Entropy optimization in CNTs based nanomaterial flow induced by rotating disks: A study on the accuracy of statistical declaration and probable error

Present model analyze the flow and heat transfer of water-based carbon nanotubes (CNTs) [Formula: see text] ferrofluid flow between two radially stretchable rotating disks in the presence of a uniform magnetic field. A study for entropy generation analysis is carried out to measure the irreversibility of the system. Using similarity transformation, the governing equations in the model are transformed into a set of nonlinear coupled differential equations in non-dimensional form. The nonlinear coupled differential equations are solved numerically through the finite element method. Variable viscosity, variable thermal conductivity, thermal radiation, and volume concentration have a crucial role in heat transfer enhancement. The results for the entropy generation rate, velocity distributions, and temperature distribution are graphically presented in the presence of physical and geometrical parameters of the flow. Increasing the values of ferromagnetic interaction number, Reynolds number, and temperature-dependent viscosity enhances the skin friction coefficients on the surface and wall of the lower disk. The local heat transfer rate near the lower disk is reduced in the presence of Harman number, Reynolds number, and Prandtl number. The ferrohydrodynamic flow between two rotating disks might be useful to optimize the use of hybrid nanofluid for liquid seals in rotating machinery.

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Entropy Optimization in Nonlinear Mixed Convective Flow of Nanomaterials Through Porous Space

Journal of Non-Equilibrium Thermodynamics ◽

10.1515/jnet-2019-0048 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Tasawar Hayat ◽

Ikram Ullah ◽

Ahmad Alsaedi ◽

Shaher Momani

Keyword(s):

Convective Flow ◽

Second Law Of Thermodynamics ◽

Second Law ◽

Porous Space ◽

Arrhenius Activation Energy ◽

Suction Parameter ◽

Electrically Conducting ◽

Entropy Optimization ◽

Dimensionless Variables ◽

Mixed Convective Flow

Abstract Our intention in this article is to investigate entropy optimization in nonlinear mixed convective unsteady magnetohydrodynamic flow of nanomaterials in porous space. An exponentially stretched sheet creates the liquid flow. Nanomaterial is considered electrically conducting. The concentration and energy expressions comprise viscous dissipation, Joule heating, thermophoresis and Brownian motion aspects. Arrhenius activation energy is considered. Computation of entropy generation based upon the second law of thermodynamics is made. Nonlinear partial expressions are obtained via suitable dimensionless variables. Resultant expressions are tackled by the OHAM technique. Features of numerous variables on entropy, temperature, velocity and concentration are graphically visualized. Skin friction and the temperature gradient at the surface are also elaborated. Comparative analysis is deliberated in tabulated form to validate the previously published outcomes. Velocity is reduced significantly via the suction parameter. The entropy rate increases for higher values of Brinkman, Biot and Hartmann numbers.

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QMC integration errors and quasi-asymptotics

Monte Carlo Methods and Applications ◽

10.1515/mcma-2020-2067 ◽

2020 ◽

Vol 26 (3) ◽

pp. 171-176

Author(s):

Ilya M. Sobol ◽

Boris V. Shukhman

Keyword(s):

Monte Carlo ◽

Error Estimate ◽

Numerical Experiments ◽

Probable Error ◽

Quasi Monte Carlo ◽

Integration Error ◽

Asymptotic Error ◽

Dimensional Cube ◽

Integration Errors ◽

Mc Method

AbstractA crude Monte Carlo (MC) method allows to calculate integrals over a d-dimensional cube. As the number N of integration nodes becomes large, the rate of probable error of the MC method decreases as {O(1/\sqrt{N})}. The use of quasi-random points instead of random points in the MC algorithm converts it to the quasi-Monte Carlo (QMC) method. The asymptotic error estimate of QMC integration of d-dimensional functions contains a multiplier {1/N}. However, the multiplier {(\ln N)^{d}} is also a part of the error estimate, which makes it virtually useless. We have proved that, in the general case, the QMC error estimate is not limited to the factor {1/N}. However, our numerical experiments show that using quasi-random points of Sobol sequences with {N=2^{m}} with natural m makes the integration error approximately proportional to {1/N}. In our numerical experiments, {d\leq 15}, and we used {N\leq 2^{40}} points generated by the SOBOLSEQ16384 code published in 2011. In this code, {d\leq 2^{14}} and {N\leq 2^{63}}.

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