scholarly journals On Convective Dusty Flow Past a Vertical Stretching Sheet with Internal Heat Absorption

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Raj Nandkeolyar ◽  
Precious Sibanda
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Internal Heat ◽  
Transverse Magnetic ◽  
Convective Heating ◽  
Joule Dissipation ◽  
Highly Nonlinear ◽  
Layer Flow

The steady two-dimensional boundary layer flow of a viscous, incompressible, and electrically conducting dusty fluid past a vertical permeable stretching sheet under the influence of a transverse magnetic field with the viscous and Joule dissipation is investigated. The fluid particles are assumed to be heat absorbing and the temperature at the surface of the sheet is a result of convective heating. The governing nonlinear partial differential equations are transformed to a set of highly nonlinear coupled ordinary differential equations using a suitable similarity transformation and the resulting system is then solved numerically. It is found inter alia that the contributions of viscous and Joule dissipation in the flow are to increase the thickness of the thermal boundary layer.

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 of nanofluid over permeable stretching sheet with convective boundary conditions

2016 ◽  
Vol 20 (6) ◽  
pp. 1835-1845 ◽  
Author(s):  
Tasawar Hayat ◽  
Maria Imtiaz ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Mass Transfer Process ◽  
Convergent Series ◽  
Convective Boundary ◽  
Layer Flow ◽  
Type Boundary ◽  
Mhd Boundary Layer Flow

Analysis has been carried out for the magnetohydrodynamic (MHD) boundary layer flow of nanofluid. The flow is caused by a permeable stretching sheet. Convective type boundary conditions are employed in modeling the heat and mass transfer process. Appropriate transformations reduce the nonlinear partial differential equations to ordinary differential equations. The convergent series solutions are constructed. Graphical results of different parameters are discussed. The behaviors of Brownian motion and thermophoretic diffusion of nanoparticles have been examined. The dimensionless expressions of local Nusselt and local Sherwood numbers have been evaluated and discussed.

Flow Over a Stretching Sheet in a Dusty Fluid With Radiation Effect

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
G. K. Ramesh ◽  
B. J. Gireesha
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Radiation Effect ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Particle Interaction ◽  
Dusty Fluid ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Fifth Order

The radiation effect on a steady two-dimensional boundary layer flow of a dusty fluid over a stretching sheet is analyzed. The governing nonlinear partial differential equations have been transformed by a similarity transformation into a system of nonlinear ordinary differential equations and then solved numerically by applying Runge Kutta Fehlberg fourth-fifth order method (RKF45 method). The effect of fluid particle interaction parameter, Prandtl number, Eckert number, and radiation parameter on heat transfer characteristics in two different general cases, namely (1) the prescribed surface temperature (PST) and (2) the prescribed heat flux (PHF) are presented graphically and discussed. The rate of heat transfer is computed and tabulated for various values of the different parameters. Comparison of the obtained numerical results is made with previously published results.

scholarly journals Similarity Solutions for an Internal Heat Generation, Thermal Radiation and Free Convection Unsteady Boundary Layer Flow over a Vertical Plate

2016 ◽  
Vol 8 (3) ◽  
pp. 341-353 ◽  
Author(s):  
M. Y. Ali ◽  
N. M. R. Zahed ◽  
M. N. Uddin ◽  
M. J. Uddin
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Boundary Layer Flow ◽  
Vertical Plate ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Unsteady Boundary Layer ◽  
Layer Flow

The present paper deals with possible similarity solution of unsteady boundary layer flow over a vertical plate in the presence of internal heat generation, thermal radiation and buoyancy force. Under suitable similarity transformations, the non-linear partial differential equations are transformed into a set of ordinary differential equations. The transformed ordinary differential equations with boundary conditions are then solved numerically by using sixth order Runge-Kutta integration scheme. The effects of the governing parameters on the flow and thermal fields are investigated and shown graphically for various parameters in the velocity and the temperature distributions. The most essential case is discussed in this paper.

scholarly journals Heat transfer analysis of MHD flow due to unsteady bi-directional stretching sheet through porous space

2016 ◽  
Vol 20 (6) ◽  
pp. 1913-1925 ◽  
Author(s):  
Iftikhar Ahmad ◽  
Manzoor Ahmad ◽  
Muhammad Sajid
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Heat Transfer Analysis ◽  
Porous Space ◽  
Special Cases ◽  
Layer Flow

In this article unsteady three dimensional MHD boundary layer flow and heat transfer analysis with constant temperature (CT) and constant heat flux (CH) in a porous medium is considered. The boundary layer flow is governed by a bidirectional stretching sheet. Similarity transformations are used to transform the governing non-linear partial differential equations to ordinary differential equations. Analytical solutions are constructed using homotopy analysis method (HAM). Convergence analysis is also presented through tabular data. The quantities of interest are the velocity, temperature, skin friction coefficient and Nusselt number. The obtained results are validated by comparisons with previously published work in special cases. The results of this parametric study are shown graphically and the physical aspects of the problem are discussed.

scholarly journals Analysis of Boundary Layer Flow and Heat Transfer along a Stretching Cylinder in a Porous Medium

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Swati Mukhopadhyay
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Heat Equations ◽  
Stretching Cylinder ◽  
Highly Nonlinear ◽  
Layer Flow

This paper presents an axi-symmetric laminar boundary layer flow of a viscous incompressible fluid and heat transfer towards a stretching cylinder embedded in a porous medium. The partial differential equations corresponding to the momentum and heat equations are converted into highly nonlinear ordinary differential equations with the help of similarity transformations. Numerical solutions of these equations are obtained by shooting method. It is found that the velocity decreases with increasing permeability parameter. The skin friction as well as the heat transfer rate at the surface is larger for a cylinder compared to a flat plate.

scholarly journals MHD Boundary Layer Flow over a Stretching Sheet: A New Stochastic Method

2021 ◽  
Vol 2021 ◽  
pp. 1-26
Author(s):  
Hakeem Ullah ◽  
Imran Khan ◽  
Mehreen Fiza ◽  
Nawaf N. Hamadneh ◽  
M. Fayz-Al-Asad ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Magnetic Parameter ◽  
Industrial Applications ◽  
Deborah Number ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

In this study, a new computing model is developed using the strength of feed-forward neural networks with the Levenberg–Marquardt scheme-based backpropagation technique (NN-BLMS). It is used to find a solution for the nonlinear system obtained from the governing equations of the magnetohydrodyanmic (MHD) boundary layer flow over a stretching sheet. Moreover, the partial differential equations (PDEs) for the MHD boundary layer flow over a stretching sheet are converting into ordinary differential equations (ODEs) with the help of similarity transformation. A dataset for the proposed NN-BLMM-based model is generated at different scenarios by a variation of various embedding parameters: Deborah number β and magnetic parameter (M). The training (TR), testing (TS), and validation (VD) of the NN-BLMS model are evaluated in the generated scenarios to compare the obtained results with the reference results. For the fluidic system convergence analysis, a number of metrics, such as the mean square error (MSE), error histogram (EH), and regression (RG) plots, are utilized for measuring the effectiveness and performance of the NN-BLMS infrastructure model. The experiments showed that comparisons between the results of proposed model and the reference results match in terms of convergence up to E-02 to E-10. This proves the validity of the NN-BLMS model. Furthermore, the results demonstrated that there is a decrease in the thickness of the boundary layer by increasing the Deborah number and magnetic parameter. The importance of the experiment can be seen due to its industrial applications such as MHD power generation, MHD generators, and MHD pumps.

scholarly journals Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
P. G. Dlamini ◽  
S. S. Motsa ◽  
M. Khumalo
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Nonlinear Partial Differential Equations ◽  
Finite Difference Schemes ◽  
Unsteady Boundary Layer ◽  
Compact Finite Difference ◽  
Flow Problems ◽  
Layer Flow

We investigate the applicability of the compact finite difference relaxation method (CFDRM) in solving unsteady boundary layer flow problems modelled by nonlinear partial differential equations. The CFDRM utilizes the Gauss-Seidel approach of decoupling algebraic equations to linearize the governing equations and solve the resulting system of ordinary differential equations using compact finite difference schemes. The CFDRM has only been used to solve ordinary differential equations modelling boundary layer problems. This work extends its applications to nonlinear partial differential equations modelling unsteady boundary layer flows. The CFDRM is validated on two examples and the results are compared to results of the Keller-box method.

scholarly journals Influence of Thermal Radiation on Magnetohydrodynamic (MHD) Boundary Layer Flow of a Viscous Fluid Over an Exponentially Stretching Sheet

2016 ◽  
Vol 21 (3) ◽  
pp. 581-592 ◽  
Author(s):  
A.S. Idowu ◽  
S. Usman
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Fluid ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Exponentially Stretching Sheet ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Exponentially Stretching ◽  
Mhd Boundary Layer Flow

Abstract Radiation on a magnetohydrodynamic (MHD) boundary layer flow of a viscous fluid over an exponentially stretching sheet was considered together with its effects. The new technique of homotopy analysis method (nHAM) was used to obtain the convergent series expressions for velocity and temperature, where the governig system of partial differential equations was transformed into ordinary differential equations. The interpretation of these expressions is shown physically through graphs. We observed that the effects of the Prandtl and magnetic number act in opposite to each other on the temperature.

scholarly journals An efficient spectral solution for unsteady boundary-layer flow and heat transfer due to a stretching sheet

2017 ◽  
Vol 21 (5) ◽  
pp. 2167-2176 ◽  
Author(s):  
Fakhrodin Mohammadi ◽  
Mohamad Rashidi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Legendre Polynomials ◽  
Stretching Sheet ◽  
Unsteady Boundary Layer ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
Layer Flow

In this paper, an efficient spectral collocation method based on the shifted Legendre polynomials is applied to study the unsteady boundary-layer flow and heat transfer due to a stretching sheet. A similarity transformation is used to reduce the governing unsteady boundary-layer 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 analytical approximate solution of this system of non-linear ordinary 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.

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