Natural convection flow maxwell fluids with generalized thermal transport and newtonian heating

Zhang, Xiaohong; Shah, Rasool; Saleem, S.; Khan, Zar Ali; Chung, Jae Dong

doi:10.1016/j.csite.2021.101226

Cited by 25 publications

(11 citation statements)

References 30 publications

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“…We recover the same velocity field expressions for all cases which are discussed above by taking Gm = 0 in Equations ( 43), ( 46)-(48) as X. H. Zhang et al [44] investigated in Equations ( 26), ( 33), ( 35) and (37). All these results validate our current results.…”

Section: Ordinary Viscous Fluidsupporting

confidence: 84%

“…Xiao-Hong Zhang et al [44] recently, investigated the flow of a generalized fractional Prabhakar-type Maxwell fluid model, without analyzing the impacts of diffusion equation, and the results obtained via application of a Laplace transformation from the proposed problem. In the considered model, a new approach was used to fractionalize the diffusion equation by applying the definition of the Prabhakar fractional operator along with the generalized Fick's law; the influence of fractionalized diffusion equation is analyzed on momentum equation.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

et al. 2022

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In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, and Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.

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Section: Ordinary Viscous Fluidsupporting

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

et al. 2022

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“…Xiao-Hong Zhang et al [25] recently demonstrated the generalized fractional Prabhakartype Maxwell fluid flow model, but ignored the diffusive flux and effect of mass diffusion, computed solution via technique of Laplace transformation. In the literature no article is available regarding the generalized fractional Prabhakar-type Oldroyd-B fluid model.…”

Section: Introductionmentioning

confidence: 99%

Impact of Newtonian Heating via Fourier and Fick’s Laws on Thermal Transport of Oldroyd-B Fluid by Using Generalized Mittag-Leffler Kernel

et al. 2022

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In this manuscript, a new approach to study the fractionalized Oldroyd-B fluid flow based on the fundamental symmetry is described by critically examining the Prabhakar fractional derivative near an infinitely vertical plate, wall slip condition on temperature along with Newtonian heating effects and constant concentration. The phenomenon has been described in forms of partial differential equations along with heat and mass transportation effect taken into account. The Prabhakar fractional operator which was recently introduced is used in this work together with generalized Fick’s and Fourier’s law. The fractional model is transfromed into a non-dimentional form by using some suitable quantities and the symmetry of fluid flow is analyzed. The non-dimensional developed fractional model for momentum, thermal and diffusion equations based on Prabhakar fractional operator has been solved analytically via Laplace transformation method and calculated solutions expressed in terms of Mittag-Leffler special functions. Graphical demonstrations are made to characterize the physical behavior of different parameters and significance of such system parameters over the momentum, concentration and energy profiles. Moreover, to validate our current results, some limiting models such as fractional and classical fluid models for Maxwell and Newtonian are recovered, in the presence of with/without slip boundary wall conditions. Further, it is observed from the graphs the velocity curves for classical fluid models are relatively higher than fractional fluid models. A comparative analysis between fractional and classical models depicts that the Prabhakar fractional model explains the memory effects more adequately.

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“…They recorded the increase in temperature field against buoyancy parameter and decrease in velocity field against fluid relaxation time. Zhang et al 2 computed exact solution of unsteady fractional Maxwell model and thermal transport mechanism is highlighted via Laplace transform procedure. They have plotted several graphs and analyzed the contribution of numerous emerging parameters in the presence/absence of slip factor.…”

Section: Introductionmentioning

confidence: 99%

Investigation of thermal performance of Maxwell hybrid nanofluid boundary value problem in vertical porous surface via finite element approach

Algehyne

El‐Zahar

Elhag

et al. 2022

Sci Rep

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The study of thermo-physical characteristics is essential to observe the impact of several influential parameters on temperature and velocity fields. The transportation of heat in fluid flows and thermal instability/stability is a charming area of research due to their wider applications and physical significance because of their utilization in different engineering systems. This report is prepared to study thermal transportation in Maxwell hybrid nanofluid past over an infinite stretchable vertical porous sheet. An inclusion of hybrid nanofluid is performed to monitor the aspects of thermal transportation. Keeping in mind the advantages of thermal failure, non-Fourier theory for heat flux model is utilized. Aspects of external heat source are also considered. The mathematical formulation for the considered model with certain important physical aspects results in the form of coupled nonlinear PDEs system. The obtained system is reduced by engaging boundary layer approximation. Afterwards, transformations have been utilized to convert the modeled PDEs system into ODEs system. The converted nonlinear ODEs system is then handled via finite element method coded in symbolic computational package MAPLE 18.0. Grid independent survey is presented for the validation of used approach and the comparative analysis has been done to confirm the reliability of obtained solution. The obtained solution is discussed and physical aspects have been explored and recorded against numerous involved influential variables. Motion into hybrid nanoparticles and nanoparticles becomes slow down versus higher values of Forchheimer and Darcy’s porous numbers. Thermal growth is enhanced for the case of hybrid nano-structures rather than for case of nanofluid. Thickness regarding momentum layer is dominated for hybrid nanoparticles rather than case of nanoparticles.

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Natural convection flow maxwell fluids with generalized thermal transport and newtonian heating

Cited by 25 publications

References 30 publications

Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

Impact of Newtonian Heating via Fourier and Fick’s Laws on Thermal Transport of Oldroyd-B Fluid by Using Generalized Mittag-Leffler Kernel

Investigation of thermal performance of Maxwell hybrid nanofluid boundary value problem in vertical porous surface via finite element approach

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