Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms

Saqib, Muhammad; Khan, Ilyas; Shafie, Sharidan

doi:10.1186/s13662-019-1988-5

Cited by 86 publications

(41 citation statements)

References 36 publications

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“…It is worth mentioning that by making φ Ag = 0 or φ TiO 2 = 0, the modified model can be successfully reduced to nanofluid expressions. The numerical values of the thermophysical properties of the nanoparticles and base fluid are presented in Table 1, and the expression can be found in Table 2 [21,43,44]. Table 2.…”

Section: Thermophysical Properties Of Hybrid Nanofluidmentioning

confidence: 99%

Symmetric MHD Channel Flow of Nonlocal Fractional Model of BTF Containing Hybrid Nanoparticles

et al. 2020

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A nonlocal fractional model of Brinkman type fluid (BTF) containing a hybrid nanostructure was examined. The magnetohydrodynamic (MHD) flow of the hybrid nanofluid was studied using the fractional calculus approach. Hybridized silver (Ag) and Titanium dioxide (TiO2) nanoparticles were dissolved in base fluid water (H2O) to form a hybrid nanofluid. The MHD free convection flow of the nanofluid (Ag-TiO2-H2O) was considered in a microchannel (flow with a bounded domain). The BTF model was generalized using a nonlocal Caputo-Fabrizio fractional operator (CFFO) without a singular kernel of order α with effective thermophysical properties. The governing equations of the model were subjected to physical initial and boundary conditions. The exact solutions for the nonlocal fractional model without a singular kernel were developed via the fractional Laplace transform technique. The fractional solutions were reduced to local solutions by limiting α → 1 . To understand the rheological behavior of the fluid, the obtained solutions were numerically computed and plotted on various graphs. Finally, the influence of pertinent parameters was physically studied. It was found that the solutions were general, reliable, realistic and fixable. For the fractional parameter, the velocity and temperature profiles showed a decreasing trend for a constant time. By setting the values of the fractional parameter, excellent agreement between the theoretical and experimental results could be attained.

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Section: Thermophysical Properties Of Hybrid Nanofluidmentioning

confidence: 99%

Symmetric MHD Channel Flow of Nonlocal Fractional Model of BTF Containing Hybrid Nanoparticles

et al. 2020

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“…The model (6)(7)(8)(9)(10) has two equilibrium points [7], the DFE point and EE point. The DFE point is:…”

Section: Equilibrium Pointsmentioning

confidence: 99%

“…Mathematical modeling has a prominent role in describing physical phenomena in various disciplines of mathematics, physical sciences, social sciences, engineering, life sciences, and many more [1][2][3][4][5][6]. The transmission of infectious diseases and the control of their spread can be studied effectively by constructing mathematical models for various strategies like vaccination and quarantine.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model

et al. 2020

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In this paper, two structure-preserving nonstandard finite difference (NSFD) operator splitting schemes are designed for the solution of reaction diffusion epidemic models. The proposed schemes preserve all the essential properties possessed by the continuous systems. These schemes are applied on a diffusive SEIQV epidemic model with a saturated incidence rate to validate the results. Furthermore, the stability of the continuous system is proved, and the bifurcation value is evaluated. A comparison is also made with the existing operator splitting numerical scheme. Simulations are also performed for numerical experiments.

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“…On the other hand, Sathish Kumar et al [12] investigated the effect of nonlinear thermal radiation on unsteady MHD flow between parallel plates. Saqib et al [13] used the Laplace transform technique to obtain exact solutions for natural convection flow model of a hybrid nanofluid in two vertical infinite parallel plates. Other recent studies [14][15][16] on the effects of various thermophysical parameters on the boundary layer flow of nanoparticles have also been reported.…”

Section: Introductionmentioning

confidence: 99%

Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids

Kebede

Haile

Awgichew

et al. 2020

Journal of Applied Mathematics

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In this paper, analytic approximation to the heat and mass transfer characteristics of a two-dimensional time-dependent flow of Williamson nanofluids over a permeable stretching sheet embedded in a porous medium has been presented by considering the effects of magnetic field, thermal radiation, and chemical reaction. The governing partial differential equations along with the boundary conditions were reduced to dimensionless forms by using suitable similarity transformation. The resulting system of ordinary differential equations with the corresponding boundary conditions was solved via the homotopy analysis method. The results of the study show that velocity, temperature, and concentration boundary layer thicknesses generally decrease as we move away from the surface of the stretching sheet and the Williamson parameter was found to retard the velocity but it enhances the temperature and concentration profiles near the surface. It was also found that increasing magnetic field strength, thermal radiation, or rate of chemical reaction speeds up the mass transfer but slows down the heat transfer rates in the boundary layer. The results of this study were compared with some previously published works under some restrictions, and they are found in excellent agreement.

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Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms

Cited by 86 publications

References 36 publications

Symmetric MHD Channel Flow of Nonlocal Fractional Model of BTF Containing Hybrid Nanoparticles

Symmetric MHD Channel Flow of Nonlocal Fractional Model of BTF Containing Hybrid Nanoparticles

Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model

Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids

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