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 ?.

scholarly journals Micropolar Fluid Flow and Heat Transfer over a Nonlinearly Stretching Plate with Viscous Dissipation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Kartini Ahmad ◽  
Anuar Ishak ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Micropolar Fluid ◽  
Skin Friction Coefficient ◽  
Keller Box Method ◽  
Flow And Heat Transfer ◽  
Micropolar Fluid Flow ◽  
Stretching Plate ◽  
Nonlinear Stretching

The flow and heat transfer of a micropolar fluid past a nonlinearly stretching plate is studied numerically, by taking into account the viscous dissipation effect. It is assumed that the plate is stretched nonlinearly from the slot where it is issued. The governing system of partial differential equations is transformed into ordinary differential equations, which are then solved numerically using a finite-difference scheme known as the Keller-box method. The effects of the governing parameters, namely, the material parameterK, the Eckert number Ec, the Prandtl number Pr, and the nonlinear stretching parametern, on the flow field and the heat transfer characteristics are obtained and discussed. The velocity and the temperature profiles are also illustrated to aid the validity of the numerical results obtained. It is found that both the local Nusselt number and the magnitude of the skin friction coefficient increase with the nonlinear stretching parametern, and the opposite trend occurs asKincreases for fixedn.

scholarly journals Flow and Heat Transfer at a Nonlinearly Shrinking Porous Sheet:The Case of Asymptotically Large Powerlaw Shrinking Rates

2013 ◽  
Vol 18 (3) ◽  
pp. 779-791 ◽  
Author(s):  
K.V. Prasad ◽  
K. Vajravelu ◽  
I. Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Temperature Fields ◽  
Shrinking Sheet ◽  
Arbitrary Power ◽  
Keller Box Method ◽  
Flow And Heat Transfer

Abstract The boundary layer flow and heat transfer of a viscous fluid over a nonlinear permeable shrinking sheet in a thermally stratified environment is considered. The sheet is assumed to shrink in its own plane with an arbitrary power-law velocity proportional to the distance from the stagnation point. The governing differential equations are first transformed into ordinary differential equations by introducing a new similarity transformation. This is different from the transform commonly used in the literature in that it permits numerical solutions even for asymptotically large values of the power-law index, m. The coupled non-linear boundary value problem is solved numerically by an implicit finite difference scheme known as the Keller- Box method. Numerical computations are performed for a wide variety of power-law parameters (1 < m < 100,000) so as to capture the effects of the thermally stratified environment on the velocity and temperature fields. The numerical solutions are presented through a number of graphs and tables. Numerical results for the skin-friction coefficient and the Nusselt number are tabulated for various values of the pertinent parameters.

scholarly journals MHD Mixed Convection Flow and Heat Transfer of a Dual Stratified Micropolar Fluid Over a Vertical Stretching/ Shrinking Sheet With Suction, Chemical Reaction and Heat Source

CFD letters ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 106-120
Author(s):  
Ansab Azam Khan ◽  
Khairy Zaimi ◽  
Suliadi Firdaus Sufahani ◽  
Mohammad Ferdows
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Source ◽  
Chemical Reaction ◽  
Sherwood Number ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Local Sherwood Number

The purpose of this study was to investigate the magnetohydrodynamic (MHD) mixed convection flow and heat transfer of a dual stratified micropolar fluid over a vertical permeable stretching/ shrinking sheet with chemical reaction and heat source. The governing nonlinear partial differential equations are reduced into a system of nonlinear ordinary differential equations using an appropriate similarity transformation. Then, the obtained ordinary differential equations are solved numerically using the boundary value problem solver (bvp4c) in MATLAB software. The numerical results are tabulated and plotted for the heat transfer characteristics, namely, the skin friction coefficient, the local Nusselt number, the local Sherwood number as well as the velocity, temperature and concentration profiles for some values of the governing parameters. The present numerical results also have been compared with the previous reported results for a particular case and the comparisons are found to be in an excellent agreement. The results indicate that the skin friction coefficient and the local Nusselt number increase with chemical reaction and heat source. The magnitude of the local Sherwood number increases with the increasing of chemical reaction parameter. However, the magnitude of the local Sherwood number decreases with heat source effect.

scholarly journals Numerical investigation of MHD stagnation-point flow and heat transfer of sodium alginate non-Newtonian nanofluid

2019 ◽  
Vol 8 (1) ◽  
pp. 179-192 ◽  
Author(s):  
Bhuvnesh Sharma ◽  
Sunil Kumar ◽  
M.K. Paswan
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Sodium Alginate ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Analytical Approximations ◽  
Temperature Distributions ◽  
Homotopy Analysis

Abstract A rigorous analysis of unsteady magnetohydrodynamic mixed convection and electrically conducting nanofluid model with a stretching/shrinking wedge is presented. First, the governing partial differential equations for momentum and energy conservation are converted to coupled nonlinear ordinary differential equations by means of exact similarity transformation. The homotopy analysis method (HAM) is employed to obtain the analytical approximations for flow velocity and temperature distributions of alumina-sodium alginate naofluid. The solution is found to be dependent on some parameters including the nanoparticle volume fraction, unsteadiness parameter, magnetic parameter, mixed convection parameter and the generalized prandtl number. A systematic study is carried out to illustrate the effects of these parameters on the velocity and temperature distributions. Also, the value of skin friction coefficient and local Nusselt number are compared with copper-sodium alginate and titania-sodium alginate nanofluids.

Unsteady Flow and Heat Transfer of a MHD Micropolar Fluid Over a Porous Stretching Sheet in the Presence of Thermal Radiation

2013 ◽  
Vol 29 (3) ◽  
pp. 559-568 ◽  
Author(s):  
G. C. Shit ◽  
R. Haldar ◽  
A. Sinha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Boundary Layer Flow ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Flow And Heat Transfer ◽  
Non Linear ◽  
Layer Flow

AbstractA non-linear analysis has been made to study the unsteady hydromagnetic boundary layer flow and heat transfer of a micropolar fluid over a stretching sheet embedded in a porous medium. The effects of thermal radiation in the boundary layer flow over a stretching sheet have also been investigated. The system of governing partial differential equations in the boundary layer have reduced to a system of non-linear ordinary differential equations using a suitable similarity transformation. The resulting non-linear coupled ordinary differential equations are solved numerically by using an implicit finite difference scheme. The numerical results concern with the axial velocity, micro-rotation component and temperature profiles as well as local skin-friction coefficient and the rate of heat transfer at the sheet. The study reveals that the unsteady parameter S has an increasing effect on the flow and heat transfer characteristics.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Induced by a Shrinking Sheet

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1175
Author(s):  
Nor Ain Azeany Mohd Nasir ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Differential Equations ◽  
Prandtl Number ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Magnetic Parameter ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer

The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of MATLAB software. The numerical results obtained are for different values of the magnetic parameter M, heat generation parameter Q, Prandtl number Pr and reciprocal of magnetic Prandtl number ε. The influences of these parameters on the flow and heat transfer characteristics are investigated and shown in tables and graphs. Two solutions are found for a certain rate of the shrinking strength. The stability of the solutions in the long run is determined, and shows that only one of them is stable. It is found that the skin friction coefficient f ″ ( 0 ) and the local Nusselt number − θ ′ ( 0 ) decrease as the magnetic parameter M increases. Further, the local Nusselt number increases as the heat generation increases.

Unsteady mixed convection flow at a three-dimensional stagnation point

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Amin Noor ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Unsteady Mixed Convection

Purpose This paper aims to probe the problem of an unsteady mixed convection stagnation point flow and heat transfer past a stationary surface in an incompressible viscous fluid numerically. Design/methodology/approach The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which is then solved numerically by a Runge – Kutta – Fehlberg method with shooting technique and a collocation method, namely, the bvp4c function. Findings The effects of the governing parameters on the fluid flow and heat transfer characteristics are illustrated in tables and figures. It is found that dual (upper and lower branch) solutions exist for both the cases of assisting and opposing flow situations. A stability analysis has also been conducted to determine the physical meaning and stability of the dual solutions. Practical implications This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans. Originality/value The case of suction on unsteady mixed convection flow at a three-dimensional stagnation point has not been studied before; hence, all generated numerical results are claimed to be novel.

scholarly journals Numerical Simulation of Transient Free Convection Flow and Heat Transfer in a Porous Medium

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Rajesh Sharma ◽  
Anuar Ishak
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Darcy Number ◽  
Convection Flow ◽  
Force Model ◽  
Moving Plate ◽  
Drag Forces ◽  
Flow And Heat Transfer ◽  
Momentum And Heat Transfer

The coupled momentum and heat transfer in unsteady, incompressible flow along a semi-infinite vertical porous moving plate adjacent to an isotropic porous medium with viscous dissipation effect are investigated. The Darcy-Forchheimer nonlinear drag force model which includes the effects of inertia drag forces is employed. The governing differential equations of the problem are transformed into a system of nondimensional differential equations which are solved numerically by the finite element method (FEM). The non-dimensional velocity and temperature profiles are presented for the influence of Darcy number, Forchheimer number, Grashof number, Eckert number, Prandtl number, plate velocity, and time. The Nusselt number is also evaluated and compared with finite difference method (FDM), which shows excellent agreement.

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.

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