The Heat Equation, Semigroups, and Brownian Motion

The essence of the present investigation is to reveal the hydrothermal variations of viscoelastic nanofluid flow in a porous medium over a stretchable surface. A higher-order chemical reaction is incorporated with thermophoresis and Brownian motion. Similarity conversions reduce the resulting equations into their dimensionless form and then solved using Runge-Kutta-Fehlberg (RKF) based shooting procedure. The effects of underlying factors on the flow are discussed through various graphs and tables. Computational results for noteworthy skin friction and heat and mass transport are presented and reviewed with sensible judgment. The study reveals that the fluid velocity reduces with incremental values of the viscoelastic parameter [Formula: see text] and magnetic strength. The temperature reduces for the suction parameter with the existence of stretchable but enhances with thermophoresis and Brownian motion effects. Heat transfer rate amplifies for [Formula: see text] but declines for [Formula: see text]. Mass transfer rate increases with the increase in Brownian parameter and Schmidt number. A comparative analysis shows a better agreement with previous results in limiting scenarios.

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Magneto convective flow of casson nanofluid due to Stefan blowing in the presence of bio-active mixers

Proceedings of the Institution of Mechanical Engineers Part N Journal of Nanomaterials Nanoengineering and Nanosystems ◽

10.1177/23977914211016692 ◽

2021 ◽

pp. 239779142110166

Author(s):

Venkatesh Puneeth ◽

Sarpabhushana Manjunatha ◽

Bijjanal Jayanna Gireesha ◽

Rama Subba Reddy Gorla

Keyword(s):

Magnetic Field ◽

Brownian Motion ◽

Convective Flow ◽

Three Dimensional ◽

Induced Magnetic Field ◽

Density Profiles ◽

Casson Nanofluid ◽

And Brownian Motion ◽

Similarity Transformations ◽

The Mathematical Model

The induced magnetic field for three-dimensional bio-convective flow of Casson nanofluid containing gyrotactic microorganisms along a vertical stretching sheet is investigated. The movement of these microorganisms cause bioconvection and they act as bio-active mixers that help in stabilising the nanoparticles in the suspension. The two forces, Thermophoresis and Brownian motion are incorporated in the Mathematical model along with Stefan blowing. The resulting model is transformed to ordinary differential equations using similarity transformations and are solved using [Formula: see text] method. The Velocity, Induced Magnetic field, Temperature, Concentration of Nanoparticles, and Motile density profiles are interpreted graphically. It is observed that the Casson parameter decreases the flow velocity and enhances the temperature, concentration, and motile density profiles and also it is noticed that the blowing enhances the nanofluid profiles whereas, suction diminishes the nanofluid profiles. On the other hand, it is perceived that the rate of heat conduction is enhanced with Thermophoresis and Brownian motion.

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Nanofluids Flow Between Two Rotating Cylinders: Effects of Thermophoresis and Brownian Motion

Journal of Thermophysics and Heat Transfer ◽

10.2514/1.t4122 ◽

2013 ◽

Vol 27 (4) ◽

pp. 748-755 ◽

Cited By ~ 4

Author(s):

Meisam Habibi Matin ◽

Omid Mahian ◽

Somchai Wongwises

Keyword(s):

Brownian Motion ◽

Rotating Cylinders ◽

And Brownian Motion

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Continuous Martingales and Brownian Motion

The Mathematical Gazette ◽

10.2307/3618671 ◽

1991 ◽

Vol 75 (474) ◽

pp. 498

Author(s):

J. R. Norris ◽

D. Revuz ◽

M. Yor

Keyword(s):

Brownian Motion ◽

And Brownian Motion

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Geodesic Random Walks, Diffusion Processes and Brownian Motion on Finsler Manifolds

Journal of Geometric Analysis ◽

10.1007/s12220-021-00723-z ◽

2021 ◽

Author(s):

Tianyu Ma ◽

Vladimir S. Matveev ◽

Ilya Pavlyukevich

Keyword(s):

Brownian Motion ◽

Diffusion Process ◽

Random Walks ◽

Diffusion Processes ◽

Riemannian Metric ◽

Finsler Manifold ◽

Finsler Manifolds ◽

Bounded Geometry ◽

And Brownian Motion

AbstractWe show that geodesic random walks on a complete Finsler manifold of bounded geometry converge to a diffusion process which is, up to a drift, the Brownian motion corresponding to a Riemannian metric.

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