scholarly journals MHD MIXED CONVECTION STAGNATION-POINT FLOW OF A MICROPOLAR FLUID IN A POROUS MEDIUM TOWARDS A HEATED STRETCHING SHEET WITH THERMAL RADIATION

2012 ◽  
Vol 17 (4) ◽  
pp. 498-518 ◽  
Author(s):  
Dulal Pal ◽  
Sewli Chatterjee
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Boundary Layer Equation ◽  
Physical Parameters ◽  
Ohmic Dissipation ◽  
Local Skin ◽  
Non Linear

The present investigation is concerned with the study of heat and mass transfer characteristics on MHD boundary layer flow of an electrically conducting micropolar fluid over a non-isothermal stretching sheet embedded in a porous medium of variable thermal conductivity by applying prescribed heat flux for the heating processes. The thermal boundary layer equation takes into account of Ohmic dissipation due to transverse magnetic and electric fields. The governing system of partial differential equations is transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed non-linear coupled differential equations are linearized by quasi-linearization method and then solved very efficiently by finite-difference method. Attention has been focused to study the effects of various physical parameters on velocity, temperature and concentration in the boundary layer. Numerical data for the local skin friction coefficient, surface temperature and surface solutal concentration have also been tabulated for various parametric conditions.

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.

Non-Uniform Heat Source/Sink and Joule Heating Effects on Chemically Radiative MHD Mixed Convective Flow of Micropolar Fluid over a Stretching Sheet in Porous Medium

2018 ◽  
Vol 388 ◽  
pp. 281-302 ◽  
Author(s):  
G. Charan Kumar ◽  
Konda Jayarami Reddy ◽  
Rama Krishna Konijeti ◽  
M. Narendradh Reddy
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Heat Source ◽  
Joule Heating ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Wall Friction ◽  
Dual Nature ◽  
Uniform Heat ◽  
Non Linear

This article describes the effects of Joule heating and chemical reaction on unsteady MHD mixed convective micropolar fluid over a stretching sheet in presence of radiation, non-uniform heat source and porous medium. The arising non-linear coupled partial differential equations are reduced to a set of coupled non-linear ordinary differential equations and then solved numerically by using the Runge– Kutta–Fehlberg fourth–fifth order method along shooting technique. The graphical and tabular results elucidate the influence of different non-dimensional governing parameters on the velocity, temperature and concentration fields along with the wall friction, local Nusselt and Sherwood numbers. We found the dual nature of the solutions for suction and injection cases. A good agreement of the present results has been observed by comparing with the existing literature results.

scholarly journals Convection heat and mass transfer in a hydromagnetic flow of a micropolar fluid over a porous medium

2014 ◽  
Vol 41 (2) ◽  
pp. 93-117
Author(s):  
B.I. Olajuwon ◽  
J.I. Oahimire ◽  
M.A. Waheed
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Micropolar Fluid ◽  
Perturbation Technique ◽  
Skin Friction Coefficient ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

This study presents a mathematical analysis of a hydromagnetic boundary layer flow, heat and mass transfer characteristics on steady twodimensional flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with uniform magnetic field in the presence of thermal radiation. The governing system of partial differential equations is first transformed into a system of non- linear ordinary differential equation using the usual similarity transformation. The resulting coupled non-linear ordinary differential equations are then solved using perturbation technique. With the help of graphs, the effects of the various important parameters entering into the problem on the velocity, temperature and concentration fields within the boundary layer are separately discussed. The effects of the pertinent parameters on the wall temperature, wall solutal concentration, skin friction coefficient and the rate of heat and mass transfer are presented numerically in tabular form. The results obtained showed that these parameters have significant influence on the flow.

scholarly journals An Unsteady Flow and Melting Heat Transfer of a Nanofluid Over a Stretching Sheet Embedded in a Porous Medium

2019 ◽  
Vol 24 (2) ◽  
pp. 245-258 ◽  
Author(s):  
K. Ganesh Kumar ◽  
B.J. Gireesha ◽  
N.G. Rudraswamy ◽  
M.R. Krishnamurthy
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Unsteady Flow ◽  
Stretching Sheet ◽  
Physical Parameters ◽  
Local Skin ◽  
Melting Heat ◽  
Linear Ordinary Differential Equations ◽  
Melting Heat Transfer ◽  
Non Linear

Abstract An unsteady flow and melting heat transfer of a nanofluid over a stretching sheet was numerically studied by considering the effect of chemical reaction and thermal radiation. The governing non-linear partial differential equations describing the flow problem are reduced to a system of non-linear ordinary differential equations using the similarity transformations and solved numerically using the Runge–Kutta–Fehlberg fourth–fifth order method. Numerical results for concentration, temperature and velocity profiles are shown graphically and discussed for different physical parameters. Effect of pertinent parameters on momentum, temperature and concentration profiles along with local Sherwood number, local skin-friction coefficient and local Nusselt number are well tabulated and discussed.

An Initial Value Method for the Solution of a Class of Nonlinear Equations in Fluid Mechanics

1970 ◽  
Vol 92 (3) ◽  
pp. 503-508 ◽  
Author(s):  
T. Y. Na
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Porous Medium ◽  
Fluid Mechanics ◽  
Boundary Layer Equation ◽  
Physical Parameters ◽  
Point Boundary ◽  
Trial And Error ◽  
Initial Value ◽  
Blasius Boundary Layer

An initial value method is introduced in this paper for the solution of a class of nonlinear two-point boundary value problems. The method can be applied to the class of equations where certain physical parameters appear either in the differential equation or in the boundary conditions or both. Application of this method to two problems in Fluid Mechanics, namely, Blasius’ boundary layer equation with suction (or blowing) and/or slip and the unsteady flow of a gas through a porous medium, are presented as illustrations of this method. The trial-and-error process usually required for the solution of such equations is eliminated.

scholarly journals Numerical study of heat transfer of a micropolar fluid through a porous medium with radiation

2018 ◽  
Vol 22 (1 Part B) ◽  
pp. 557-565 ◽  
Author(s):  
Fakhrodin Mohammadi ◽  
Mohammad Rashidi
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Collocation Method ◽  
Micropolar Fluid ◽  
Legendre Polynomials ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Shifted Legendre Polynomials ◽  
Non Linear

An efficient Spectral Collocation method based on the shifted Legendre polynomials was applied to get solution of heat transfer of a micropolar fluid through a porous medium with radiation. A similarity transformation is applied to convert the governing equations to a system of non-linear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of derivative are used for producing an approximate solution for this system of non-linear differential equations. The main advantage of the proposed method is that the need for guessing and correcting the initial values during the solution procedure is eliminated and a stable solution with good accuracy can be obtained by using the given boundary conditions in the problem. A very good agreement is observed between the obtained results by the proposed Spectral Collocation method and those of previously published ones.

NATURAL CONVECTION BOUNDARY LAYER FLOW ALONG A SPHERE EMBEDDED IN A POROUS MEDIUM FILLED WITH A NANOFLUID

2014 ◽  
Vol 44 (2) ◽  
pp. 149-157
Author(s):  
A. M. RASHAD
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Extended Model ◽  
Local Skin ◽  
Layer Flow

 A boundary-layer analysis is presented for the natural convec tion boundary layer flow about a sphere embedded in a porous medium filled with a nanofluid using Brinkman-ForchheimerDarcy extended model. The model used for the nanofluid incorporates the ef fects of Brownian motion and thermophoresis. The governing partial differential equa tions are transformed into a set of nonsimilar equations and solved numerically by an efficient implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity, temperature, and nanoparticles volume fraction profiles as well as the local skin-friction coefficient, local Nusselt and Sherwood numbers is illustrated graphically to show interesting features of the solutions.

Entropy Generation on Maxwell Fluid Flow Past an Inclined Stretching Plate with Slip and Convective Surface Conditon: Darcy-Forchheimer Model

2019 ◽  
Vol 26 ◽  
pp. 62-83
Author(s):  
Tunde Abdulkadir Yusuf ◽  
Jacob Abiodun Gbadeyan
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Entropy Generation ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study the effect of entropy generation on two dimensional magnetohydrodynamic (MHD) flow of a Maxwell fluid over an inclined stretching sheet embedded in a non-Darcian porous medium with velocity slip and convective boundary condition is investigated. Darcy-Forchheimer based model was employed to describe the flow in the porous medium. The non-linear thermal radiation is also taken into account. Similarity transformation is used to convert the non-linear partial differential equations to a system of non-linear ordinary differential equations. The resulting transformed equations are then solved using the Homotopy analysis method (HAM). Influence of various physical parameters on the dimensionless velocity profile, temperature profile and entropy generation are shown graphically and discussed in detail while the effects of these physical parameters on velocity gradient and temperature gradient are aided with the help of Table. Furthermore, comparison of some limiting cases of this model was made with existing results. The results obtained are found to be in good agreement with previously published results. Moreover, increase in local inertial coefficient parameter is found to decrease the entropy generation rate.

scholarly journals Computational study of unsteady couple stress magnetic nanofluid flow from a stretching sheet with Ohmic dissipation

2019 ◽  
Vol 233 (2-4) ◽  
pp. 49-63 ◽  
Author(s):  
Mahesh Kumar ◽  
G Janardhana Reddy ◽  
N Naresh Kumar ◽  
O Anwar Bég
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Couple Stress ◽  
Stretching Sheet ◽  
Magnetic Parameter ◽  
Aluminium Oxide ◽  
Ohmic Dissipation ◽  
Non Linear ◽  
Layer Flow ◽  
Sheet Stretching

To provide a deeper insight of the transport phenomena inherent to the manufacturing of magnetic nano-polymer materials, in the present work a mathematical model is developed for time-dependent hydromagnetic rheological nano-polymer boundary layer flow and heat transfer over a stretching sheet in the presence of a transverse static magnetic field. Joule heating (Ohmic dissipation) and viscous heating effects are included since these phenomena arise frequently in magnetic materials processing. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. The Tiwari–Das nanoscale model is adopted which permits different nanoparticles to be simulated (in this article, both copper–water and aluminium oxide–water nanofluids are considered). Similarity transformations are utilized to convert the governing partial differential conservation equations into a system of coupled, non-linear ordinary differential equations with appropriate wall and free stream boundary conditions. The shooting technique is used to solve the reduced non-linear coupled ordinary differential boundary value problem via MATLAB symbolic software. Validation with published results from the literature is included for the special cases of non-dissipative and Newtonian nanofluid flows. Fluid velocity and temperature profiles for both copper and aluminium oxide (Al2O3) nanofluids are observed to be enhanced with greater non-Newtonian couple stress parameter and magnetic parameter, whereas the opposite trend is computed with greater values of unsteadiness parameter. The boundary layer flow is accelerated with increasing buoyancy parameter, elastic sheet stretching parameter and convection parameter. Temperatures are generally increased with greater couple stress rheological parameter and are consistently higher for the aluminium oxide nanoparticle case. Temperatures are also boosted with magnetic parameter and exhibit an overshoot near the wall when magnetic parameter exceeds unity (magnetic force exceeds viscous force). A decrease in temperatures is induced with increasing sheet stretching parameter. Increasing Eckert number elevates temperatures considerably. With greater nanoparticle volume fraction, both skin friction and Nusselt number are elevated, and copper nanoparticles achieve higher magnitudes than aluminium oxide.

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