Effect of fractional derivatives on transient MHD flow and radiative heat transfer in a micro-parallel channel at high zeta potentials

Abdulhameed, Mohammed; Muhammad, Masdi; Gital, Abdulsalam Ya’u; Yakubu, D. G.; Khan, Ilyas

doi:10.1016/j.physa.2018.12.019

Cited by 25 publications

(6 citation statements)

References 29 publications

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“…Chakraborty and Paul [16] analyzed the MHD EOF in narrow microchannels and obtained optimized flow rates. Driven by combination of electroosmotic, pressure and magnetic forces, unsteady MHD EOF of incompressible viscous fluid through a circular tube was developed with the Caputo Fabrizio time fractional derivative by Abdulhameed et al [17] Chakraborty et al [18] analyzed thermal behavior of MHD EOF in narrow channels taking viscous dissipation and Joule heating into account under constant wall heat flux. Abdulhameed et al [19] investigated the MHD EOF flow acted by an arbitrary time-dependent pressure gradient, electric field force and Lorentz force and heat transfer through a cylindrical microchannel.…”

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic Electroosmotic Flow with Patterned Charged Surface and Modulated Wettability in a Parallel Plate Microchannel*

Hao¹,

Jian²

2019

Commun. Theor. Phys.

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This paper investigates the magnetohydrodynamic (MHD) electroosmotic flow (EOF) of Newtonian fluid through a zeta potential modulated parallel plate microchannel with patterned hydrodynamic slippage. The driven mechanism of the flow originates from the Lorentz force generated by the interaction of externally imposed lateral electric field Ey and vertical magnetic field Bz and electric field force produced by an externally applied electric field Ex . It is assumed that the wall zeta potential and the slip length are periodic functions of axial coordinate x, an analytical solution of the stream function is achieved by utilizing the method of separation of variables and perturbation expansion. The pictures of streamlines are plotted and the vortex configurations produced in flow field due to patterned wall potential and hydrodynamic slippage are discussed. Based on the stream function, the velocity field and volume flow rate are obtained, which are greatly depend on some dimensionless parameters, such as slip length ls , electrokinetic width λ, the amplitude δ of the patterned slip length, the amplitude m of the modulated zeta potential and Hartmann number Ha. The variations of velocity and volume flow rate with these dimensionless parameters are discussed in details. These theoretical results may provide some guidance effectively operating micropump in practical nanofluidic applications.

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Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic Electroosmotic Flow with Patterned Charged Surface and Modulated Wettability in a Parallel Plate Microchannel*

Hao¹,

Jian²

2019

Commun. Theor. Phys.

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“…FC has taken advanteges and popularity of modelling with memory effects [11] , [12] , [13] , [14] . Further, FC and mathematical modelling are applicable in many areas of science, biology and engineering for details see, [15] , [16] , [17] , [18] , [19] , [20] . The current work will investigate the system (3) in the form of system (3) for fractional order analysis under Caputo fractional operator.…”

Section: Introductionmentioning

confidence: 99%

On the analysis of Caputo fractional order dynamics of Middle East Lungs Coronavirus (MERS-CoV) model

Ain

Anjum

Din

et al. 2022

Alexandria Engineering Journal

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“…Because of this advantage, the fractional calculus has taken on the importance and popularity of modeling realistic cases, especially those with memory effects [ 21 – 23 ]. Furthermore, applications of the fractional calculus and mathematical modeling are found in many fields of social sciences, engineering, and mathematical biology [ 24 – 32 ]. Given this importance, we feel inspired to investigate and examine a new fractional version of the model involving Caputo operator.…”

Section: Introductionmentioning

confidence: 99%

Caputo SIR model for COVID-19 under optimized fractional order

Alshomrani¹,

Ullah²,

Băleanu

2021

Adv Differ Equ

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Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Having seen such a drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. The major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 1 April to 15 March 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam–Hyers and its generalized version. The best parameters have been obtained via the nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than the classical version of the SIR model (Brauer et al. in Mathematical Models in Epidemiology 2019). Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case ($\nu =1$ ν = 1 ). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.

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Effect of fractional derivatives on transient MHD flow and radiative heat transfer in a micro-parallel channel at high zeta potentials

Cited by 25 publications

References 29 publications

Magnetohydrodynamic Electroosmotic Flow with Patterned Charged Surface and Modulated Wettability in a Parallel Plate Microchannel*

Magnetohydrodynamic Electroosmotic Flow with Patterned Charged Surface and Modulated Wettability in a Parallel Plate Microchannel*

On the analysis of Caputo fractional order dynamics of Middle East Lungs Coronavirus (MERS-CoV) model

Caputo SIR model for COVID-19 under optimized fractional order

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