scholarly journals Investigation of mixed convection magnetized Casson nanomaterial flow with activation energy and gyrotactic microorganisms

2021 ◽  
Author(s):  
Fazal Haq ◽  
Muzher Saleem ◽  
Muhammad Ijaz Khan
Keyword(s):  
Activation Energy ◽  
Mixed Convection ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Lewis Number ◽  
Fluid Temperature ◽  
Surface Drag ◽  
Radiation Chemical ◽  
Gyrotactic Microorganisms

Abstract Present article addresses mixed convection magnetohydrodynamic Casson nanomaterial flow by stretchable cylinder. The effects of thermal, solutal and motile density stratifications at the boundary of the surface are accounted. Flow governing expressions are acquired considering aspects of permeability, thermal radiation, chemical reaction, viscous dissipation and activation energy. The obtained flow model is made dimensionless through transformations and then tackled by NDsolve code in Mathematica. Physical impacts of sundry variables on nanomaterial velocity, temperature distribution, volume fraction of microorganisms and mass concentration is investigated through plots. Furthermore, quantities of engineering interest like surface drag force, heat transfer rate, density number and Sherwood number are computed and analyzed. We observed that fluid velocity diminishes for higher curvature variable, Casson fluid material variable, Hartmann number and permeability parameter. Fluid temperature has a direct relation with Eckert number, thermophoresis variable, Brownian dispersal parameter, Prandtl number and Hartmann number. Volume fraction of gyrotactic microorganisms is decreasing function of bioconvection Lewis number, stratification parameter and bioconvection Peclet number. Detailed observations are itemized at the end.

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.

scholarly journals Magnetized and non-magnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Abdullah Dawar ◽  
Zahir Shah ◽  
Hashim M. Alshehri ◽  
Saeed Islam ◽  
Poom Kumam
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Fluid Velocity ◽  
Lewis Number ◽  
Casson Fluid ◽  
Stretching Cylinder ◽  
Concentration Difference ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Homotopy Analysis

AbstractThis study presents the magnetized and non-magnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder. The mathematical modeling is presented in the form of partial differential equations and then transformed into ordinary differential equations (ODEs) utilizing suitable similarity transformations. The analytical solution of the transformed ODEs is presented with the help of homotopy analysis method (HAM). The convergence analysis of HAM is also presented by mean of figure. The present analysis consists of five phases. In the first four phases, we have compared our work with previously published investigations while phase five is consists of our new results. The influences of dimensionless factors like a magnetic parameter, thermal radiation, curvature parameter, Prandtl number, Brownian motion parameter, Schmidt number, heat generation, chemical reaction parameter, thermophoresis parameter, Eckert number, and concentration difference parameter on physical quantities of interests and flow profiles are shown through tables and figures. It has been established that with the increasing Casson parameter (i.e. $$\beta \to \infty$$ β → ∞ ), the streamlines become denser which results the increasing behavior in the fluid velocity while on the other hand, the fluid velocity reduces for the existence of Casson parameter (i.e. $$\beta = 1.0$$ β = 1.0 ). Also, the streamlines of stagnation point Casson fluid flow are highly wider for the case of magnetized fluid as equated to non-magnetized fluid. The higher values of bioconvection Lewis number, Peclet number, and microorganisms’ concentration difference parameter reduces the motile density function of microorganisms while an opposite behavior is depicted against density number.

scholarly journals Numerical method approach for magnetohydrodynamic radiative ferrofluid flows over a solid sphere surface

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 379-385
Author(s):  
Yasin Mat ◽  
Muhammad Mohamed ◽  
Zulkhibri Ismail ◽  
Basuki Widodo ◽  
Mohd Salleh
Keyword(s):  
Boundary Layer ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Solid Sphere ◽  
Skin Friction Coefficient ◽  
Fluid Temperature ◽  
Sphere Surface ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Layer Flow

In this paper, the theoretical study on the laminar boundary-layer flow of ferrofluid with influences of magnetic field and thermal radiation is investigated. The viscosity of ferrofluid flow over a solid sphere surface is examined theoretically for magnetite volume fraction by using boundary-layer equations. The governing equations are derived by applied the non-similarity transformation then solved numerically by utilizing the Keller-box method. It is found that the increments in ferro-particles (Fe3O4) volume fraction declines the fluid velocity but elevates the fluid temperature at a sphere surface. Consequently, the results showed viscosity is enhanced with the increase of the ferroparticles volume fraction and acts as a pivotal role in the distribution of velocity, temperature, reduced skin friction coefficient, and reduced Nusselt number of ferrofluid.

scholarly journals Assisting and Opposing Stagnation Point Pseudoplastic Nano Liquid Flow towards a Flexible Riga Sheet: A Computational Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Aysha Rehman ◽  
Azad Hussain ◽  
Sohail Nadeem
Keyword(s):  
Brownian Motion ◽  
Mixed Convection ◽  
Hartmann Number ◽  
Lewis Number ◽  
Weissenberg Number ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Diverse Range ◽  
Flow Equations ◽  
Buongiorno Model

Nanofluids are used as coolants in heat transport devices like heat exchangers, radiators, and electronic cooling systems (like a flat plate) because of their improved thermal properties. The preeminent perspective of this study is to highlight the influence of combined convection on heat transfer and pseudoplastic non-Newtonian nanofluid flow towards an extendable Riga surface. Buongiorno model is incorporated in the present study to tackle a diverse range of Reynolds numbers and to analyze the behavior of the pseudoplastic nanofluid flow. Nanofluid features are scrutinized through Brownian motion and thermophoresis diffusion. By the use of the boundary layer principle, the compact form of flow equations is transformed into component forms. The modeled system is numerically simulated. The effects of various physical parameters on skin friction, mass transfer, and thermal energy are numerically computed. Fluctuations of velocity increased when modified Hartmann number and mixed convection parameter are boosted, where it collapses for Weissenberg number and width parameter. It can be revealed that the temperature curve gets down if modified Hartmann number, mixed convection, and buoyancy ratio parameters upgrade. Concentration patterns diminish when there is an incline in width parameter and Lewis number; on the other hand, it went upward for Brownian motion parameter, modified Hartmann, and Prandtl number.

Steady Mixed Convection Flow on a Horizontal Circular Cylinder Embedded in a Porous Medium Filled by a Nanofluid Containing Gyrotactic Micro-Organisms

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
L. Tham ◽  
R. Nazar ◽  
I. Pop
Keyword(s):  
Porous Medium ◽  
Circular Cylinder ◽  
Mixed Convection ◽  
Volume Fraction ◽  
Local Density ◽  
Lewis Number ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Micro Organisms ◽  
Horizontal Circular Cylinder

In this paper, the steady mixed convection boundary layer flow past a horizontal circular cylinder with a constant surface temperature embedded in a porous medium saturated by a nanofluid containing both nanoparticles and gyrotactic micro-organisms in a stream flowing vertically upwards for both cases of a heated and cooled cylinder is numerically studied. The resulting system of nonlinear partial differential equations is solved numerically using an implicit finite-difference scheme. By considering the governing parameters, namely, the mixed convection parameter λ, the bioconvection Lewis number Lb, the traditional Lewis number Le, the bioconvection Péclet number Pb, the buoyancy ratio Nr, the bioconvection Rayleigh number Rb, the Brownian motion Nb, and the thermophoresis Nt, the numerical results are obtained and discussed for the skin friction coefficient, the local Nusselt number, the local Sherwood number, the local density number of the motile micro-organisms as well as the velocity, temperature, nanoparticle volume fraction, and density motile micro-organisms profiles.

scholarly journals MHD Williamson Nanofluid Flow over a Slender Elastic Sheet of Irregular Thickness in the Presence of Bioconvection

Nanomaterials ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 2297
Author(s):  
Fuzhang Wang ◽  
Muhammad Imran Asjad ◽  
Saif Ur Rehman ◽  
Bagh Ali ◽  
Sajjad Hussain ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Variable Viscosity ◽  
Fluid Velocity ◽  
Lewis Number ◽  
Computational Procedure ◽  
Fluid Temperature ◽  
Nanofluid Flow ◽  
Runge Kutta Method ◽  
Fifth Order

Bioconvection phenomena for MHD Williamson nanofluid flow over an extending sheet of irregular thickness are investigated theoretically, and non-uniform viscosity and thermal conductivity depending on temperature are taken into account. The magnetic field of uniform strength creates a magnetohydrodynamics effect. The basic formulation of the model developed in partial differential equations which are later transmuted into ordinary differential equations by employing similarity variables. To elucidate the influences of controlling parameters on dependent quantities of physical significance, a computational procedure based on the Runge–Kutta method along shooting technique is coded in MATLAB platform. This is a widely used procedure for the solution of such problems because it is efficient with fifth-order accuracy and cost-effectiveness. The enumeration of the results reveals that Williamson fluid parameter λ, variable viscosity parameter Λμ and wall thickness parameter ς impart reciprocally decreasing effect on fluid velocity whereas these parameters directly enhance the fluid temperature. The fluid temperature is also improved with Brownian motion parameter Nb and thermophoresis parameter Nt. The boosted value of Brownian motion Nb and Lewis number Le reduce the concentration of nanoparticles. The higher inputs of Peclet number Pe and bioconvection Lewis number Lb decline the bioconvection distribution. The velocity of non-Newtonian (Williamson nanofluid) is less than the viscous nanofluid but temperature behaves oppositely.

A bio-convective investigation for flow of Casson nanofluid with activation energy applications

2021 ◽  
pp. 095765092110393
Author(s):  
Fazal Haq ◽  
Muzher Saleem ◽  
M Ijaz Khan ◽  
Sami Ullah Khan ◽  
Mohammed Jameel ◽  
...  
Keyword(s):  
Activation Energy ◽  
Numerical Data ◽  
Casson Fluid ◽  
Surface Drag ◽  
Gyrotactic Microorganisms ◽  
Shooting Technique ◽  
Transfer Rates ◽  
Constitutive Theories ◽  
Energy Applications ◽  
Buoyancy Forces

Here theoretical analysis of heat, mass and motile microorganisms transfer rates in Casson fluid flow over stretched permeable surface of cylinder is studied. Investigated is carried out in the presence of suspended nanoparticles and self-propelled gyrotactic microorganisms. The effects of buoyancy forces, magnetic field and thermal radiation are considered. The nanoparticles with suitable suspension are stabilized through mutual effects of buoyancy forces and bioconvection. Furthermore, activation energy and Darcy- Forchheimer effects on bio nanofluid flow are accounted. The constitutive theories are executed to develop the model formulation. The obtained model is made dimensionless trough appropriate transformations. The dimensionless flow model is tackled by built-in algorithm of shooting technique. Impact of flow controlling constraints parameters is physically elaborated by making graphical illustrations. The outcomes based on numerical data against essential engineering formulations like surface drag force, Nusselt, density and Sherwood numbers are tabulated. Main outcomes are successfully summarized in terms of closing remarks.

Combined effects of ferromagnetic particles and magnetic field on mixed convection in the Falkner-Skan system using DRA

2019 ◽  
Vol 29 (2) ◽  
pp. 814-832 ◽  
Author(s):  
Mohamed Kezzar ◽  
Nawel Boumaiza ◽  
Ismail Tabet ◽  
Nourreddine Nafir
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Analytical Solution ◽  
Mixed Convection ◽  
Shooting Method ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Physical Parameters ◽  
Content Type ◽  
Runge Kutta

Purpose This paper aims to traitted the combined effects of ferromagnetic particles and magnetic field on mixed convection in the Falkner Skan equation using analytical solution by the Duan–Rach method. Design/methodology/approach Visualization and grouping of effects of various physical parameters such as electrical conductivity of ferro-particles (electrical conductivity calculated using Maxwell model), ferro fluid volume fraction for Magnetite-Fe3O4-water and magnetic field represented by the Hartmann number in a set of third- and second-order nonlinear coupled ordinary differential equations. This set of equations is analytically processed using the Duan–Rach Approach (DRA). Findings Obtained DRA results are validated using a numerical solution (Runge–Kutta–Fehlberg-based shooting method). The main objective of this research is to analyze the influence of physical parameters, in particular electrical conductivity, Ferrofluid volume fraction in the case of Magnetite-Fe3O4-water, in addition to the types of solid nanoparticles and Hartmann number on dynamic and thermal distributions (velocity/temperature). Results of the comparison between the numerical solution (Runge–Kutta–Fehlberg-based shooting method) and the analytical solution (DRA) show that the DRA data are in good agreement with numerical data and available literature. Originality/value The study uses Runge–Kutta–Fehlberg-based shooting method) and the analytical solution (DRA) to investigate the effect of mixed convection, in the presence of Ferro particles (Magnetite-Fe3O4) in a basic fluid (water for example) and subjected to an external magnetic field on the Falkner–Skan system.

scholarly journals MHD Mixed Convection in a Lid-Driven Cavity with a Bottom Trapezoidal Body: Two-Phase Nanofluid Model

Energies ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2943 ◽  
Author(s):  
Muhammad Sadiq ◽  
Ammar Alsabery ◽  
Ishak Hashim
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Solid Body ◽  
Richardson Number ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Convection Heat Transfer ◽  
Building Design ◽  
Current Work ◽  
Two Phase

The current work examines the effects of a bottom trapezoidal solid body and a magnetic field on mixed convection in a lid-driven square cavity. The Al 2 O 3 -water nanofluid used is assumed to obey Buongiorno’s two-phase model. An isothermal heater is placed on the bottom base of the trapezoid solid body, while the cavity’s vertical walls are kept cold at temperature T c . The top moving wall and the remaining portions of the cavity’s bottom wall are thermally insulated. The Galerkin weighted residual finite element method is employed to solve the dimensionless governing equations. The parameters of interest are the Richardson number ( 0 . 01 ≤ R i ≤ 100 ), Hartmann number ( 0 ≤ H a ≤ 50 ) , nanoparticle volume fraction ( 0 ≤ ϕ ≤ 0 . 04 ), and the length of the bottom base of the trapezoidal solid body. The obtained results show that increasing the Richardson number or decreasing the Hartmann number tends to increase the heat transfer rate. In addition, both the thermophoresis and Brownian motion greatly improve the convection heat transfer. It is believed that the current work is a good contribution to many engineering applications such as building design, thermal management of solar energy systems, electronics and heat exchange.

scholarly journals Non-linear MHD convective flow of Carreau nanofluid over an exponentially stretching surface with activation energy and viscous dissipation

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
K. S. Srinivasa Babu ◽  
A. Parandhama ◽  
R. Bhuvana Vijaya
Keyword(s):  
Activation Energy ◽  
Brownian Motion ◽  
Viscous Dissipation ◽  
Fluid Velocity ◽  
Fluid Temperature ◽  
Stretching Surface ◽  
And Brownian Motion ◽  
Non Linear ◽  
Carreau Nanofluid ◽  
Increasing Function

AbstractNumerical approach for a non-linear mixed convective magnetohydrodynamic two-dimensional Carreau nanofluid through an exponentially permeable stretching surface with viscous dissipation and velocity slip under the influence of Arrhenius activation energy in chemical reaction is reported. The effects of thermophoresis and Brownian motion are considered. The governing nonlinear equations of this model are transmuted into ODE’s through similarity variables and solved them with a shooting method based on R-K 4th order. Responses of fluid velocity, transfer rates (heat and mass) versus pertinent parameters of the problem for suitable values are obtained and the computational calculations for friction coefficient, Nusselt number and Sherwood number for the both suction and injections regions are presented in plots and tables. It is found that fluid velocity is an increasing function of Weissenberg number. Momentum boundary layer thickness is depressed by magnetic field impact. Increasing trend in Carreau fluid temperature is noticed due to larger values of thermophoresis and Brownian motion effects. Concentration field is a decreasing function of Brownian motion but an increasing function of thermophoresis. Activation energy augments the concentration curves and lowered by Schmidt number. Comparison of the results is made with already published results and we got good agreement.

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