Influence of Non-Linear Boussinesq Approximation and Convective Thermal Boundary Condition on MHD Natural Convection Flow of a Couple Stress-Nanofluid in a Porous Medium

2019 ◽  
Vol 26 ◽  
pp. 45-61
Author(s):  
Mhamed Tayeb ◽  
Mohamed Nadjib Bouaziz ◽  
Salah Hanini
Keyword(s):  
Differential Equations ◽  
Couple Stress ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Linear Part ◽  
Boussinesq Approximation ◽  
Convection Flow ◽  
Non Linear ◽  
Convective Thermal ◽  
Buongiorno Model

Nonlinear density and temperature variation’s role (NDT) on the magnetohydrodynamic (MHD) natural convective flow of couple stress fluid with nanoparticles through a vertical porous channel modeled as Darcy-Forchheimer flow is the purpose of our work. The nanoparticles volume fraction is taken into consideration (Buongiorno model). The nonlinear partial differential equations governing this flow were transformed into ordinary differential equations via the similarity technique and simulated numerically using Matlab, following boundary value problem (BVP4c) code. Graphical illustrations, including non-dimensional velocity, temperature, concentration, nanoparticle’s concentration and numerical results containing Nusselt and Sherwood numbers were presented for different values of the non-linear part of the Boussinesq approximation; couple stress parameter, and the Biot number on the walls.

Double Diffusive Convection in Flow Couple Stress Nanofluid in a Permeable Wall Vertical Channel in the Presence of a Magnetic Field

2019 ◽  
Vol 26 ◽  
pp. 30-44
Author(s):  
Noureddine Messaoudi ◽  
Mohamed Nadjib Bouaziz ◽  
Hamza Ali Agha
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Couple Stress ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Strong Impact

In this work, the flow of a couple stress nanofluid in a vertical channel with heat and mass transfer in the presence of a magnetic field and taking account the Brownian motion, the thermophoresis as well as the effect of Soret and Dufour was simulated numerically using Matlab following the code bvp4c. The nonlinear partial differential equations governing this particular flow are transformed into a system of ordinary differential equations via the similarity technique. The influence of the parameters describing the behavior of the problem studied on the velocity, temperature, concentration and volume fraction fields of the nanoparticles, as well as on the coefficient of friction, Nusselt and Sherwood numbers, were highlighted for the end of the study. understand their effect on heat and mass transfer. The rheology of the nanofluid and the magnetic field have a strong impact on the velocity and temperature profiles, while the parameters of Brownian motion and thermophoresis promote heat transfer.

scholarly journals Mathematical analysis of bio-convective micropolar nanofluid

2019 ◽  
Vol 6 (3) ◽  
pp. 233-242 ◽  
Author(s):  
Sohail Nadeem ◽  
Muhammad Naveed Khan ◽  
Noor Muhammad ◽  
Shafiq Ahmad
Keyword(s):  
Differential Equations ◽  
Microbial Fuel Cells ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Convection Flow ◽  
Micropolar Nanofluid ◽  
Exponentially Stretching ◽  
Micro Organisms

Abstract The present investigation concentrates on three dimensional unsteady forced bio-convection flow of a viscous fluid. An incompressible flow of a micropolar nanofluid encloses micro-organisms past an exponentially stretching sheet with magnetic field is analyzed. By employing convenient transformation the partial differential equations are converted into the ordinary differential equations which are non-linear. By using shooting method to solved these equations numerically. The influence of the determining parameters on the velocity, temperature, micro-rotation, nanoparticle volume fraction, microorganism are incorporated. The skin friction, heat transfer rate, and the microorganism rate are analyzed. The results depicts that the value of the wall shear stress and Nusselt number are declined while an enhancement take place in the microorganism number. The slip parameters increases the velocity, thermal energy, and microorganism number consequentially. The present investigation are important in improving achievement of microbial fuel cells.

scholarly journals Soret and dufour effects on free convection flow of a couple stress fluid in a vertical channel with chemical reaction

2013 ◽  
Vol 19 (1) ◽  
pp. 45-55 ◽  
Author(s):  
D. Srinivasacharya ◽  
K. Kaladhar
Keyword(s):  
Differential Equations ◽  
Chemical Reaction ◽  
Couple Stress ◽  
Vertical Channel ◽  
Couple Stress Fluid ◽  
Convection Flow ◽  
Parallel Plates ◽  
Soret And Dufour Effects ◽  
Similarity Transformations ◽  
Dufour Number

The Soret and Dufour effects in the presence of chemical reaction on natural convection heat and mass transfer of a couple stress fluid in a vertical channel formed by two vertical parallel plates is presented. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using Homotopy Analysis Method (HAM). Profiles of dimensionless velocity, temperature and concentration are shown graphically for various values of Dufour number, Soret number, Couple stress parameter and chemical reaction parameter.

Coriolis effects on MHD newtonian flow over a rotating non-uniform surface

2020 ◽  
pp. 095440622096973
Author(s):  
Abayomi S Oke ◽  
Winifred N Mutuku ◽  
Mark Kimathi ◽  
Isaac Lare Animasaun
Keyword(s):  
Differential Equations ◽  
Lorentz Force ◽  
Coriolis Force ◽  
Stokes Equations ◽  
Physical Phenomenon ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Simultaneous Increase ◽  
Convection Flow ◽  
The Impact

The roles of the simultaneous effect of Coriolis force and Lorentz force (resulting from MHD flow) in Sunspots, solar wind, and many other natural and physical phenomenon is undoubtedly significant. The impact of fluids heated by the Sun is influenced by the rotation of the earth’s surface and this necessitates the study of fluid flow over such surface as the Earth. For this reason, the significance of Coriolis force on MHD free-convection flow of Newtonian fluid over the rotating upper horizontal surface of paraboloid of revolution is explored. The relevant body forces are derived and included in the Navier-Stokes equations to obtain appropriate equations governing the flow. By nondimensionalizing the governing equations using similarity variables, the system of nonlinear partial differential equations is reduced to a system of nonlinear ordinary differential equations which is solved using Runge-Kutta-Gills method along with Shooting technique and the results are depicted graphically. It is observed that simultaneous increase in both Coriolis force and Lorentz force causes an increase in the temperature profile of the flow. It is also observed that the effect of increasing Coriolis force on the Skin Friction and heat transfer rate is counter-balanced by increasing Lorentz force.

Investigation of MHD Natural Convection Flow Exposed to Constant Magnetic Field via Generalized Differential Quadrature Method

2014 ◽  
Author(s):  
Elgiz Baskaya ◽  
Melih Fidanoglu ◽  
Guven Komurgoz ◽  
Ibrahim Ozkol
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Constant Magnetic Field ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Convection Flow ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential

In this work, nanofluid flow characteristics of an inclined channel flow exposed to constant magnetic field and pressure gradient is investigated. The nanofluid considered is water based Cu nanoparticles with a volume fraction of 0.06. The viscous dissipation is taken into account in the energy equation and the governing differential equations are nondimensionalized. The coupled one dimensional differential equations are solved via Generalized Differential Quadrature Method (GDQM) discretization followed by Newton Raphson method. Furthermore, the effect of magnetic field, inclination angle of the channel and volume fraction on nanoparticles in the nanofluid on velocity and temperature profiles are examined and represented by figures to give a thorough understanding of the system behavior. Designing systems utilizing nanofluids optimally, is highly dependent to achieving accurate model definitions figuring their inherent performance.

scholarly journals Role of Brownian Motion and Thermophoresis Effects on Hydromagnetic Flow of Nanofluid Over a Nonlinearly Stretching Sheet with Slip Effects and Solar Radiation

2019 ◽  
Vol 24 (3) ◽  
pp. 489-508
Author(s):  
S.P. Anjali Devi ◽  
S. Mekala
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Velocity Slip ◽  
Physical Parameters ◽  
Nonlinear Thermal Radiation ◽  
Hydromagnetic Flow ◽  
Nonlinearly Stretching Sheet

Abstract Hydromagnetic flow of water based nanofluids over a nonlinearly stretching sheet in the presence of velocity slip, temperature jump, magnetic field, nonlinear thermal radiation, thermophoresis and Brownian motion has been studied. The article focuses on Cu water nanofluid and Ag water nanofluid. The similarity transformation technique is adopted to reduce the governing nonlinear partial differential equations into nonlinear ordinary differential equations and then they are solved numerically utilizing the Nachistem – Swigert shooting method along with the fourth order Runge Kutta integration technique. The influence of physical parameters on the flow, temperature and nanoparticle volume fraction are presented through graphs. Also the values of the skin friction coefficient at the wall and nondimensional rate of heat transfer are given in a tabular form. A comparative study with previous published results is also made.

scholarly journals Mixed convection flow of Jeffrey fluid along an inclined stretching cylinder with double stratification effect

2017 ◽  
Vol 21 (2) ◽  
pp. 849-862 ◽  
Author(s):  
Tasawar Hayat ◽  
Sajid Qayyum ◽  
Muhammad Farooq ◽  
Ahmad Alsaedi ◽  
Muhammad Ayub
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Variable Temperature ◽  
Heat Transfer Analysis ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Convection Boundary Layer ◽  
Stretching Cylinder ◽  
Double Stratification ◽  
Non Linear

This paper addresses double stratified mixed convection boundary layer flow of Jeffrey fluid due to an impermeable inclined stretching cylinder. Heat transfer analysis is carried out with heat generation/absorption. Variable temperature and concentration are assumed at the surface of cylinder and ambient fluid. Non-linear partial differential equations are reduced into the non-linear ordinary differential equations after using the suitable transformations. Convergent series solutions are computed. Effects of various pertinent parameters on the velocity, temperature, and concentration distributions are analyzed graphically. Numerical values of skin friction coefficient, Nusselt, and Sherwood numbers are also computed and discussed.

Nonlinear Approximation for Natural Convection Flow Near a Vertical Plate with Thermal Radiation Effect

2021 ◽  
Author(s):  
Basant K. Jha ◽  
Gabriel Samaila
Keyword(s):  
Natural Convection ◽  
Temperature Gradient ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Nonlinear Approximation ◽  
Vertical Wall ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Flow Formation ◽  
Non Linear

Abstract A non-linear approximation for natural convection boundary layer flow near a vertical wall under the influence of thermal radiation is analysed. The governing equation comprises of the set of non-linear partial differential equations is transformed into ordinary differential equations via the similarity transformation. The final dimensionless equations are solved numerically using the Runge Kutta Ferlberg fourth-fifth order (RKF45) method. The effects of the embedded parameters affecting the flow formation, temperature distribution, Nusselt number and the Skin friction are thoroughly examined. It is found that the temperature gradient is proportional to the thermal radiation near the plate whereas inversely proportional to the temperature gradient far away from the plate. The flow formation in the boundary enhanced near the vertical wall with thermal radiation parameter increase but remain constant in the free stream region. The rate of heat transfer enhanced with the thermal radiation whereas decreases with other embedded parameters under consideration.

scholarly journals Effect of Thermal Radiation on Magneto-Convection of a Micropolar Nanoliquid towards a Non-Linear Stretching Surface with Convective Boundary

2018 ◽  
Vol 7 (4.10) ◽  
pp. 417
Author(s):  
K. Jagan ◽  
S. Sivasankaran ◽  
M. Bhuvaneswari ◽  
S. Rajan
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Convective Boundary Condition ◽  
Convection Flow ◽  
Stretching Surface ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Boundary Parameter ◽  
Non Linear

The objective of this paper is to analyze the effect of thermal radiation on MHD mixed convection flow of a micropolar nanoliquid   towards a non-linear stretching surface with convective boundary condition. The governing equations are converted into non-linear    ordinary differential equations by using suitable similarity transformations. The homotopy analysis method is used for solving the non-linear ordinary differential equations. The temperature profiles increase due to increase in thermal radiation parameter. The microrotation   profile increases when boundary parameter is increased. Also, the skin friction coefficient and local Nusselt are plotted for various    parameters.  

scholarly journals Electrical Unsteady MHD Natural Convection Flow of Nanofluid with Thermal Stratification and Heat Generation/Absorption

MATEMATIKA ◽  
2018 ◽  
Vol 34 (2) ◽  
pp. 393-417 ◽  
Author(s):  
Yahaya Shagaiya Daniel ◽  
Abdul Aziz Zainal ◽  
Zuhaila Ismail ◽  
Faisal Salah
Keyword(s):  
Natural Convection ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Thermal Stratification ◽  
Nonlinear Partial Differential Equations ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Reaction Heat ◽  
Radiation Chemical

In this paper, we analyzed the effects of thermal radiation, chemical reaction, heat generation/absorption, magnetic and electric fields on unsteady natural convection flow and heat transfer due to nanofluid over a permeable stretching sheet. The transport equations used passively controlled boundary condition rather than actively. A similarity solution is employed to transformed the governing equations from nonlinear partial differential equations to a set of ordinary differential equations, and then solve using Keller box method. It was found that the temperature is a decreasing function with the thermal stratification due to the fact the density of the fluid in the lower vicinity is much higher compared to the upper region, whereas the thermal radiation, viscous dissipation and heat generation enhanced the nanofluid temperature and thermal layer thickness.

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