Mixed Bioconvective Flow Over a Wedge in Porous Media Drenched with a Nanofluid

2019 ◽  
Vol 8 (8) ◽  
pp. 1692-1703 ◽  
Author(s):  
Ali J. Chamkha ◽  
Hossam A. Nabwey ◽  
Z.M.A. Abdelrahman ◽  
A.M. Rashad
Keyword(s):  
Mathematical Model ◽  
Volume Fraction ◽  
Wedge Angle ◽  
Nanoparticle Volume Fraction ◽  
Gyrotactic Microorganisms ◽  
Convection Regime ◽  
Convective Parameter ◽  
Implicit Finite Difference ◽  
Bioconvective Flow ◽  
Vertical Wedge

A mathematical model is accentuated the mixed bioconvective flow on a vertical wedge in a Darcy porous medium filled with a nanofluid containing both nanoparticles and gyrotactic microorganisms. Thermophoresis and Brownian motion impacts are addressed to consolidate energy and concentration equations with passivelycontrolled boundary conditions. A mixed convective parameter for the whole regime of the mixed convective is appointed. The system of governing partial differential equations is converted into a non-similar set, which are then solved by an implicit finite difference method. By taking the impacts of the varying pertinent parameters, namely, the bioconvection nanofluids and wedge angle parameters in the entire mixed convection regime, the numerical results are analyzed graphically for the dimensionless the velocity, temperature, nanoparticle volume fraction and the density motile microorganisms profiles as well as the local Nusselt and motile microorganism numbers.

Mixed Bioconvective Flow Over a Wedge in Porous Media Drenched with a Nanofluid

2020 ◽  
Vol 9 (1) ◽  
pp. 24-35
Author(s):  
Ali J. Chamkha ◽  
Hossam A. Nabwey ◽  
Z. M. A. Abdelrahman ◽  
A. M. Rashad
Keyword(s):  
Mathematical Model ◽  
Volume Fraction ◽  
Wedge Angle ◽  
Nanoparticle Volume Fraction ◽  
Gyrotactic Microorganisms ◽  
Convection Regime ◽  
Convective Parameter ◽  
Implicit Finite Difference ◽  
Bioconvective Flow ◽  
Vertical Wedge

A mathematical model is accentuated the mixed bioconvective flow on a vertical wedge in a Darcy porous medium filled with a nanofluid containing both nanoparticles and gyrotactic microorganisms. Thermophoresis and Brownian motion impacts are addressed to consolidate energy and concentration equations with passivelycontrolled boundary conditions. A mixed convective parameter for the whole regime of the mixed convective is appointed. The system of governing partial differential equations is converted into a non-similar set, which are then solved by an implicit finite difference method. By taking the impacts of the varying pertinent parameters, namely, the bioconvection nanofluids and wedge angle parameters in the entire mixed convection regime, the numerical results are analyzed graphically for the dimensionless the velocity, temperature, nanoparticle volume fraction and the density motile microorganisms profiles as well as the local Nusselt and motile microorganism numbers.

scholarly journals Mixed convection over a horizontal circular cylinder embedded in porous medium immersed in a nanofluid with convective boundary conditions at lower stagnation point: A numerical solution

2018 ◽  
Vol 189 ◽  
pp. 02004
Author(s):  
Sarif Norhafizah Md ◽  
Sallhe Mohd Zuki ◽  
Roslinda Nazar
Keyword(s):  
Porous Medium ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Bottom Surface ◽  
Nanoparticle Volume Fraction ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Convective Parameter

This study aims to examine the effect of governing parameters on the flow and heat transfer of the steady mixed convection flow embedded in porous medium with convective boundary conditions. The resulting system of nonlinear partial differential equations is solved numerically. The special case at the lower stagnation point of the cylinder is observed and the case where bottom surface of the cylinder is heated by convection from hot fluids is considered. Numerical solutions are obtained for the velocity, temperature and nanoparticle volume fraction profiles for two values of governing parameters namely convective parameter γ and Lewis number Le. It is found that as the convective parameter γ increases, velocity profile, temperature and nanoparticle volume fraction profile also increases.

scholarly journals A numerical study on MHD double diffusive nonlinear mixed convective nanofluid flow around a vertical wedge with diffusion of liquid hydrogen

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Prabhugouda Mallanagouda Patil ◽  
Madhavarao Kulkarni
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Volume Fraction ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Wedge Angle ◽  
Liquid Hydrogen ◽  
Partial Differential ◽  
Double Diffusive ◽  
Vertical Wedge

AbstractThe present study focuses on double diffusive nonlinear (quadratic) mixed convective flow of nanoliquid about vertical wedge with nonlinear temperature-density-concentration variations. This study is found to be innovative and comprises the impacts of quadratic mixed convection, magnetohydrodynamics, diffusion of nanoparticles and liquid hydrogen flow around a wedge. Highly coupled nonlinear partial differential equations (NPDEs) and boundary constraints have been used to model the flow problem, which are then transformed into a dimensionless set of equations utilizing non-similar transformations. Further, a set of NPDEs would be linearized with the help of Quasilinearization technique, and then, the linear partial differential equations are transformed into a block tri-diagonal system through using implicit finite difference scheme, which is solved using Verga’s algorithm. The study findings were explored through graphs for the fluid velocity, temperature, concentration, nanoparticle volume fraction distributions and its corresponding gradients. One of the important results of this study is that the higher wedge angle values upsurge the friction between the particles of the fluid and the wedge surface. Rising Schmidt number declines the concentration distribution and enhances the magnitude of Sherwood number. Nanofluid’s temperature increases with varying applied magnetic field. The present study has notable applications in the designing and manufacturing of wedge-shaped materials in space aircrafts, construction of dams, thermal systems, oil and gas industries, etc.

scholarly journals Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

scholarly journals Finite Element Study for Magnetohydrodynamic (MHD) Tangent Hyperbolic Nanofluid Flow over a Faster/Slower Stretching Wedge with Activation Energy

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 25
Author(s):  
Bagh Ali ◽  
Rizwan Ali Naqvi ◽  
Amna Mariam ◽  
Liaqat Ali ◽  
Omar M. Aldossary
Keyword(s):  
Activation Energy ◽  
Finite Element ◽  
Volume Fraction ◽  
Wedge Angle ◽  
Energy Parameter ◽  
Reliability And Validity ◽  
Lewis Number ◽  
Convergence Criteria ◽  
Convective Boundary ◽  
Differential Formulation

The below work comprises the unsteady flow and enhanced thermal transportation for Carreau nanofluids across a stretching wedge. In addition, heat source, magnetic field, thermal radiation, activation energy, and convective boundary conditions are considered. Suitable similarity functions use to transmuted partial differential formulation into the ordinary differential form, which is solved numerically by the finite element method and coded in Matlab script. Parametric computations are made for faster stretch and slowly stretch to the surface of the wedge. The progressing value of parameter A (unsteadiness), material law index ϵ, and wedge angle reduce the flow velocity. The temperature in the boundary layer region rises directly with exceeding values of thermophoresis parameter Nt, Hartman number, Brownian motion parameter Nb, ϵ, Biot number Bi and radiation parameter Rd. The volume fraction of nanoparticles rises with activation energy parameter EE, but it receded against chemical reaction parameter Ω, and Lewis number Le. The reliability and validity of the current numerical solution are ascertained by establishing convergence criteria and agreement with existing specific solutions.

Theoretical Analysis of CFD-DEM Mathematical Model Solution Change With Varying Computational Cell Size

2018 ◽  
Author(s):  
Annette Volk ◽  
Urmila Ghia
Keyword(s):  
Mathematical Model ◽  
Standard Deviation ◽  
Cell Size ◽  
Volume Fraction ◽  
Particle Diameter ◽  
Independent Solution ◽  
Model Verification ◽  
Computational Cell ◽  
Drag Laws ◽  
Fraction Method

Successful verification and validation is crucial to build confidence in the application of coupled Computational Fluid Dynamics - Discrete Element Method (CFD-DEM). Model verification includes ensuring a mesh-independent solution, which poses a major difficulty in CFD-DEM due to the complicated solution relationship with computational cell size. In this paper, we investigate the theoretical relationship between the solution and computational cell size by tracing the effects of a change in cell size through the mathematical model. The porosity profile for simulations of fixed-particle beds is determined to be Gaussian, and the average and standard deviation of the representative distribution are reported against cell size. We find the standard deviation of bed porosity increases exponentially as the cell size is reduced, and the drag calculations are very sensitive to changes in the porosity standard deviation, resulting in an exponential change in expected drag when the cell size is small relative to the particle diameter. The divided volume fraction method of porosity calculation is shown to be superior to the centred volume fraction method, as it reduces the porosity standard deviation. The sensitivity of five popular drag laws to changes in the porosity profile is presented, and the Ergun and Beetstra drag laws are shown to be the least sensitive to changes in the cell size.

scholarly journals Marangoni convection in layers of water-based nanofluids under the effect of rotation

2021 ◽  
Vol 19 (1) ◽  
pp. 1029-1046
Author(s):  
Abeer H. Bakhsh ◽  
Abdullah A. Abdullah
Keyword(s):  
Marangoni Convection ◽  
Volume Fraction ◽  
Steady State Solution ◽  
Horizontal Layer ◽  
Brownian Diffusion ◽  
Nanoparticle Volume Fraction ◽  
Rigid Surface ◽  
Fixed Temperature ◽  
Modified Model ◽  
Conservation Condition

Abstract A linear stability analysis is performed for the onset of Marangoni convection in a horizontal layer of a nanofluid heated from below and affected by rotation. The top boundary of the layer is assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition while the bottom boundary is assumed to be a rigid surface with fixed temperature. The motion of the nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. A modification model is used in which the effects of Brownian diffusion and thermophoresis are taken into consideration by new expressions in the nanoparticle mass flux. Also, material properties of the nanofluid are modelled by non-constant constitutive expressions depending on nanoparticle volume fraction. The steady-state solution is shown to be well approximated by an exponential distribution of the nanoparticle volume fraction. The Chebyshev-Tau method is used to obtain the critical thermal and nanoparticle Marangoni numbers. Different stability boundaries are obtained using the modified model and the rotation.

scholarly journals Molecular-Theory of High Frequency Dielectric Susceptibility of Nematic Nanocomposites

Crystals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 970
Author(s):  
Mikhail A. Osipov ◽  
Alexey S. Merekalov ◽  
Alexander A. Ezhov
Keyword(s):  
Plasmon Resonance ◽  
High Frequency ◽  
Volume Fraction ◽  
Simple Expression ◽  
Dielectric Anisotropy ◽  
Dielectric Susceptibility ◽  
Nanoparticle Volume Fraction ◽  
Effective Polarizability ◽  
Dielectric And Optical Properties ◽  
Analytical Expressions

A molecular-statistical theory of the high frequency dielectric susceptibility of the nematic nanocomposites has been developed and approximate analytical expressions for the susceptibility have been obtained in terms of the effective polarizability of a nanoparticle in the nematic host, volume fraction of the nanoparticles and the susceptibility of the pure nematic phase. A simple expression for the split of the plasmon resonance of the nanoparticles in the nematic host has been obtained and it has been shown that in the resonance frequency range the high frequency dielectric anisotropy of the nanocomposite may be significantly larger than that of the pure nematic host. As a result, all dielectric and optical properties of the nanocomposite related to the anisotropy are significantly enhanced which may be important for emerging applications. The components of the dielectric susceptibility have been calculated numerically for particular nematic nanocomposites with gold and silver nanoparicles as functions of the nanoparticle volume fraction and frequency. The splitting of the plasmon resonance has been observed together with the significant dependence on the nanoparticle volume fraction and the parameters of the nematic host phase.

scholarly journals Investigation of porosity effect on flexural analysis of doubly curved FGM conoids

2019 ◽  
Vol 26 (1) ◽  
pp. 435-448
Author(s):  
Md Irfan Ansari ◽  
Ajay Kumar ◽  
Danuta Barnat-Hunek ◽  
Zbigniew Suchorab ◽  
Bartłomiej Kwiatkowski
Keyword(s):  
Mathematical Model ◽  
Shear Strain ◽  
Transverse Shear ◽  
Volume Fraction ◽  
Current Model ◽  
Lower Surface ◽  
Functionally Graded ◽  
Transverse Shear Strain ◽  
Flexural Analysis ◽  
Doubly Curved

AbstractThe flexural analysis of doubly curved functionally graded porous conoids was performed in the present paper. The porosities inside functionally graded materials (FGMs) can occur during the fabrication and lead to the occurrence of micro-voids in the materials. The mathematical model includes expansion of Taylor’s series up to the third degree in thickness coordinate and normal curvatures in in-plane displacement fields. Since there is a parabolic variation in transverse shear strain deformation across the thickness coordinate, the shear correction factor is not necessary. The condition of zero-transverse shear strain at upper and lower surface of conoidal shell is implemented in the present model. The improvement in the 2D mathematical model enables to solve problems of moderately thick FGM porous conoids. The distinguishing feature of the present shell from the other shells is that maximum transverse deflection does not occur at its centre. The improved mathematical model was implemented in finite element code written in FORTRAN. The obtained numerical results were compared with the results available in the literature. Once validated, the current model was employed to study the effect of porosity, boundary condition, volume fraction index, loading pattern and others geometric parameters.

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