scholarly journals Fluid Flow and Heat Transfer Analysis of a Nanofluid Containing Motile Gyrotactic Micro-Organisms Passing a Nonlinear Stretching Vertical Sheet in the Presence of a Non-Uniform Magnetic Field; Numerical Approach

2021 ◽  
Author(s):  
Farshad Moradi Kashkooli ◽  
M. Soltani ◽  
Kaamran Raahemifar
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Sherwood Number ◽  
Uniform Magnetic Field ◽  
Local Density ◽  
Heat Transfer Analysis ◽  
Energy Concentration ◽  
Local Skin ◽  
Micro Organisms ◽  
Nonlinear Stretching

The behavior of a water-based nanofluid containing motile gyrotactic micro-organisms passing an isothermal nonlinear stretching sheet in the presence of a non-uniform magnetic field is studied numerically. The governing partial differential equations including continuity, momentums, energy, concentration of the nanoparticles, and density of motile micro-organisms are converted into a system of the ordinary differential equations via a set of similarity transformations. New set of equations are discretized using the finite difference method and have been linearized by employing the Newton’s linearization technique. The tri-diagonal system of algebraic equations from discretization is solved using the well-known Thomas algorithm. The numerical results for profiles of velocity, temperature, nanoparticles concentration and density of motile micro-organisms as well as the local skin friction coefficient Cfx, the local Nusselt number Nux, the local Sherwood number Shx and the local density number of the motile microorganism Nnx are expressed graphically and described in detail. This investigation shows the density number of the motile micro-organisms enhances with rise of M, Gr/Re2, Pe and Ω but it decreases with augment of Rb and n. Also, Sherwood number augments with an increase of M and Gr/Re2, while decreases with n, Rb, Nb and Nr. To show the validity of the current results, a comparison between the present results and the existing literature has been carried out.

scholarly journals Fluid Flow and Heat Transfer Analysis of a Nanofluid Containing Motile Gyrotactic Micro-Organisms Passing a Nonlinear Stretching Vertical Sheet in the Presence of a Non-Uniform Magnetic Field; Numerical Approach

2021 ◽  
Author(s):  
Farshad Moradi Kashkooli ◽  
M. Soltani ◽  
Kaamran Raahemifar
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Sherwood Number ◽  
Uniform Magnetic Field ◽  
Local Density ◽  
Heat Transfer Analysis ◽  
Energy Concentration ◽  
Local Skin ◽  
Micro Organisms ◽  
Nonlinear Stretching

The behavior of a water-based nanofluid containing motile gyrotactic micro-organisms passing an isothermal nonlinear stretching sheet in the presence of a non-uniform magnetic field is studied numerically. The governing partial differential equations including continuity, momentums, energy, concentration of the nanoparticles, and density of motile micro-organisms are converted into a system of the ordinary differential equations via a set of similarity transformations. New set of equations are discretized using the finite difference method and have been linearized by employing the Newton’s linearization technique. The tri-diagonal system of algebraic equations from discretization is solved using the well-known Thomas algorithm. The numerical results for profiles of velocity, temperature, nanoparticles concentration and density of motile micro-organisms as well as the local skin friction coefficient Cfx, the local Nusselt number Nux, the local Sherwood number Shx and the local density number of the motile microorganism Nnx are expressed graphically and described in detail. This investigation shows the density number of the motile micro-organisms enhances with rise of M, Gr/Re2, Pe and Ω but it decreases with augment of Rb and n. Also, Sherwood number augments with an increase of M and Gr/Re2, while decreases with n, Rb, Nb and Nr. To show the validity of the current results, a comparison between the present results and the existing literature has been carried out.

scholarly journals Computation of electroconductive gyrotactic bioconvection under nonuniform magnetic field: Simulation of smart bio-nanopolymer coatings for solar energy

2020 ◽  
Vol 34 (05) ◽  
pp. 2050028 ◽  
Author(s):  
Madhu Aneja ◽  
Sapna Sharma ◽  
Sireetorn Kuharat ◽  
O. Anwar Beg
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Differential Equations ◽  
Sherwood Number ◽  
Nonuniform Magnetic Field ◽  
Ohmic Dissipation ◽  
Local Skin ◽  
Brownian Motion And Thermophoresis ◽  
Micro Organisms

The water-based bioconvection of a nanofluid containing motile gyrotactic micro-organisms (moves under the effects of gravity) over a nonlinear inclined stretching sheet in the presence of a nonuniform magnetic field has been investigated. This regime is encountered in the bio-nanomaterial electroconductive polymeric processing systems currently being considered for third-generation organic solar coatings, anti-fouling marine coatings, etc. Oberbeck–Boussinesq approximation along with ohmic dissipation (Joule heating) is considered in the problem. The governing equations of the flow are nonlinear partial differential equations and are converted into ordinary differential equations via similarity transformations. These equations are then solved by the Finite Element Method. The effect of various important parameters on nondimensional velocity, temperature distribution, nanoparticle concentration, the density of motile micro-organisms is analyzed graphically in detail. It is observed from the obtained results that the flow velocity decreases with rising angle of inclination [Formula: see text] while temperature, nanoparticle’s concentration and density of motile micro-organisms increase. The local skin friction coefficient, Nusselt number, Sherwood number, motile micro-organism’s density number are calculated. It is noticed that increasing the Brownian motion and thermophoresis parameter leads to an increase in temperature of fluid which results in a reduction in Nusselt number. On the contrary, the Sherwood number rises with an increase in Brownian motion and thermophoresis parameter. Also, interesting features of the flow dynamics are elaborated and new future pathways for extension of the study identified in bio-magneto-nano polymers (BMNPs) for solar coatings.

Viscous Dissipation and Joule Heating Effects on MHD Bioconvection Flow of a Nanofluid Containing Gyrotactic Microorganisms Over a Vertical Isothermal Cone

2020 ◽  
Vol 9 (3) ◽  
pp. 242-255
Author(s):  
Hossam A. Nabwey ◽  
S. M. M. El-Kabeir ◽  
A. M. Rashad ◽  
M. M. M. Abdou
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Sherwood Number ◽  
Local Density ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Gyrotactic Microorganisms ◽  
Local Skin Friction ◽  
Local Sherwood Number

The main objective of the present study is to explore the flow of a nanofluid containing gyrotactic microorganisms over a vertical isothermal cone surface in the presence of viscous dissipation and Joule heating. The combined effects of a transverse magnetic field and Navier slip in the flow are considered. Using appropriate transforms the set of partial differential equations governing the flow are converted to a set of ordinary differential equations. Influence of the parameters governing the flow is shown for velocity, temperature, concentration and motilemicroorganisms as well as local skin Friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms number. An increasing in the value of Eckert number rises the velocity of the fluid and reduce the temperature, concentration and density of motile microorganisms profiles, while buoyancy ratio Nr and magnetic field parameters increase local skin friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms number decrease as a result of the presence of Lorentz force which resist the motion of the flow. On the other hand, the motile microorganisms boundary layer thickness decreases with an increasing on the bioconvection Lewis number.

A study for steady nanofluid flow between parallel plates

2017 ◽  
Vol 34 (8) ◽  
pp. 2514-2527 ◽  
Author(s):  
Syed Tauseef Mohyud-din ◽  
Muhammad Asad Iqbal ◽  
Muhammad Shakeel
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Uniform Magnetic Field ◽  
Design Methodology ◽  
Magnetic Parameter ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Content Type ◽  
Viscosity Parameter ◽  
Variation Of Parameters

Purpose In this paper, the authors study the behavior of heat and mass transfer between parallel plates of a steady nanofluid flow in the presence of a uniform magnetic field. In the model of nanofluids, the essential effect of thermophoresis and Brownian motion has been encompassed. Design/methodology/approach The variation of parameters method has been exploited to solve the differential equations of nanofluid model. The legitimacy of the variation of parameters method has been corroborated by a comparison of foregoing works by many authors on viscous fluid. Findings An analysis of the model is performed for different parameters, namely, viscosity parameter, Brownian parameter, thermophoretic parameter and magnetic parameter. Originality/value The variation of parameters method proves to be very effective in solving nonlinear system of ordinary differential equations which frequently arise in fluid mechanics.

Nonuniform Magnetic Field Effects in MHD Slider Bearing

1972 ◽  
Vol 94 (1) ◽  
pp. 101-105 ◽  
Author(s):  
M. I. Anwar ◽  
C. M. Rodkiewicz
Keyword(s):  
Magnetic Field ◽  
Theoretical Analysis ◽  
Differential Equations ◽  
Uniform Magnetic Field ◽  
Hartmann Number ◽  
Load Capacity ◽  
Nonuniform Magnetic Field ◽  
Magnetic Field Effects ◽  
Slider Bearing ◽  
Electrically Conducting

A theoretical analysis is made of a slider bearing using an electrically conducting lubricant in the presence of a nonuniform magnetic field applied perpendicularly to the bearing surfaces. In the differential equations inertia terms are retained and the solution is obtained numerically for low Hartmann numbers. The results indicate that the contribution of inertia terms decreases with the increase of Hartmann number and that the nonuniform magnetic field gives higher load capacity than the comparable uniform magnetic field.

scholarly journals Effectiveness of Magnetized Flow on Nanofluid Containing Gyrotactic Micro-Organisms over an Inclined Stretching Sheet with Viscous Dissipation and Constant Heat Flux

Fluids ◽  
2021 ◽  
Vol 6 (7) ◽  
pp. 253
Author(s):  
Hossam A. Nabwey ◽  
S.M.M. El-Kabeir ◽  
A.M. Rashad ◽  
M.M.M. Abdou
Keyword(s):  
Heat Flux ◽  
Viscous Dissipation ◽  
Stretching Sheet ◽  
Local Density ◽  
Constant Heat Flux ◽  
Integration Scheme ◽  
Constant Heat ◽  
Local Skin ◽  
Micro Systems ◽  
Micro Organisms

The bioconvection phenomenon, through the utilization of nanomaterials, has recently encountered significant technical and manufacturing applications. Bioconvection has various applications in bio-micro-systems due to the improvement it brings in mixing and mass transformation, which are crucial problems in several micro-systems. The present investigation aims to explore the bioconvection phenomenon in magneto-nanofluid flow via free convection along an inclined stretching sheet with useful characteristics of viscous dissipation, constant heat flux, solutal, and motile micro-organisms boundary conditions. The flow analysis is addressed based on the Buongiorno model with the integration of Brownian motion and thermophoresis diffusion effects. The governing flow equations are changed into ordinary differential equations by means of appropriate transformation; they were solved numerically using the Runge–Kutta–Fehlberg integration scheme shooting technique. The influence of all the sundry parameters is discussed for local skin friction coefficient, local Nusselt number, local Sherwood number, and local density of the motile micro-organisms number.

scholarly journals Numerical Solution of MHD Viscoelastic Nanofluid Flow over a Stretching Sheet with Partial Slip and Heat Source/Sink

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Mania Goyal ◽  
Rama Bhargava
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Heat Source ◽  
Uniform Magnetic Field ◽  
Stretching Sheet ◽  
Partial Slip ◽  
Local Similarity ◽  
Source Sink

We analyze the effect of velocity slip boundary condition on the flow and heat transfer of non-Newtonian nanofluid over a stretching sheet with a heat source/sink, under the action of a uniform magnetic field, orientated normally to the plate. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of local similarity transformations. The differential equations are solved by the variational finite element method (FEM). We have examined the effects of different controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, uniform magnetic field, viscoelastic parameter, Prandtl number, heat source/sink parameter, Lewis number, and the slip parameter on the flow field and heat transfer characteristics. Graphical display of the numerical examination is performed to illustrate the influence of various flow parameters on the velocity, temperature, concentration, and Nusselt and Sherwood numbers distributions. The present study has many applications in coating and suspensions, cooling of metallic plate, paper production, heat exchangers technology, and materials processing exploiting.

Dual Solutions for Heat and Mass Transfer in MHD Bio-Convective Flow over a Stretching/Shrinking Surface with Suction/Injection

2015 ◽  
Vol 21 ◽  
pp. 84-101 ◽  
Author(s):  
M. Satish Kumar ◽  
Naramgari Sandeep ◽  
B. Rushi Kumar
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Volume Fraction ◽  
Local Density ◽  
Internal Heat ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Nonlinear Stretching ◽  
Shrinking Surface

The objective of the present study is to investigate the heat and mass transfer characteristics of the MHD stagnation-point flow of gyrotactic microorganisms contained nanofluid past a nonlinear stretching/shrinking sheet in presence of space and temperature dependent internal heat generation/absorption with suction/injection. The governing partial differential equations are transformed to system of ordinary differential equations by using similarity transformation and then solved numerically using Runge-Kutta based shooting technique. The influence of non-dimensional governing parameters on velocity, temperature, nanoparticle volume fraction and density of the motile microorganisms along with friction factor, local Nusselt number, local Sherwood number and the local density of the motile microorganisms was discussed and presented through graphs and tables. Dual solutions are presented for certain range of suction and injection parameters. The validity of the present results compared with the existed results.

Heat Transfer Analysis on Axisymmetric Mhd Flow of a Micropolar Fluid Between the Radially Stretching Sheets

2011 ◽  
Vol 27 (4) ◽  
pp. 607-617 ◽  
Author(s):  
T. Hayat ◽  
M. Nawaz ◽  
A. A. Hendi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Axisymmetric Flow ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Heat Transfer Analysis ◽  
Physical Parameters ◽  
Local Skin ◽  
Homotopy Analysis

ABSTRACTThe effect of heat transfer on the axisymmetric flow of MHD micropolar fluid between two radially stretching sheets is described. The governing partial differential equations are reduced into the ordinary differential equations by using transformations. The resulting problems are solved by homotopy analysis method (HAM). Dimensionless velocities and temperature are plotted for the variation of influential parameters. The local skin friction coefficient, local couple stress coefficient and Nusselt number are tabulated with respect to the influence of several physical parameters.

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