<scp>CVFEM</scp> based numerical investigation and mathematical modeling of surface dependent magnetized <scp>copper‐oxide</scp> nanofluid flow using new model of porous space

Sheikholeslami, M.; Khan, M. Ijaz; Chu, Yu‐Ming; Kadry, Seifedine; Khan, Waqar Azeem

doi:10.1002/num.22592

Cited by 11 publications

(4 citation statements)

References 37 publications

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“…The governing equations are manipulated through Method of Lines (MOL) which can covert the PDE into a system of ODEs. Then the resulting system of ODEs are solved efficiently using the Runge-Kutta method of order four (RK4) [21][22][23][24][25][26][27][28][29][30][31][32]. For spatial discretization, the finite difference scheme of 6th (seven-point) and 8th (nine-point) order accurate is employed to solve the PDEs of proposed model but graphs are presented only for 8th order scheme.…”

Section: The Numerical Solutions and Discussionmentioning

confidence: 99%

Numerical investigation of oxygen transport in the retinal artery with higher order accuracy by using seven and nine point finite difference technique: a comparative study

Riaz¹,

Hamid²,

Khan³

et al. 2021

Phys. Scr.

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The model explains the special distribution of oxygen pressure, typically normal breathing pressure with time-dependent diffusion including depletion of oxygen by normal metabolism. The model considered here has four sections described as the inner retina, the outer retina, the fluid layer, and the choriocapillaris. The oxygen transportation is considered through these four layers with metabolism in each layer that consumes oxygen. For the numerical investigation of the diffusion model, the method of lines (MOL) with Runge–Kutta (RK4) method is implemented. For the spatial derivatives, the different 6th (seven-point) and 8th order (nine-point) finite difference schemes are used to achieve higher accuracy. Three various models are thoroughly focused in the study. The normal metabolism rate of oxygen through each layer is found in the first case while abnormal rate is predicted in the second case and in third case; the vision loss due to extensive stage of hypoxia is observed. The key finding of the study comes in terms of getting higher accuracy by seven-point and nine-point formula as compared to five-point formula. All the major results are tabulated and sketched diagrammatically.

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Section: The Numerical Solutions and Discussionmentioning

confidence: 99%

Numerical investigation of oxygen transport in the retinal artery with higher order accuracy by using seven and nine point finite difference technique: a comparative study

Riaz¹,

Hamid²,

Khan³

et al. 2021

Phys. Scr.

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show abstract

“…The mathematical model represented by the equations ( 2), ( 4) and (10) are in terms of nonlinear partial differential equations. Thus, to obtain the analytical solution is quite challenging.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Sharma et al 9 scrutinized the worth of Soret and Dufour impacts on the flow of natural convective nanofluid via a stretched sheet assuming the inclined magnetic field. Moreover, Sheikholeslami et al 10 observed that the convection mode of nanofluid is strongly affected by the nanoparticle's shapes. Ma et al 11 examined that by enhancing the width of the baffle the average values of Nusselt numbers can be improved.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of heat absorbing and radiative hydromagnetic nanofluids through a stretching surface with chemical reaction and viscous dissipation

Hussain

Mishra²,

Seth

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part E:

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The hydromagnetic dissipative, heat-absorbing, chemically reactive and optically thick radiative flow of nanofluid over a stretchable surface together with heat and mass transport phenomena is investigated. The prevailing partial differential equations (PDE) of the mathematical model are changed by incorporating apt similarity variables in the form of nonlinear similarity equations. Further, these similarity equations are solved numerically utilizing the Runge-Kutta Fehlberg technique in conjunction with the shooting method. For the numerical explorations, three kinds of nanofluids are prepared by disseminating very fine nanoparticles of titanium oxide (TiO2), aluminium oxide (Al2O3) and copper (Cu) into water. The significance of numerous regulatory flow parameters on the nanofluid velocity, nanofluid temperature, local Nusselt number, species concentration, wall velocity gradient and mass flow rates are examined through different graphical results. Additionally, a quadratic regression approximation analysis is accomplished to analyze the connection between the heat transport rate and regulatory flow parameters. The numerical results reveal that the temperature of Cu-water based nanofluid temperature gets enhanced owing to improvement in the strength of radiation, viscous dissipation and magnetic effects. Further, regression approximation analysis unveils that a slight change in the velocity slip parameter leads in the optimal perturbation in both the shear stress values and heat transfer rate at the stretchable surface. Finally, the validation of numerical results and the developed algorithm of employed computational technique have been done by making a comparison of computed results with the available results under restricted situations.

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“…Prasad et al [15] studied the variation in viscosity on MHD flow on stretching surfaces. Various studies are carried on dusty nanofluids which can be seen in literature [16][17][18][19][20][21]. Sheikholeslami et al [22] studied the heat transfer and physical properties of nanofluids.…”

Section: : Introductionmentioning

confidence: 99%

Dynamics of Marangoni Convection in Hybrid Nanomaterials Flow With Dust Particles Random Motion

Khan¹

2021

Preprint

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Here we are working on the flow of dust particles in hybrid nanofluid. Marangoni convective flow of hybrid nanofluid is accounted by considering silver and copper as nanoparticles and water as base fluid. Dust particles and nanoparticles are used in this flow are spherical type. For thermal conductivity we have considered the Maxwell model. Porous medium is placed over a stretching sheet. Flow is generated via stretching sheet. MHD effects are also considered. Nonlinear equation of fluid phase and dust phase are converted in to ODE's by suitable transformations. These ordinary differential equations are solved numerically. Effect of involved dimensionless variables against velocity and temperature of hybrid nanofluid and dust phase, skin friction and Nusselt number of hybrid nanofluid is studied through graphs and tables. It is observed that temperature and velocity is more in case of hybrid nanofluid as compared to dust phase. Velocity of Ag-Cu water hybrid nanofluid enhances for greater mass concentration of dust particles. Velocity in both phase decay for higher porosity variable. Good match of results are seen by comparing current situation to earlier study in particular case.

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CVFEM based numerical investigation and mathematical modeling of surface dependent magnetized copper‐oxide nanofluid flow using new model of porous space

Cited by 11 publications

References 37 publications

Numerical investigation of oxygen transport in the retinal artery with higher order accuracy by using seven and nine point finite difference technique: a comparative study

Numerical investigation of oxygen transport in the retinal artery with higher order accuracy by using seven and nine point finite difference technique: a comparative study

Dynamics of heat absorbing and radiative hydromagnetic nanofluids through a stretching surface with chemical reaction and viscous dissipation

Dynamics of Marangoni Convection in Hybrid Nanomaterials Flow With Dust Particles Random Motion

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