Two‐phase fluid motion through porous medium with volume fraction: An application of MATLAB bvp4c solver technique

Dey, Debasish; Chutia, Barbie

doi:10.1002/htj.22374

Cited by 9 publications

(5 citation statements)

References 11 publications

(12 reference statements)

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“…The first solution is comparatively easy to find within a CPU time of 20 s, however, for the second solution, it is very difficult to get a little more time i.e., 40 s. The detailed procedure of the scheme was given in the book of Shampine et al 64 as well as in many other published works of literature (see Refs. 65 – 67 ). For verification of our scheme, the values of gradients of the upper branch solutions for different values of are matched with the available published work of Grosan and Pop 68 for the limiting case when , and .…”

Section: Introductionmentioning

confidence: 99%

Heat transfer analysis of buoyancy opposing radiated flow of alumina nanoparticles scattered in water-based fluid past a vertical cylinder

Alharbi

Khan

Zaib

et al. 2023

Sci Rep

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Cooling and heating are two critical processes in the transportation and manufacturing industries. Fluid solutions containing metal nanoparticles have higher thermal conductivity than conventional fluids, allowing for more effective cooling. Thus, the current paper is a comparative exploration of the time-independent buoyancy opposing and heat transfer flow of alumina nanoparticles scattered in water as a regular fluid induced via a vertical cylinder with mutual effect of stagnation-point and radiation. Based on some reasonable assumptions, the model of nonlinear equations is developed and then tackled numerically employing the built-in bvp4c MATLAB solver. The impacts of assorted control parameters on gradients are investigated. The outcomes divulge that the aspect of friction factor and heat transport upsurge by incorporating alumina nanoparticles. The involvement of the radiation parameter shows an increasing tendency in the heat transfer rate, resulting in an enhancement in thermal flow efficacy. In addition, the temperature distribution uplifts due to radiation and curvature parameters. It is discerned that the branch of dual outcomes exists in the opposing flow case. Moreover, for higher values of the nanoparticle volume fraction, the reduced shear stress and the reduced heat transfer rate increased respectively by almost 1.30% and 0.0031% for the solution of the first branch, while nearly 1.24%, and 3.13% for the lower branch solution.

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Section: Introductionmentioning

confidence: 99%

Heat transfer analysis of buoyancy opposing radiated flow of alumina nanoparticles scattered in water-based fluid past a vertical cylinder

Alharbi

Khan

Zaib

et al. 2023

Sci Rep

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show abstract

“…(18) , (19) , (20) , (21) , (22) , (23) , (24) are solved numerically [ 5 , 9 ] by the command NDSolve by using the software Mathematica. In the meantime, many researchers used the bvp4c [ [51] , [52] , [53] ] solver available in the Matlab software to solve nonlinear ODEs. If the boundary error terms are below the tolerance error,

the calculation simulation will converge.…”

Section: Methodsmentioning

confidence: 99%

Numerical study for bioconvection peristaltic flow of Sisko nanofluid with Joule heating and thermal radiation

Nisar,

Ahmed,

Ghazwani

et al. 2023

Heliyon

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“…The solver also requests to control the error in the solution through the residuals in the boundary conditions, both for each subinterval and at the system boundaries. There are some rules for the specification of absolute error in the solutions and the relative error allowed to broadcast between iterations 28,29 . Besides this, we have considered here 100 initial mesh points, 0.001 for the relative error and 0.000001 for the absolute error.…”

Section: Numerical Methods and Validationmentioning

confidence: 99%

“…There are some rules for the specification of absolute error in the solutions and the relative error allowed to broadcast between iterations. 28,29 Besides this, we have considered here 100 initial mesh points, 0.001 for the relative error and 0.000001 for the absolute error. At the whole article, we have considered m = 100 g, f T = 298 K, and Pr = 6.2.…”

Section: Off-centered Stagnation Point Flow: Problem Schematic and Fo...mentioning

confidence: 99%

Zinc oxide–silver/water hybrid nanofluid flow toward an off‐centered rotating disk using temperature‐dependent experimental‐based thermal conductivity

et al. 2022

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Herein, the off‐centered stagnation flow and heat transfer of zinc oxide–silver/water hybrid nanofluid over a rotating disk according to the mass‐based algorithm is studied. It is assumed that the nanoparticles have a spherical shape. Also, the velocity slip between the base fluid and nanoparticles is negligible. The Prandtl number is kept constant at 6.2. In addition, it has been used an experimental relation for effective thermal conductivity which is a function of volume fraction and temperature. The governing partial differential equations are converted to dimensionless ordinary differential equation (ODE)s by the similarity transformation method. The simplified ODEs are solved numerically by the bvp4c function from MATLAB which is an efficient and reliable code according to the three‐stage Lobatto IIIa formula. The influence of rotational parameters and both nanoparticles masses on the profiles and quantities of engineering interest are presented and discussed in detail. It is shown that the flow becomes complicated when there is a distance between the flow axis and the disk axis. Under determined conditions for a hybrid nanofluid with 30‐g mass for both nanoparticles and 100‐g mass for pure water, adding 30 g of the second nanoparticle's mass into the base fluid leads to enhance all hydrodynamic quantities of engineering interest by about 4.3%, while dispersing 30 g of the first nanoparticle's mass inside water results in decreasing the similarity temperature gradient at the surface about 3.6%. Also, when the disk rotates faster, the maximum radial velocity near the disk, s′(0) and f″(0) increases.

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Two‐phase fluid motion through porous medium with volume fraction: An application of MATLAB bvp4c solver technique

Cited by 9 publications

References 11 publications

Heat transfer analysis of buoyancy opposing radiated flow of alumina nanoparticles scattered in water-based fluid past a vertical cylinder

Heat transfer analysis of buoyancy opposing radiated flow of alumina nanoparticles scattered in water-based fluid past a vertical cylinder

Numerical study for bioconvection peristaltic flow of Sisko nanofluid with Joule heating and thermal radiation

Zinc oxide–silver/water hybrid nanofluid flow toward an off‐centered rotating disk using temperature‐dependent experimental‐based thermal conductivity

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