Numerical Solutions of Micropolar Nanofluid over an Inclined Surface Using Keller Box Analysis

The Brownian motion and thermophoretic impacts attained a noticeable intention of the recent researchers because these factors trigger the thermal conductivity of the nanofluid. In this study, we focus on radiation and Soret effects on a slanted stretchable sheet. Buongiorno’s model is taken into account with Brownian motion and thermophoretic effects. Compatible transformations are implemented to attain the nonlinear differential equation from the boundary value PDE’s. The physical quantities of practical interest are treated by graphically as well as numerically. For numerical results, the Keller box technique is applied. The numerical outcomes through tabulated magnitudes performed a good settlement with already existing results. Energy transfer rate against involved factor exhibited via graphs. Energy and mass transport rates enhance against increment in Soret factor while skin friction diminishes. Moreover, Nusselt number and Sherwood number decrease on improving inclination while skin friction increases.

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Keller-Box Simulation for the Buongiorno Mathematical Model of Micropolar Nanofluid Flow over a Nonlinear Inclined Surface

Processes ◽

10.3390/pr7120926 ◽

2019 ◽

Vol 7 (12) ◽

pp. 926 ◽

Cited By ~ 1

Author(s):

Khuram Rafique ◽

Muhammad Imran Anwar ◽

Masnita Misiran ◽

Ilyas Khan ◽

Asiful H. Seikh ◽

...

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Similarity Transformations ◽

Flow Parameters ◽

Box Scheme ◽

Micropolar Nanofluid ◽

Brownian Motion And Thermophoresis ◽

Buongiorno Model ◽

Inclined Surface ◽

Physical Quantities

Brownian motion and thermophoresis diffusions are the fundamental ideas of abnormal upgrading in thermal conductivity via binary fluids (base fluid along with nanoparticles). The influence of Brownian motion and thermophoresis are focused on in the Buongiorno model. In this problem, we considered the Buongiorno model with Brownian motion and thermophoretic effects. The nonlinear ordinary differential equations are recovered from the partial differential equations of the boundary flow via compatible similarity transformations and then employed to the Keller-box scheme for numerical results. The physical quantities of our concern including skin friction, Nusselt number, and Sherwood number along with velocity, temperature and concentration profile against involved effects are demonstrated. The impacts of the involved flow parameters are drawn in graphs and tabulated forms. The inclination effect shows an inverse relation with the velocity field. Moreover, the velocity profile increases with the growth of the buoyancy effect.

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Numerical Analysis with Keller-Box Scheme for Stagnation Point Effect on Flow of Micropolar Nanofluid over an Inclined Surface

Symmetry ◽

10.3390/sym11111379 ◽

2019 ◽

Vol 11 (11) ◽

pp. 1379 ◽

Cited By ~ 4

Author(s):

Rafique ◽

Anwar ◽

Misiran ◽

Khan ◽

Seikh ◽

...

Keyword(s):

Differential Equations ◽

Skin Friction ◽

Stagnation Point ◽

Nonlinear Differential Equations ◽

Stagnation Region ◽

Similarity Transformations ◽

Box Scheme ◽

Mass Fluxes ◽

Micropolar Nanofluid ◽

Inclined Surface

The prime aim of this paper is to probe the flow of micropolar nanofluid towards an inclined stretching surface adjacent to the stagnation region with Brownian motion and thermophoretic impacts. The chemical reaction and heat generation or absorption are also taken into account. The energy and mass transport of the micropolar nanofluid flow towards an inclined surface are discussed. The numerical solution is elucidated for the converted non-linear ordinary differential equation from the set of partial nonlinear differential equations via compatible similarity transformations. A converted system of ordinary differential equations is solved via the Keller-box scheme. The stretching velocity and external velocity are supposed to change linearly by the distance from the stagnation point. The impacts of involved parameters on the concerned physical quantities such as skin friction, Sherwood number, and energy exchange are discussed. These results are drawn through the graphs and presented in the tables. The energy and mass exchange rates show a direct relation with the stagnation point. In the same vein, skin friction diminishes with the growth of the stagnation factor. Heat and mass fluxes show an inverse correspondence with the inclination factor.

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Unsteady forced bioconvection slip flow of a micropolar nanofluid from a stretching/shrinking sheet

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

10.1177/1740349915613817 ◽

2016 ◽

Vol 230 (4) ◽

pp. 177-187 ◽

Cited By ~ 9

Author(s):

Nur Amalina Abdul Latiff ◽

Md Jashim Uddin ◽

O Anwar Bég ◽

Ahmad Izani Ismail

Keyword(s):

Skin Friction ◽

Microbial Fuel Cells ◽

Transfer Rate ◽

Volume Fraction ◽

Slip Flow ◽

Velocity Slip ◽

Shrinking Sheet ◽

Local Skin ◽

Linear Ordinary Differential Equations ◽

Micropolar Nanofluid

The unsteady forced bioconvection boundary layer flow of a viscous incompressible micropolar nanofluid containing microorganisms over a stretching/shrinking sheet is studied numerically. A mathematical model, with the aid of appropriate transformations, is presented. The transformed non-linear ordinary differential equations are solved numerically by the Runge–Kutta–Fehlberg fourth- to fifth-order numerical method. The effect of the governing parameters on the dimensionless velocity, micro-rotation, temperature, nanoparticle volume fraction and microorganism as well as the local skin friction coefficient, the heat transfer rate and microorganisms transfer rate is thoroughly examined. The findings show that the value of skin friction and Nusselt number are decreased and microorganism number is increased as velocity slip, thermal slip and microorganism slip parameter are increased, respectively. Results from this investigation were compared with previous investigations demonstrating very good correlation. The present results are relevant to improving the performance of microbial fuel cells deploying nanofluids.

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Brownian Motion and Thermophoretic Diffusion Effects on Micropolar Type Nanofluid Flow with Soret and Dufour Impacts over an Inclined Sheet: Keller-Box Simulations

Energies ◽

10.3390/en12214191 ◽

2019 ◽

Vol 12 (21) ◽

pp. 4191 ◽

Cited By ~ 5

Author(s):

Khuram Rafique ◽

Muhammad Imran Anwar ◽

Masnita Misiran ◽

Ilyas Khan ◽

Asiful H. Seikh ◽

...

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Soret Effect ◽

Nanofluid Flow ◽

Soret And Dufour Effects ◽

Similarity Transformations ◽

Stretching Factor ◽

Micropolar Nanofluid ◽

Nonlinear Stretching ◽

Physical Quantities

The principal objective of the current study is to analyze the Brownian motion and thermophoretic impacts on micropolar nanofluid flow over a nonlinear inclined stretching sheet taking into account the Soret and Dufour effects. The compatible similarity transformations are applied to obtain the nonlinear ordinary differential equations from the partial differential equations. The numerical solution of the present study obtained via the Keller-Box technique. The physical quantities of interest are skin friction, Sherwood number, and heat exchange, along with several influences of material parameters on the momentum, temperature, and concentration are elucidated and clarified with diagrams. A decent settlement can be established in the current results with previously published work in the deficiency of incorporating effects. It is found that the growth of the inclination and nonlinear stretching factor decreases the velocity profile. Moreover, the growth of the Soret effect reduces the heat flux rate and wall shear stress.

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Computational Study of Scission Neutrons in Low-Energy Fission: Stationary and Time-Dependent Approaches

Communications in Computational Physics ◽

10.4208/cicp.040210.270810a ◽

2011 ◽

Vol 9 (4) ◽

pp. 917-936 ◽

Cited By ~ 6

Author(s):

M. Rizea ◽

N. Carjan

Keyword(s):

Eigenvalue Problems ◽

Numerical Solutions ◽

Computational Study ◽

Sparse Matrices ◽

Practical Interest ◽

Time Dependent ◽

Axially Symmetric ◽

Finite Difference Approximations ◽

Sudden Approximation ◽

Physical Quantities

AbstractThe emission of scission neutrons from fissioning nuclei is of high practical interest. To study this process we have used the sudden approximation and also a more realistic approach that takes into account the scission dynamics. Numerically, this implies the solution of the bi-dimensional Schrödinger equation, both stationary and time-dependent. To describe axially symmetric extremely deformed nuclear shapes, we have used the Cassini parametrization. The Hamiltonian is discretized by using finite difference approximations of the derivatives. The main computational challenges are the solution of algebraic eigenvalue problems and of linear systems with large sparse matrices. We have employed appropriate procedures (Arnoldi and bi-conjugate gradients). The numerical solutions have been used to evaluate physical quantities, like the number of emitted neutrons per scission event, the primary fragments’ excitation energy and the distribution of the emission points.

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Dual solutions of a micropolar nanofluid flow with radiative heat mass transfer over stretching/shrinking sheet using spectral quasilinearization method

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-01-2019-0028 ◽

2019 ◽

Vol 16 (2) ◽

pp. 238-255 ◽

Cited By ~ 3

Author(s):

Mangwiro Magodora ◽

Hiranmoy Mondal ◽

Precious Sibanda

Keyword(s):

Brownian Motion ◽

Error Analysis ◽

Micropolar Fluid ◽

Numerical Solutions ◽

Surface Radiation ◽

Shrinking Sheet ◽

Quasilinearization Method ◽

Spectral Collocation ◽

Content Type ◽

Micropolar Nanofluid

Purpose The purpose of this paper is to focus on the application of Chebyshev spectral collocation methodology with Gauss Lobatto grid points to micropolar fluid over a stretching or shrinking surface. Radiation, thermophoresis and nanoparticle Brownian motion are considered. The results have attainable scientific and technological applications in systems involving stretchable materials. Design/methodology/approach The model equations governing the flow are transformed into non-linear ordinary differential equations which are then reworked into linear form using the Newton-based quasilinearization method (SQLM). Spectral collocation is then used to solve the resulting linearised system of equations. Findings The validity of the model is established using error analysis. The velocity, temperature, micro-rotation, skin friction and couple stress parameters are conferred diagrammatically and analysed in detail. Originality/value The study obtains numerical explanations for rapidly convergent solutions using the spectral quasilinearization method. Convergence of the numerical solutions was monitored using the residual error analysis. The influence of radiation, heat and mass parameters on the flow are depicted graphically and analysed. The study is an extension on the work by Zheng et al. (2012) and therefore the novelty is that the authors tend to take into account nanoparticles, Brownian motion and thermophoresis in the flow of a micropolar fluid.

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MHD Glauert Flow of a Hybrid Nanofluid with Heat Transfer

Journal of Advanced Research in Fluid Mechanics and Thermal Sciences ◽

10.37934/arfmts.86.2.91100 ◽

2021 ◽

Vol 86 (2) ◽

pp. 91-100

Author(s):

Iskandar Waini ◽

Anuar Ishak ◽

Ioan Pop

Keyword(s):

Heat Transfer ◽

Friction Coefficient ◽

Skin Friction ◽

Heat Transfer Rate ◽

Transfer Rate ◽

Numerical Solutions ◽

Skin Friction Coefficient ◽

Hybrid Nanoparticles ◽

Hybrid Nanofluid ◽

Variable Surface

This paper examines the wall jet flow and heat transfer of the Glauert problem with the effect of the hybrid nanoparticles. Also, the influence of the magnetic field and the variable surface temperature are taken into consideration. Here, we consider copper (Cu) and alumina (Al2O3) as the hybrid nanoparticles while water is the base fluid. The governing equations are reduced to the similarity equations using similarity transformations. Then, the numerical solutions are obtained by using the bvp4c function in MATLAB software. The findings reveal that hybrid nanofluid provides a higher heat transfer rate compared to regular nanofluid. Besides, the heat transfer rate and the skin friction coefficient increase in the presence of nanoparticles. Moreover, the rise of the temperature index parameter contributes to the enhancement of the heat transfer rate, but it does not affect the skin friction coefficient. The stronger magnetic strength led to the reduction of the heat transfer rate and the skin friction coefficient.

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Stratified Flow of Micropolar Nanofluid over Riga Plate: Numerical Analysis

Energies ◽

10.3390/en15010316 ◽

2022 ◽

Vol 15 (1) ◽

pp. 316

Author(s):

Khuram Rafique ◽

Hammad Alotaibi ◽

Nida Ibrar ◽

Ilyas Khan

Keyword(s):

Numerical Analysis ◽

Fluid Velocity ◽

Nonlinear Partial Differential Equations ◽

Practical Interest ◽

Physical Parameters ◽

Boundary Layer Equations ◽

Micropolar Nanofluid ◽

Riga Plate ◽

The Impact ◽

Physical Quantities

In this article, we present a numerical analysis of the energy and mass transport behavior of microrotational flow via Riga plate, considering suction or injection and mixed convection. The thermal stratified parameters of nanofluid are captured using an interpretation of the well-known Keller box model, which helps us to determine the characteristic properties of the physical parameters. The formulated boundary layer equations (nonlinear partial differential equations) are transformed into coupled ODEs with nonlinearities for the stratified controlled regimes. The impact of embedded flow and all physical quantities of practical interest, such as velocity, temperature, and concentration profile, are inspected and presented through tables and graphs. We found that the heat transfer on the surface decreases for the temperature stratification factor as mass transfer increases. Additionally, the fluid velocity increases as the modified Hartmann number increases.

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Free Convective Mass Transfer at Isosceles Triangular Surfaces of Varying Inclination

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc20032080 ◽

2003 ◽

Vol 68 (11) ◽

pp. 2080-2092 ◽

Cited By ~ 1

Author(s):

Martin Keppert ◽

Josef Krýsa ◽

Anthony A. Wragg

Keyword(s):

Mass Transfer ◽

Transfer Rate ◽

Mass Transfer Rate ◽

Mass Transfer Process ◽

Sulfate Solution ◽

Convective Mass Transfer ◽

Varying Length ◽

Inclined Surface ◽

Vertical Case ◽

Limiting Diffusion Current

The limiting diffusion current technique was used for investigation of free convective mass transfer at down-pointing up-facing isosceles triangular surfaces of varying length and inclination. As the mass transfer process, copper deposition from acidified copper(II) sulfate solution was used. It was found that the mass transfer rate increases with inclination from the vertical to the horizontal position and decreases with length of inclined surface. Correlation equations for 7 angles from 0 to 90° were found. The exponent in the ShL-RaL correlation ranged from 0.247 for the vertical case, indicating laminar flow, to 0.32 for inclinations of 60 to 90°, indicating mixed or turbulent flow. The general correlation ShL = 0.358(RaL sin θ)0.30 for the RaL sin θ range from 7 × 106 to 2 × 1011 and inclination range from 15 to 90° was obtained.

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Thermal analysis of higher-order chemical reactive viscoelastic nanofluids flow in porous media via stretching surface

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/09544062211008481 ◽

2021 ◽

pp. 095440622110084

Author(s):

Mohamed R Eid ◽

F Mabood

Keyword(s):

Brownian Motion ◽

Transfer Rate ◽

Fluid Velocity ◽

Mass Transfer Rate ◽

Higher Order ◽

Flow In Porous Media ◽

Viscoelastic Parameter ◽

Suction Parameter ◽

And Brownian Motion ◽

Magnetic Strength

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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