Analysis of natural convection flows of Jeffrey fluid with Prabhakar-like thermal transport

Khan, Zar Ali; Haider, Nadeem; El‐Zahar, Essam R.; Yook, Se-Jin

doi:10.1016/j.csite.2022.102079

Cited by 13 publications

(10 citation statements)

References 35 publications

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“…Invoking the Boussinesq approximation and the parallel flow hypothesis [37], the basic flow equations in Cartesian coordinate system are written, with consideration of the thermal radiation effect, as [4,41]…”

Section: Governing Equationsmentioning

confidence: 99%

\begin{equation} \frac{\partial P}{\partial X}=\frac{\partial S_{XY}}{\partial Y}-(\rho \beta )_{hnf} g (T-T_{0})\sin \phi , \end{equation}

\begin{equation} \frac{\partial P}{\partial Y}=(\rho \beta )_{hnf} g (T-T_{0})\cos \phi , \end{equation}

\begin{equation} (\rho C_p)_{hnf}U\frac{\partial T}{\partial X}=k_{hnf} \frac{\partial ^2 T}{\partial Y^2}-\frac{\partial q_{r}}{\partial Y}, \end{equation}

the corresponding boundary conditions are

U (0) badbreak= 0, U (L) goodbreak= - Γ_{1} \frac{\partial U}{\partial Y} |_{Y = L}, goodbreak- \frac{\partial T}{\partial Y} |_{Y = 0} = \partial ...

…”

Section: Governing Equationsmentioning

confidence: 99%

“…By far, it has several applications in polymer industries and biological field. Theoretically, the Jeffery fluid model has been applied to some flow and heat transfer problems [2][3][4]. These successful applications exhibit the validity of the Jeffery fluid model.…”

Section: Introductionmentioning

confidence: 99%

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Fully developed opposing mixed convection of a Jeffery tri‐hybrid nanofluid between two parallel inclined plates subjected to wall‐slip condition

Bibi,

2023

Z Angew Math Mech

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We analyze the effect of wall slip on the fully developed reverse mixed convection of Jeffery nanofluids between two inclined parallel plates with uniform wall heat flux conditions. The theory of tri‐hybrid water‐based nanoparticles with unique shapes, namely, cylindrical (copper), spherical (titanium oxide), and platelet (aluminum oxide) for heat transfer enhancement is utilized since it has better heat performance applicable in a dynamic of fuels and coolant in automobiles as compared with regular Newtonian fluid and nanofluid. The equations describing the above transport phenomena are nondimensional through appropriate scale transformations. Analytical solutions for velocity, temperature, and pressure distributions are obtained. Four different flow regimes including no reversal, bottom reversal, top reversal, and on both walls reversal are found for different combinations of buoyancy and pressure. Particularly, we notice that the wall slip significantly affects flow reversal. Furthermore, we notice that Magyari 's conclusion that the results of the homogeneous nanofluid flow model can be recovered from the corresponding Newtonian fluid model has great limitations. Besides, the effect of several physical factors on velocity and temperature distributions and important physical quantities, including skin friction coefficient and Nusselt number, are analyzed and graphically discussed.

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Section: Governing Equationsmentioning

confidence: 99%

\begin{equation} \frac{\partial P}{\partial X}=\frac{\partial S_{XY}}{\partial Y}-(\rho \beta )_{hnf} g (T-T_{0})\sin \phi , \end{equation}

\begin{equation} \frac{\partial P}{\partial Y}=(\rho \beta )_{hnf} g (T-T_{0})\cos \phi , \end{equation}

\begin{equation} (\rho C_p)_{hnf}U\frac{\partial T}{\partial X}=k_{hnf} \frac{\partial ^2 T}{\partial Y^2}-\frac{\partial q_{r}}{\partial Y}, \end{equation}

the corresponding boundary conditions are

U (0) badbreak= 0, U (L) goodbreak= - Γ_{1} \frac{\partial U}{\partial Y} |_{Y = L}, goodbreak- \frac{\partial T}{\partial Y} |_{Y = 0} = \partial ...

…”

Section: Governing Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Fully developed opposing mixed convection of a Jeffery tri‐hybrid nanofluid between two parallel inclined plates subjected to wall‐slip condition

Bibi,

2023

Z Angew Math Mech

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“…According to Caputo-Fabrizio [23], a new defnition with a nonsingular kernel has been proposed to solve the singularity problem in CFD. Tis new concept was utilized in the research of several scholars [24][25][26][27][28]. Te C-F fractional derivative is commonly used by academics to explore the memory efect.…”

Section: Introductionmentioning

confidence: 99%

“…In this procedure, the Caputo time-fractional derivative (CTFD) with a solitary power law kernel is used. Recently, Khan et al [39] have investigated the free convection fow of the Prabhakar fractional Jefrey fuid on an oscillated vertical plate with homogeneous heat fux. With the help of the Laplace transform and Boussinesq approximation, precise solutions for dimensionless momentum may be found.…”

Section: Introductionmentioning

confidence: 99%

A Generalized Two‐Phase Free Convection Flow of Dusty Jeffrey Fluid between Infinite Vertical Parallel Plates with Heat Transfer

Khan

Asogwa²,

Alqahtani

et al. 2022

Journal of Mathematics

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In blood flow and fluid mechanics, Jeffrey fluid has a vital role because of its viscoelastic characteristics. The application of Caputo–Fabrizio time-fractional derivatives for dusty-type Jeffrey fluid is discussed in this article. The concept of free convection flow of dusty Jeffrey fluid between infinite vertical parallel static plates is generalized. Free convection and buoyant force produce the flow. Furthermore, the fluid contains homogeneous dispersion of all spherical dust particles. Heat transmission is therefore taken into account for free convection. Nondimensional variables are used to write the dusty Jeffrey fluid classical model in dimensionless form. Also, the dimensionless model is transformed into a generalized dusty Jeffrey fluid model via a fractional derivative. Using the finite sine and Laplace method, the governing equations of the generalized dusty Jeffrey fluid model have been solved exactly. Numerical computation is used to study the physics of velocity and temperature profiles for a variety of embedded parameters. The collected results are discussed in detail and are shown graphically in this report. Mathcad-15 is used to plot the graphical outcomes for Jeffrey fluid, dust particle, and temperature profiles. Furthermore, skin friction and the Nusselt number are calculated. Table demonstrates how the rate of heat transmission reduces as the Peclet number’s value rises. Similarly, Table demonstrates that skin friction increases as the fractional parameter rises. By increasing the dusty Jeffrey fluid parameter λ , both velocity profiles are retarded.

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Fractional analysis of unsteady magnetohydrodynamics Jeffrey flow over an infinite vertical plate in the presence of Hall current

Abbas,

Nazar

2024

Math Methods in App Sciences

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The impact of Hall current on the multiphase thermal transfer of an incompressible electrically conductive Jeffrey flow over an infinitely vertical plate when heat absorption and chemical reaction are present has been examined. Partial differential equations have been used to describe the process, accounting for heat and mass transfer effects. This study uses extended Fourier's and Fick's laws together with the recently announced constant proportional Caputo (CPC) fractional operator. The fractional model is converted into a nondimensional form by applying some appropriate quantities. The nondimensional produced fractional model for momentum, heat, and diffusion equations based on the CPC fractional operator has been calculated semi‐analytically by applying the Laplace method. The Mathcad 15 software to sketch the graphs for several factors, like the Grashof number, mass Grashof number, Schmidt number, Prandtl number, Hall, and magnetic field parameters, is used to describe the velocity profile. Additionally, a graphical explanation is provided for the influence of the appeared parameters, particularly the effect of the fractional parameters. It is concluded that the result of the fluid model developed by the generalized constitutive relations is more accurate and generalized than the results of the artificially contracted fractional model. A fractional derivative is therefore the ideal option to achieve controlled concentration, temperature, and velocity. The current study is immediately relevant to geophysical, cosmically fluid dynamics, medical, biological, and any other processes that are significantly enhanced by a low gas density and a high magnetic field.

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Analysis of natural convection flows of Jeffrey fluid with Prabhakar-like thermal transport

Cited by 13 publications

References 35 publications

Fully developed opposing mixed convection of a Jeffery tri‐hybrid nanofluid between two parallel inclined plates subjected to wall‐slip condition

Fully developed opposing mixed convection of a Jeffery tri‐hybrid nanofluid between two parallel inclined plates subjected to wall‐slip condition

A Generalized Two‐Phase Free Convection Flow of Dusty Jeffrey Fluid between Infinite Vertical Parallel Plates with Heat Transfer

Fractional analysis of unsteady magnetohydrodynamics Jeffrey flow over an infinite vertical plate in the presence of Hall current

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