scholarly journals Forced Convective of Micropolar Fluid on a Stretching Surface of Another Quiescent Fluid

MATEMATIKA ◽  
2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Nurazleen Abdul Majid ◽  
Nurul Farahain Mohammad ◽  
Abdul Rahman Mohd Kasim ◽  
Sharidan Shafie
Keyword(s):  
Differential Equations ◽  
Micropolar Fluid ◽  
Similarity Transformation ◽  
Convection Flow ◽  
Governing Equations ◽  
Stretching Surface ◽  
Strong Concentration ◽  
Lower Fluid ◽  
Forced Convection Flow ◽  
Quiescent Fluid

In this paper, the problem of forced convection flow of micropolar fluid of lighter density impinging orthogonally on another heavier density of micropolar fluid on a stretching surface is investigated. The boundary layer governing equations are transformed from partial differential equations into a system of nonlinear ordinary differential equations using similarity transformation and solved numerically using dsolve function in Maple software version 2016. The velocity, microrotation and temperature of micropolar fluid are analyzed. It is found that both upper fluid and lower fluid display opposite behaviour when micropolar parameter K various with strong concentration n = 0, Pr = 7 and stretching parameter lambda = 0.5. The results also show that stretching surface exert the force that increasing the velocity of micropolar fluid.

scholarly journals Mixed convection of micropolar fluid on a permeable stretching surface of another quiescent fluid

2020 ◽  
Vol 16 (4) ◽  
pp. 487-492
Author(s):  
Nurazleen Abdul Majid ◽  
Nurul Farahain Mohammad ◽  
Abdul Rahman Mohd Kasim ◽  
Sharidan Shafie
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Mixed Convection ◽  
Micropolar Fluid ◽  
Research Subjects ◽  
Governing Equations ◽  
Stretching Surface ◽  
Shooting Technique ◽  
Micropolar Fluid Flow ◽  
Quiescent Fluid

In recent decades, micropolar fluid has been one of the major interesting research subjects due to the numerous applications such as blood, paint, body fluid, polymers, colloidal fluid and suspension fluid. However, the behavior of micropolar fluid flow over a permeable stretching surface of another quiescent fluid with a heavier density of micropolar fluid under the condition of mixed convection is still unknown. Thus, the current work aims to investigate numerically the mixed convection of micropolar fluid flow over a permeable stretching surface of another quiescent fluid. In this research, the similarity transformation is implemented to reduce the boundary layer governing equations from partial differential equations to a system of nonlinear ordinary differential equations. Then, this model is solved numerically using shooting technique with Runge-Kutta-Gill method and applied in Jupyter Notebook using Python 3 language. The behavior of micropolar fluid in terms of velocity, skin friction, microrotation and temperature are analyzed.

scholarly journals Effects of Thermal Radiation on Mixed Convection Flow of a Micropolar Fluid from an Unsteady Stretching Surface with Viscous Dissipation and Heat Generation/Absorption

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Khilap Singh ◽  
Manoj Kumar
Keyword(s):  
Mixed Convection ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Micropolar Fluid ◽  
Numerical Solutions ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Stretching Surface ◽  
Local Skin ◽  
Unsteady Mixed Convection

A numerical model is developed to examine the effects of thermal radiation on unsteady mixed convection flow of a viscous dissipating incompressible micropolar fluid adjacent to a heated vertical stretching surface in the presence of the buoyancy force and heat generation/absorption. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The model contains nonlinear coupled partial differential equations which have been converted into ordinary differential equation by using the similarity transformations. The dimensionless governing equations for this investigation are solved by Runge-Kutta-Fehlberg fourth fifth-order method with shooting technique. Numerical solutions are then obtained and investigated in detail for different interesting parameters such as the local skin-friction coefficient, wall couple stress, and Nusselt number as well as other parametric values such as the velocity, angular velocity, and temperature.

scholarly journals Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet in a micropolar fluid

2013 ◽  
Vol 17 (2) ◽  
pp. 525-532
Author(s):  
Nor Yacob ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Leading Edge ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Electrically Conducting ◽  
Keller Box Method ◽  
Flow And Heat Transfer ◽  
The Magnetic Field

An analysis is carried out for the steady two-dimensional mixed convection flow adjacent to a stretching vertical sheet immersed in an incompressible electrically conducting micropolar fluid. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the leading edge. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically using a finite difference scheme known as the Keller box method. The effects of magnetic and material parameters on the flow and heat transfer characteristics are discussed. It is found that the magnetic field reduces both the skin friction coefficient and the heat transfer rate at the surface for any given K and ?. Conversely, both of them increase as the material parameter increases for fixed values of M and ?.

Numerical simulations of MHD forced convection flow of micropolar fluid inside a right-angled triangular cavity saturated with porous medium: Effects of vertical moving wall

2019 ◽  
Vol 97 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Mubbashar Nazeer ◽  
N. Ali ◽  
Tariq Javed
Keyword(s):  
Porous Medium ◽  
Prandtl Number ◽  
Forced Convection ◽  
Micropolar Fluid ◽  
Richardson Number ◽  
Hartmann Number ◽  
Darcy Number ◽  
Convection Flow ◽  
Penalty Parameter ◽  
Forced Convection Flow

The present article explores the effects of moving lid on the forced convection flow of micropolar fluid inside a right-angle triangular cavity saturated with porous medium. The base and hypotenuse or inclined sides of the cavity are maintained at constant temperatures, while the vertical side of the enclosure is adiabatic and moving with constant velocity in upward or downward direction. The flow equations are simulated by using the robust finite element numerical technique. The pressure term from the momentum equations is eliminated by using the penalty parameter. For a consistent solution, the value of the penalty parameter is selected as 107. The simulations are performed for the cases based on the direction of moving lid. The numerical outcomes are shown in terms of streamlines, temperature contours, and local and average Nusselt numbers for sundry parameters, such as micropolar parameter, Reynolds number, Richardson number, Darcy number, Hartmann number, and Prandtl number. It is observed that the shape of the inner circulating cell is elliptic when the lid is moving in the upward direction and fluid is clear (Newtonian fluid). It is also found that average Nusselt number in both cases increases with increasing Prandtl number, Richardson number, micropolar parameter, and Darcy number, whereas it decreases with increasing Hartmann number. Further, it achieves a maximum when the lid is moving in the downward direction, regardless of the choice of involved parameters. The numerical code is also validated with previous published results. The investigation of the current study is beneficial in porous heat exchangers, construction of triangular-shaped solar collectors, rigid crystal, polymeric fluid transport, etc.

Numerical Study of Micropolar Fluid Flow Past an Impervious Sphere

2018 ◽  
Vol 388 ◽  
pp. 344-349
Author(s):  
D.V. Jayalakshmamma ◽  
P.A. Dinesh ◽  
D.V. Chandrashekhar
Keyword(s):  
Differential Equation ◽  
Fluid Flow ◽  
Micropolar Fluid ◽  
Similarity Transformation ◽  
Numerical Study ◽  
Transformation Method ◽  
Governing Equations ◽  
Shooting Technique ◽  
Micropolar Fluid Flow ◽  
Incompressible Micropolar Fluid

The numerical study of axi-symmetric, steady flow of an incompressible micropolar fluid past an impervious sphere is presented by assuming uniform flow far away from the sphere. The continuity, linear and angular momentum equations are considered for incompressible micropolar fluid in accordance with Eringen. The governing equations of the physical problem are transformed to ordinary differential equation with variable co-efficient by using similarity transformation method. The obtained differential equation is then solved numerically by assuming the shooting technique. The effect of coupling and coupling stress parameter on the properties of the fluid flow is studied and demonstrated by graphs.

MHD free convection flow of a micropolar fluid past a vertical porous plate

2002 ◽  
Vol 80 (12) ◽  
pp. 1661-1673 ◽  
Author(s):  
K A Helmy ◽  
H F Idriss ◽  
S E Kassem
Keyword(s):  
Micropolar Fluid ◽  
Porous Plate ◽  
Infinite Plate ◽  
Numerical Approach ◽  
Convection Flow ◽  
Heated Plate ◽  
Governing Equations ◽  
State Space Approach ◽  
The Laplace Transform ◽  
Space Approach

The present work is concerned with the unsteady flow of an incompressible, viscous, conducting micropolar fluid, through a porous medium, over an infinite plate that is started into motion in its own plane by an impulse. A uniform magnetic field acts in a direction perpendicular to the plate. The governing equations are solved using a state space approach and the inversion of the Laplace transform is carried out, using a numerical approach. The technique is applied to a heated-plate problem and to a problem pertaining to a plate under uniform heating. Numerical results concerning temperature (for both problems), velocity, and microrotation are given and are illustrated graphically. PACS Nos.: 47.00, 65.00, 47.50, 76.00

scholarly journals Role of Slip Velocity in a Magneto-Micropolar Fluid Flow from a Radiative Surface with Variable Permeability: A Numerical Study

2017 ◽  
Vol 22 (3) ◽  
pp. 637-651
Author(s):  
B.K. Sharma ◽  
V. Tailor ◽  
M. Goyal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Numerical Study ◽  
Slip Flow ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Variable Permeability

AbstractAn analysis is presented to describe the hydromagnetic mixed convection flow of an electrically conducting micropolar fluid past a vertical plate through a porous medium with radiation and slip flow regime. A uniform magnetic field has been considered in the study which absorbs the micropolar fluid with a varying suction velocity and acts perpendicular to the porous surface of the above plate. The governing non-linear partial differential equations have been transformed into linear partial differential equations, which are solved numerically by applying the explicit finite difference method. The numerical results are presented graphically in the form of velocity, micro-rotation, concentration and temperature profiles, the skin-friction coefficient, the couple stress coefficient, the rate of heat and mass transfers at the wall for different material parameters.

scholarly journals MHD Heat and Mass Transfer Forced Convection Flow along a Vertical Stretching Sheet with Heat Generation and Radiation

1970 ◽  
Vol 46 (2) ◽  
pp. 169-176
Author(s):  
MA Samad ◽  
S Ahmed
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Forced Convection ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Convection Flow ◽  
Concentration Profiles ◽  
Forced Convection Flow

The present study comprises of steady two dimensional magnetohydrodynamic heat and mass transfer forced convection flow along a vertical stretching sheet in the presence of magnetic field with radiation. The nonlinear partial differential equations governing the flow field occurring in the problem have been transformed to dimensionless nonlinear ordinary differential equations by introducing suitably selected similarity variables. The ensuing equations are simultaneously solved by applying Nachtsheim-Swigert shooting iteration technique with sixth order Runge-Kutta integration scheme. The results in the form of velocity, temperature and concentration profiles are then displayed graphically. The corresponding skin-friction coefficient, Nusselt number and Sherwood number are displayed graphically and also in tabular form as well. Several important parameters such as the prandtl number (Pr), radiation parameter (N), magnetic field parameter (M), heat source parameter (Q), schmidt number (Sc), suction parameter (fw ) and eckert number (Ec) are confronted. The effects of these parameters on the velocity, temperature and concentration profiles are investigated. Key Words: MHD; Forced convection; Stretching sheet; Radiation; Heat generation. DOI: http://dx.doi.org/10.3329/bjsir.v46i2.8183 Bangladesh J. Sci. Ind. Res. 46(2), 169-176, 2011

scholarly journals Thermal radiation and magnetic field effects on unsteady mixed convection flow and mass transfer over a porous stretching surface with heat generation

2013 ◽  
Vol 18 (4) ◽  
pp. 1151-1164 ◽  
Author(s):  
G.V.R. Reddy ◽  
B.A. Reddy ◽  
N.B. Reddy
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Convection Flow ◽  
Physical Parameters ◽  
Mixed Convection Flow ◽  
Stretching Surface ◽  
Porous Stretching Surface

Abstract The effects of thermal radiation and mass transfer on an unsteady hydromagnetic boundary layer mixed convection flow along a vertical porous stretching surface with heat generation are studied. The fluid is assumed to be viscous and incompressible. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables. Numerical solutions of these equations are obtained by using the Runge-Kutta fourth order method along with the shooting technique. Velocity, temperature, concentration, the skin-friction coefficient, Nusselt number and Sherwood number for variations in the governing thermo physical parameters are computed, analyzed and discussed.

Radiation effect on heat transfer over a stretching surface

2000 ◽  
Vol 78 (12) ◽  
pp. 1107-1112 ◽  
Author(s):  
E MA Elbashbeshy
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Radiation Effect ◽  
Convection Flow ◽  
Radiation Parameter ◽  
Stretching Surface ◽  
Boundary Layer Equations ◽  
Temperature Parameter ◽  
Forced Convection Flow

We determine the effect of radiation on the forced convection flow of an optically dense incompressible fluid along a heated horizontal stretching surface. The boundary-layer equations are transformed to ordinary differential equations containing a radiation parameter R*, velocity exponent parameter M, Prandtl number P r, and surface temperature parameter θ ω. The effect of these parameters are studied. Graphical results for the velocity and temperature are presented and discussed. PACS Nos.: 44.40+a, 47.27-i

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