Effects of Suction and Freestream Velocity on a Hydromagnetic Stagnation-Point Flow and Heat Transport in a Newtonian Fluid Toward a Stretching Sheet

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
P. G. Siddheshwar ◽  
N. Meenakshi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Transport ◽  
Newtonian Fluid ◽  
Stretching Sheet ◽  
Forced Flow ◽  
Stream Velocity ◽  
Freestream Velocity ◽  
Exponential Order ◽  
Order Surface

Forced flow of an electrically conducting Newtonian fluid due to an exponentially stretching sheet is studied numerically. Free stream velocity is present and so is suction at the sheet. The governing coupled, nonlinear, partial differential equations of flow and heat transfer are converted into coupled, nonlinear, ordinary differential equations by similarity transformation and are solved numerically using shooting method, and curve fitting on the data is done by differential transform method together with Padé approximation. Prescribed exponential order surface temperature (PEST) and prescribed exponential order surface heat flux are considered for investigation of heat transfer related quantities. The influence of Chandrasekhar number, suction/injection parameter, and freestream parameter on heat transport is presented and discussed. Coefficient of friction and heat transport is also evaluated in the study. The results are of interest in extrusions and such other processes.

Stagnation-Point Flow and Heat Transfer of a Casson Fluid towards a Stretching Sheet

2012 ◽  
Vol 67 (1-2) ◽  
pp. 70-76 ◽  
Author(s):  
Meraj Mustafa ◽  
Tasawar Hayat ◽  
Pop Ioan ◽  
Awatif Hendi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Analytic Solutions ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Stream Velocity ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis

This article reports the flow of a Casson fluid in the region of stagnation-point towards a stretching sheet. The characteristics of heat transfer with viscous dissipation are also analyzed. The partial differential equations representing the flow and heat transfer of the Casson fluid are reduced to ordinary differential equations through suitable transformations. The flow is therefore governed by the Casson fluid parameter β, the ratio of the free stream velocity to the velocity of the stretching sheet a=c, the Prandtl number Pr, and the Eckert number Ec. The analytic solutions in the whole spatial domain have been computed by the homotopy analysis method (HAM). The dimensionless expressions for the skin friction coefficient and the local Nusselt number have been calculated and discussed.

Stagnation-Point Flow over an Exponentially Shrinking/Stretching Sheet

2011 ◽  
Vol 66 (12) ◽  
pp. 705-711 ◽  
Author(s):  
Sin Wei Wong ◽  
Abu Omar Awang ◽  
Anuar Ishak
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Free Stream ◽  
Stagnation Point Flow ◽  
Stream Velocity ◽  
Heat Transfer Characteristics ◽  
Keller Box Method ◽  
Flow And Heat Transfer ◽  
Box Method

The steady two-dimensional stagnation-point flow of an incompressible viscous fluid over an exponentially shrinking/stretching sheet is studied. The shrinking/stretching velocity, the free stream velocity, and the surface temperature are assumed to vary in a power-law form with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations before being solved numerically by a finite difference scheme known as the Keller-box method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique.

Heat transfer of three-dimensional micropolar fluid on a Riga plate

2020 ◽  
Vol 98 (1) ◽  
pp. 32-38 ◽  
Author(s):  
S. Nadeem ◽  
M.Y. Malik ◽  
Nadeem Abbas
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Surface Temperature ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Nonlinear Ordinary Differential Equations ◽  
Exponential Order ◽  
Riga Plate

In this article, we deal with prescribed exponential surface temperature and prescribed exponential heat flux due to micropolar fluids flow on a Riga plate. The flow is induced through an exponentially stretching surface within the time-dependent thermal conductivity. Analysis is performed inside the heat transfer. In our study, two cases are discussed here, namely prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). The governing systems of the nonlinear partial differential equations are converted into nonlinear ordinary differential equations using appropriate similarity transformations and boundary layer approach. The reduced systems of nonlinear ordinary differential equations are solved numerically with the help of bvp4c. The significant results are shown in tables and graphs. The variation due to modified Hartman number M is observed in θ (PEST) and [Formula: see text] (PEHF). θ and [Formula: see text] are also reduced for higher values of the radiation parameter Tr. Obtained results are compared with results from the literature.

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 Triple Solutions of Carreau Thin Film Flow with Thermocapillarity and Injection on an Unsteady Stretching Sheet

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3177 ◽  
Author(s):  
Kohilavani Naganthran ◽  
Ishak Hashim ◽  
Roslinda Nazar
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Differential Equations ◽  
Film Thickness ◽  
Stretching Sheet ◽  
Film Flow ◽  
Problem Solver ◽  
Thin Film Flow ◽  
Unsteady Stretching Sheet ◽  
Negative Film

Thin films and coatings which have a high demand in a variety of industries—such as manufacturing, optics, and photonics—need regular improvement to sustain industrial productivity. Thus, the present work examined the problem of the Carreau thin film flow and heat transfer with the influence of thermocapillarity over an unsteady stretching sheet, numerically. The sheet is permeable, and there is an injection effect at the surface of the stretching sheet. The similarity transformation reduced the partial differential equations into a system of ordinary differential equations which is then solved numerically by the MATLAB boundary value problem solver bvp4c. The more substantial effect of injection was found to be the reduction of the film thickness at the free surface and development of a better rate of convective heat transfer. However, the increment in the thermocapillarity number thickens the film, reduces the drag force, and weakens the rate of heat transfer past the stretching sheet. The triple solutions are identified when the governing parameters vary, but two of the solutions gave negative film thickness. Detecting solutions with the most negative film thickness is essential because it implies the interruption in the laminar flow over the stretching sheet, which then affects the thin film growing process.

scholarly journals Analysis of Magnetic Properties of Nano-Particles Due to a Magnetic Dipole in Micropolar Fluid Flow over a Stretching Sheet

Coatings ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 170 ◽  
Author(s):  
Liaqat Ali ◽  
Xiaomin Liu ◽  
Bagh Ali ◽  
Saima Mujeed ◽  
Sohaib Abdal ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Differential Equations ◽  
Magnetic Dipole ◽  
Stretching Sheet ◽  
Nano Particles ◽  
Boundary Parameter ◽  
The Impact

This article explores the impact of a magnetic dipole on the heat transfer phenomena of different nano-particles Fe (ferromagnetic) and Fe3O4 (Ferrimagnetic) dispersed in a base fluid ( 60 % water + 40 % ethylene glycol) on micro-polar fluid flow over a stretching sheet. A magnetic dipole in the presence of the ferrities of nano-particles plays an important role in controlling the thermal and momentum boundary layers. The use of magnetic nano-particles is to control the flow and heat transfer process through an external magnetic field. The governing system of partial differential equations is transformed into a system of coupled nonlinear ordinary differential equations by using appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The impact of different physical parameters on the velocity, the temperature, the Nusselt number, and the skin friction coefficient is shown. The velocity profile decreases in the order Fe (ferromagnetic fluid) and Fe3O4 (ferrimagnetic fluid). Furthermore, it was observed that the Nusselt number is decreasing with the increasing values of boundary parameter ( δ ) , while there is controversy with respect to the increasing values of radiation parameter ( N ) . Additionally, it was observed that the ferromagnetic case gained maximum thermal conductivity, as compared to ferrimagnetic case. In the end, the convergence of the finite element solution was observed; the calculations were found by reducing the mesh size.

MHD mixed convection stagnation-point flow of a viscoelastic fluid towards a stretching sheet in a porous medium with heat generation and radiation

2015 ◽  
Vol 93 (5) ◽  
pp. 532-541 ◽  
Author(s):  
M. Modather M. Abdou ◽  
E. Roshdy EL-Zahar ◽  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Viscoelastic Fluid ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Heat Transfer Characteristics

An analysis was carried out to study the effect of thermal radiation on magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid near the stagnation point of a vertical stretching sheet in a porous medium with internal heat generation–absorption. The flow is generated because of linear stretching of the sheet and influenced by the uniform magnetic field that is applied horizontally in the flow region. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically using an accurate implicit finite difference scheme. A comparison of the obtained results with previously published numerical results is done and the results are found to be in good agreement. The effects of the viscoelastic fluid parameter, magnetic field parameter, nonuniform heat source–sink, and the thermal radiation parameter on the heat transfer characteristics are presented graphically and discussed. The values of the skin friction coefficient and the local Nusselt number are tabulated for both cases of assisting and opposing flows.

Stagnation Point Flow through a Porous Medium towards a Radially Stretching Sheet in the Presence of Uniform Suction or Injection and Heat Generation

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Hazem Ali Attia ◽  
Karem Mahmoud Ewis ◽  
Mostafa A. M. Abdeen
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Stagnation Point ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Stagnation Point Flow ◽  
Uniform Suction ◽  
Flow Through ◽  
Energy Equations

An analysis is made of the steady laminar axisymmetric stagnation point flow of an incompressible viscous fluid in a porous medium impinging on a permeable radially stretching sheet with heat generation or absorption. A uniform suction or blowing is applied normal to the plate which is maintained at a constant temperature. Similarity transformation is used to transform the governing partial differential equations to ordinary differential equations. The finite difference method and generalized Thomas algorithm are used to solve the governing nonlinear momentum and energy equations. The effects of the uniform suction/blowing velocity, the stretching parameter and the heat generation/absorption coefficient on both the flow field and heat transfer are presented and discussed. The results indicate that increasing the stretching parameter or the suction/blowing velocity decreases both the velocity and thermal boundary layer thicknesses. The effect of the stretching parameter on the velocity components is more apparent for suction than blowing while its effect on the temperature and rate of heat transfer at the wall is clearer in the case of blowing than suction.

scholarly journals Effect of radiation and porosity parameter on magnetohydrodynamic flow due to stretching sheet in porous media

2011 ◽  
Vol 15 (2) ◽  
pp. 517-526 ◽  
Author(s):  
Phool Singh ◽  
Tomer Singh ◽  
Sandeep Kumar ◽  
Deepa Sinha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Stretching Sheet ◽  
Transverse Magnetic ◽  
Stream Velocity ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Porosity Parameter ◽  
Volumetric Rate ◽  
Two Dimensional Flow

An analysis is made for the steady two-dimensional flow of a viscous incompressible electrically conducting fluid in the vicinity of a stagnation point on a stretching sheet. Fluid is considered in a porous medium under the influence of (i)transverse magnetic field, (ii)volumetric rate of heat generation/absorption in the presence of radiation effect. Rosseland approximation is used to model the radiative heat transfer. The governing boundary layer equations are transformed to ordinary differential equations by taking suitable similarity variables. In the present reported work the effect of porosity parameter, radiation parameter, magnetic field parameter and the Prandtl number on flow and heat transfer characteristics have been discussed. Variation of above discussed parameters with the ratio of free stream velocity parameter to stretching sheet parameter have been graphically represented.

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