϕ)}^{2.5}}, ρ_{n f} = ρ_{f} ()(, 1 - ϕ + ϕ \frac{ρ_{s}}{ρ_{f}}), D_{n f} = D_{f} {false(1 - ϕ false)}^{2.5} .

…”

Section: Mathematical Developmentmentioning

confidence: 99%

Thermophoretic particle deposition and heat generation analysis of Newtonian nanofluid flow through magnetized Riga plate

et al. 2021

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“…Finally, in Akgül et al's study [34], the magnetohydrodynamics effects on heat transfer phenomena was examined. Wang et al [35] discussed the Casson nanofluid with a modified Mittag-Leffler kernel of a Prabhakar form of unsteady thermal transportation flow.…”

Section: Introductionmentioning

confidence: 99%

Advancement of Non-Newtonian Fluid with Hybrid Nanoparticles in a Convective Channel and Prabhakar’s Fractional Derivative—Analytical Solution

et al. 2021

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The present paper deals with the advancement of non-Newtonian fluid containing some nanoparticles between two parallel plates. A novel fractional operator is used to model memory effects, and analytical solutions are obtained for temperature and velocity fields by the method of Laplace transform. Moreover, a parametric study is elaborated to show the impact of flow parameters and presented in graphical form. As a result, dual solutions are predicted for increasing values of fractional parameters for short and long times. Furthermore, by increasing nanoparticle concentration, the temperature can be raised along with decreasing velocity. A fractional approach can provide new insight for the analytical solutions which makes the interpretation of the results easier and enable the way of testing possible approximate solutions.

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“…The Prabhakar integral operator was introduced by Prabhakar in 1971, 17 and this overall model of fractional calculus has been intensively studied in recent years. [18][19][20][21] It has discovered a number of interesting applications, including in viscoelasticity, 22,23 nanofluids, 24 stochastic processes, 25 options pricing, 26 and anomalous dielectrics. 14 Fractional differential equations involving Prabhakar-type operators have been analysed using various methods, including compactness of operators 27 and stability of dynamical systems.…”

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confidence: 99%

A catalogue of semigroup properties for integral operators with Fox–Wright kernel functions

2022

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The Fox-Wright function is a very general form of function, covering many families of special functions as particular cases. Any special function can be used as a kernel for a fractional integral operator, but which of these operators will satisfy desiderata such as a semigroup property for composition? This paper provides a rigorous categorisation of all such fractional integral operators which have a semigroup property in any of their parameters. We discover that nearly all possible semigroup properties arise from the Chu-Vandermonde identity, with the Prabhakar fractional calculus emerging as one special case. For any integral operator with such a semigroup property, it is possible to construct a complete model of fractional calculus, including both integral and derivative operators which interact with each other in a natural way.

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Unsteady thermal transport flow of Casson nanofluids with generalized Mittag–Leffler kernel of Prabhakar's type

Cited by 82 publications

References 42 publications

Thermophoretic particle deposition and heat generation analysis of Newtonian nanofluid flow through magnetized Riga plate

Thermophoretic particle deposition and heat generation analysis of Newtonian nanofluid flow through magnetized Riga plate

Advancement of Non-Newtonian Fluid with Hybrid Nanoparticles in a Convective Channel and Prabhakar’s Fractional Derivative—Analytical Solution

A catalogue of semigroup properties for integral operators with Fox–Wright kernel functions

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