Continuum flow model of MHD Casson nanofluid over a rotating disk with multiple slips by Khuram Rafique, Aisha M. Alqahtani, Ayesha Rehman, Najla A. Mohammed, Ilyas Khan

“…The present study articulates the various features of Casson nanofluid flow over a rotating disk along Brownian motion and thermophoresis effects. In addition the influences of thermal radiations along with Sore effect are taken in to account. …”
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Analytic Simulation for Magnetohydrodynamic Unsteady Buongiorno Model Hybrid Nanofluid Flow over Stretching by Muhammad Jawad, Salah Boulaaras, Niaz Ali Shah, Rashid Jan, Sulima Ahmed Zubair

“…Hybrid nanofluid (Al2O3-Cu/H2O) flows with magnetohydrodynamic and heat source or sink. Brownian motion and thermophoresis were incorporated using the Buongiorno model. …”
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Artificial neural network analysis of Jeffrey hybrid nanofluid with gyrotactic microorganisms for optimizing solar thermal collector efficiency by Anup Kumar, Bhupendra K. Sharma, Bandar Almohsen, Laura M. Pérez, Kamil Urbanowicz

“…The mechanism of thermophoresis and Brownian motion for the graphene and silver nanoparticles are also encountered in the suspension of water-based heat transfer fluid. …”
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Large N limit of the Yang–Mills measure on compact surfaces II: Makeenko–Migdal equations and the planar master field by Antoine Dahlqvist, Thibaut Lemoine

“…Our result on the torus justifies the introduction of an interpolation between free and classical convolution of probability measures, defined with the free unitary Brownian motion but differing from t-freeness of [5] that was defined in terms of the liberation process of Voiculescu [67]. …”
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Thermo-Magneto-Solutal Squeezing Flow of Nanofluid between Two Parallel Disks Embedded in a Porous Medium: Effects of Nanoparticle Geometry, Slip and Temperature Jump Conditions by M. G. Sobamowo, A. T. Akinshilo, A. A. Yinusa

“…Through the approximate analytical solutions, parametric studies are carried out to investigate the effects of nanoparticle size and shape, Brownian motion parameter, nanoparticle parameter, thermophoresis parameter, Hartmann number, Lewis number and pressure gradient parameters, slip, and temperature jump boundary conditions on thermo-solutal and hydromagnetic behavior of the nanofluid. …”
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MHD Williamson Nanofluid Flow over a Stretching Sheet through a Porous Medium under Effects of Joule Heating, Nonlinear Thermal Radiation, Heat Generation/Absorption, and Chemical... by J. Bouslimi, M. Omri, R. A. Mohamed, K. H. Mahmoud, S. M. Abo-Dahab, M. S. Soliman

“…On the other hand, the effect of Brownian motion and thermophoresis coefficients was considered. …”
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Construction of optimised theoretical model using ANOVA -Taguchi methodology for transient flow of Carreau nanofluid through microchannel prone to radiation by Pradeep Kumar, Felicita Almeida, Ajaykumar AR, Qasem Al-Mdallal

“…Buongiorno model is employed, which emphasizes the repercussions of Brownian motion and thermophoresis phenomena; also, mixed-convective flow is accounted. …”
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MOVIMENTO BROWNIANO: APLICAÇÃO EM ESTRATÉGIAS DE BUSCA by Matheus Dias Carvalho, Ricardo de Carvalho Falcão, Antonio Marcos de Oliveira Siqueira

“… This article has elucidated information about Brownian Motion in the ring, something that is still little explored in the literature. …”
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Influence of dual stratification on the magnetohydrodynamic flow of Jeffrey nanofluid over an exponentially stretching permeable sheet with viscous dissipation and Joule heating by M. Siva Sankari, M. Eswara Rao, Fuad A. Awwad, Emad A. A. Ismail, O. D. Makinde, Waris Khan

“…The study includes transference equations that consider the influences of thermophoresis and Brownian motion on particle deposition. The analysis examines the impact of a nanofluid through a porous, exponentially elongating sheet, focusing on the double-stratification effects on heat and mass transference. …”
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The non-Fourier–Fick’s heat and mass flux effect in a bioconvective nanofluid flow over a stretching cylinder with suction/injection and convective conditions by Endale Ersino Bafe, Mitiku Daba Firdi, Lemi Guta Enyadene

“…The analysis includes the effects of non-Fourier and non-Fick fluxes, suction/injection, convective heat and mass transfer, and motile microorganisms under mixed convection, nonlinear thermal radiation, porosity, Ohmic dissipation, chemical reactions with Arrhenius activation energy, and Brownian motion. The governing equations are transformed into nonlinear ODEs and solved using a spectral local linearization method. …”
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Dissipative disorder analysis of Homann flow of Walters B fluid with the applications of solar thermal energy absorption aspects by Latif Ahmad, Assmaa Abd-Elmonem, Saleem Javed, Muhammad Yasir, Umair Khan, Yalcin Yilmaz, Aisha M. Alqahtani

“…The flow with heat and mass balance aspects are further characterize with the inclusion of thermophoretic and Brownian motion factors. The flow configuration is interpreted in terms of gravitationally affected vertical cylindrical disk, for a better understanding of the impact of irreversible processes, more physical effects in terms of heating source/sink, chemical reaction and solar thermal radiation. …”
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Ciliary peristalsis flow of hydromagnetic Sutterby nanofluid through symmetric channel: Viscous dissipation in case of variable electrical conductivity by Sameh A. Hussein, Sameh E. Ahmed, Anas A.M. Arafa

“…Buongiorno’s nanofluid approach, that involves Brownian motion and thermophoresis aspects is considered. …”
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Numerical investigation of heat and mass transfer for unsteady multiphase flow in a vented cavity filled with hybrid nanofluid by Muhammad Ashhad Shahid, Mojtaba Dayer, Muhammad Adil Sadiq, Haris Ali, Ishak Hashim

“…The investigation employs a novel dimensionless mathematical model to explore these dynamics using Buongiorno’s approach, which considers Brownian motion and thermophoresis in nanofluids. Numerical simulations are conducted utilizing the Finite Element Method (FEM) to discretize the dimensionless governing equations. …”
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Solving the Black–Scholes European options model using the reduced differential transform method with powered modified log-payoff function by S.E. Fadugba, A.M. Udoye, S.C. Zelibe, S.O. Edeki, C. Achudume, A.A. Adeyanju, O. Makinde, P.A. Bankole, M.C. Kekana

“…Importantly, this model operates under the assumption that assets follow geometric Brownian motion and do not yield dividends. The findings from this study highlight the potential of RDTM as a powerful tool in the realm of financial mathematics, offering substantial improvements in the computational efficiency and accuracy of option pricing models.…”
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A comprehensive numerical study exploring the significance of thermally reactive bioconvection in Falkner-Skan flow of Williamson nanomaterials influenced by activation energy and... by M. Israr Ur Rehman, Haibo Chen, Aamir Hamid, Wu Qian, Refka Ghodhbani, Mohamed Hussien

“…The analysis is further improved by adding thermophoretic diffusion and Brownian motion to the energy and concentration equations Bio-fuels, enzymes, industry, bio-sensors, petroleum, and a number of other novel biotechnological features are also influenced by the bioconvective mechanisms in nanomaterials. …”
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Analytical simulations for rate type nanomaterial stretching flow with dual convection by Manzoor Ahmad, Sami Ullah Khan, Syeda Quratulain, Adnan, M. Waqas, Hakim AL Garalleh, Nurnadiah Zamri, Dilsora Abduvalieva, Manish Gupta

“…The heat and mass transfer analysis is predicted with insight of Brownian motion and thermophoresis phenomenon. The flow is subject to bidirectional surface maintaining the uniform velocity. …”
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MHD flow of Williamson nanofluid using effective similarity variable considering viscous dissipation and thermal radiation over a non-linear stretching surface via OHAM by Muhammad Awais Sherani, Muhammad Sohail, Ibrahim Mahariq, Syed Tehseen Abbas

“…Concentration diminishes with the augmentation of Sc, Cr, and Nbt due to intensified Brownian motion and molecular interactions. It is observed that λ and M increase the value of skin friction, but −θ'(0), indicating heat transfer efficiency, increases with Pr, Le, and Nbt but declines with Rd and Nc. …”
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The 𝑀-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey by Francesco Mainardi, Antonio Mura, Gianni Pagnini

“…When these generalized diffusion processes are properly characterized with stationary increments, the 𝑀-Wright function is shown to play the same key role as the Gaussian density in the standard and fractional Brownian motions. Furthermore, these processes provide stochastic models suitable for describing phenomena of anomalous diffusion of both slow and fast types.…”
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Stochastic Neutron Population with Temperature Feedback Effects Using the Implicit Runge-Kutta Scheme by Daniel Suescún-Díaz

“…These equations are solved through the implicit Runge-Kutta scheme of order 1.5 with up to 500 Brownian motions. The computational cost can be reduced by using the analytical expression of the square root of the covariance matrix. …”
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