Numerical investigation of heat and mass transfer flow under the influence of silicon carbide by means of plasma-enhanced chemical vapor deposition vertical reactor

Shirvan, Kamel Milani; Ellahi, R.; Sheikholeslami, Tahereh Fanaie; Behzadmehr, A.

doi:10.1007/s00521-017-2954-3

Cited by 10 publications

(3 citation statements)

References 28 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

“…Hameed et al [24] examined the fractional order second grade fluid peristaltic transport in a vertical cylinder. A variety of numerical techniques have been used to find solutions to the classical models [25][26][27][28][29][30], and these techniques have been further combined to find solutions for fractional order problems.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Forced Convection Carbon Nanotube Nanofluid Flow Passing Over a Thin Needle

et al. 2019

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In the fields of fluid dynamics and mechanical engineering, most nanofluids are generally not linear in character, and the fractional order model is the most suitable model for representing such phenomena rather than other traditional approaches. The forced convection fractional order boundary layer flow comprising single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs) with variable wall temperatures passing over a needle was examined. The numerical solutions for the similarity equations were obtained for the integer and fractional values by applying the Adams-type predictor corrector method. A comparison of the SWCNTs and MWCNTs for the classical and fractional schemes was investigated. The classical and fractional order impact of the physical parameters such as skin fraction and Nusselt number are presented physically and numerically. It was observed that the impact of the physical parameters over the momentum and thermal boundary layers in the classical model were limited; however, while utilizing the fractional model, the impact of the parameters varied at different intervals.

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“…Sheikholeslami and Ganji [21] examined the Cu-H 2 O nanofluid flow under the impact of Marangoni convection. The numerical approach to find the solution of a different type of problem was previously discussed [22][23][24][25][26][27]. The numerical scheme of Runge Kutta method of order 4 (RK-4) was used in their study to determine the impact of the physical parameters and numerical outputs.…”

Section: Introductionmentioning

confidence: 99%

Integer and Non-Integer Order Study of the GO-W/GO-EG Nanofluids Flow by Means of Marangoni Convection

et al. 2019

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Characteristically, most fluids are not linear in their natural deeds and therefore fractional order models are very appropriate to handle these kinds of marvels. In this article, we studied the base solvents of water and ethylene glycol for the stable dispersion of graphene oxide to prepare graphene oxide-water (GO-W) and graphene oxide-ethylene glycol (GO-EG) nanofluids. The stable dispersion of the graphene oxide in the water and ethylene glycol was taken from the experimental results. The combined efforts of the classical and fractional order models were imposed and compared under the effect of the Marangoni convection. The numerical method for the non-integer derivative that was used in this research is known as a predictor corrector technique of the Adams–Bashforth–Moulton method (Fractional Differential Equation-12) or shortly (FDE-12). The impact of the modeled parameters were analyzed and compared for both GO-W and GO-EG nanofluids. The diverse effects of the parameters were observed through a fractional model rather than the traditional approach. Furthermore, it was observed that GO-EG nanofluids are more efficient due to their high thermal properties compared with GO-W nanofluids.

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Numerical investigation of heat and mass transfer flow under the influence of silicon carbide by means of plasma-enhanced chemical vapor deposition vertical reactor

Cited by 10 publications

References 28 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

Fractional Order Forced Convection Carbon Nanotube Nanofluid Flow Passing Over a Thin Needle

Integer and Non-Integer Order Study of the GO-W/GO-EG Nanofluids Flow by Means of Marangoni Convection

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