scholarly journals Successive Linearization Analysis of the Effects of Partial Slip, Thermal Diffusion, and Diffusion-Thermo on Steady MHD Convective Flow due to a Rotating Disk

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
S. S. Motsa ◽  
S. Shateyi
Keyword(s):  
Thermal Diffusion ◽  
Nonlinear Boundary ◽  
Rotating Disk ◽  
Linearization Method ◽  
Partial Slip ◽  
Similarity Transformations ◽  
Highly Nonlinear ◽  
Successive Linearization Method ◽  
And Diffusion ◽  
The Magnetic Field

We proposed a general formulation of the successive linearization method for solving highly nonlinear boundary value problem arising in rotating disk flow. The problem was studied under the effects of partial slip, thermal diffusion, and diffusion-thermo. The governing fundamental conservation equations of mass, momentum, angular momentum, energy, and concentration are transformed into a system of ordinary differential equations by means of similarity transformations. A parametric study illustrating the influence of the magnetic field, slip factor, Eckert number, Dufour and Soret numbers was carried out.

Dissipative effects on a chemically and thermally radiative heat fluid flow past a shrinking porous sheet

2020 ◽  
pp. 1-14
Author(s):  
A. Shahid ◽  
M. Ali Abbas ◽  
H.L. Huang ◽  
S.R. Mishra ◽  
M.M. Bhatti
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Linearization Method ◽  
Surface Drag ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Dissipative Effects ◽  
Successive Linearization Method

The present study analyses the dissipative influence into an unsteady electrically conducting fluid flow embedded in a pervious medium over a shrinkable sheet. The behavior of thermal radiation and chemical reactions are also contemplated. The governing partial differential equations are reformed to ordinary differential equations by operating similarity transformations. The numerical outcomes for the arising non-linear boundary value problem are determined by implementing the Successive linearization method (SLM) via Matlab software. The velocity, temperature, and concentration magnitudes for distant values of the governing parametric quantities are conferred, and their conduct is debated via graphical curves. The surface drag coefficient increases, whereas the local Nusselt number and Sherwood number decreases for enhancing unsteadiness parameter across suction parameter. Moreover, the magnetic and suction parameters accelerate velocity magnitudes while by raising porosity parameter, velocity decelerates. Larger numeric of thermal radiation parameter and Eckert number accelerates the temperature profile while by enhancing Prandtl number it decelerates. Schmidt number and chemical reaction parameters slowdowns the concentration distribution, and the chemical reaction parameter influences on the point of chemical reaction that benefits the interface mass transfer. It is expected that the current achieved results will furnish fruitful knowledge in industrious utilities.

scholarly journals Effect of magnetic field, heat generation and absorption on nanofluid flow over a nonlinear stretching sheet

2020 ◽  
Vol 11 ◽  
pp. 976-990
Author(s):  
Santoshi Misra ◽  
Govardhan Kamatam
Keyword(s):  
Magnetic Field ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Partial Slip ◽  
Nanoparticle Suspension ◽  
Dimensionless Parameters ◽  
Similarity Transformations ◽  
Highly Nonlinear ◽  
Layer Flow ◽  
The Impact

The study of magnetohydrodynamic flow of a nanoparticle suspension under the influence of varied dimensionless parameters has been the focus of research in contemporary times. This work models the effect of magnetic field, heat generation and absorption parameter in a steady, laminar, two-dimensional boundary layer flow of a nanofluid over a permeable stretching sheet at a given surface temperature and partial slip. The highly nonlinear governing equations are solved numerically using similarity transformations with suitable boundary conditions and converted to ordinary differential equations. A computational model is setup using FORTRAN, where a relevant Adam’s predictor–corrector method is employed to solve the equations. The impact of the dimensionless parameters, including the Brownian motion, thermophoresis, magnetic field, heat generation and absorption parameters, on the velocity, temperature and nanoparticle concentration of fluid flow are analysed systematically.

scholarly journals A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
S. S. Motsa
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Nonlinear Boundary ◽  
Linearization Method ◽  
Variable Boundary ◽  
Flow Problems ◽  
Local Linearization ◽  
Highly Nonlinear ◽  
Layer Flow ◽  
Local Linearization Method

We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM), is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

scholarly journals On the Successive Linearisation Approach to the Flow of Reactive Third-Grade Liquid in a Channel with Isothermal Walls

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
S. S. Motsa ◽  
O. D. Makinde ◽  
S. Shateyi
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Linearization Method ◽  
Third Grade ◽  
Efficient Technique ◽  
Analytical Scheme ◽  
Highly Nonlinear ◽  
Successive Linearization Method ◽  
Modeling Flow

The nonlinear differential equations modeling flow of a reactive third-grade liquid between two parallel isothermal plates is investigated using a novel hybrid of numerical-analytical scheme known as the successive linearization method (SLM). Numerical and graphical results obtained show excellence in agreement with the earlier results reported in the literature. A comparison with numerical results generated using the inbuilt MATLAB boundary value solverbvp4cdemonstrates that the new SLM approach is a very efficient technique for tackling highly nonlinear differential equations of the type discussed in this paper.

scholarly journals Natural Convection of Viscoelastic Fluid from a Cone Embedded in a Porous Medium with Viscous Dissipation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Gilbert Makanda ◽  
O. D. Makinde ◽  
Precious Sibanda
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Differential Equations ◽  
Surface Temperature ◽  
Viscoelastic Fluid ◽  
Fourth Order ◽  
Linearization Method ◽  
Similarity Transformations ◽  
Fluid Properties ◽  
Successive Linearization Method

We study natural convection from a downward pointing cone in a viscoelastic fluid embedded in a porous medium. The fluid properties are numerically computed for different viscoelastic, porosity, Prandtl and Eckert numbers. The governing partial differential equations are converted to a system of fourth order ordinary differential equations using the similarity transformations and then solved together by using the successive linearization method (SLM). Many studies have been carried out on natural convection from a cone but they did not consider a cone embedded in a porous medium with linear surface temperature. The results in this work are validated by the comparison with other authors.

scholarly journals The Effectiveness of Mass Transfer in the MHD Upper-Convected Maxwell Fluid Flow on a Stretched Porous Sheet near Stagnation Point: A Numerical Investigation

Inventions ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 64
Author(s):  
Anwar Shahid
Keyword(s):  
Mass Transfer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Maxwell Fluid ◽  
Linearization Method ◽  
The Novel ◽  
Governing Equations ◽  
Similarity Transformations ◽  
Successive Linearization Method ◽  
Linear Boundary Value Problem

The present inquiry studies the influence of mass transfer in magnetohydrodynamics (MHD) upper-convected Maxwell (UCM) fluid flow on a stretchable, porous subsurface. The governing partial differential equations for the flow problem are reformed to ordinary differential equations through similarity transformations. The numerical outcomes for the arising non-linear boundary value problem are determined by implementing the successive linearization method (SLM) via Matlab software. The accuracy of the SLM is confirmed through known methods, and convergence analysis is also presented. The graphical behavior for all the parametric quantities in the governing equations across the velocity and concentration magnitudes, as well as the skin friction and Sherwood number, is presented and debated in detail. A comparability inquiry of the novel proposed technique, along with the preceding explored literature, is also provided. It is expected that the current achieved results will furnish fruitful knowledge in industrious utilities and correlate with the prevailing literature.

scholarly journals Convective Hydromagentic Slip Flow with Variable Properties Due to a Porous Rotating Disk

2010 ◽  
Vol 15 ◽  
pp. 55 ◽  
Author(s):  
Mohammad M. Rahman
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Slip Flow ◽  
Rotating Disk ◽  
Heat Transfer Characteristics ◽  
Temperature Dependent ◽  
Transfer Characteristics ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Highly Nonlinear

In this paper we investigate convective heat transfer characteristics of steady hydromagnetic slip flow over a porous rotating disk taken into account the temperature dependent density, viscosity and thermal conductivity  in the presence of  Hall current, viscous dissipation and Joule heating. Using von-Karman similarity transformations we reduce the governing equations for flow and heat transfer into a system of ordinary differential equations which are highly nonlinear and coupled. The resulting nondimensional equations are solved numerically by applying Nachtsheim-Swigert iteration technique. The results show that when modeling a thermal boundary layer, with temperature dependent fluid properties, consideration of Prandtl number as constant within the boundary layer, produces unrealistic results.   therefore  Therefore it must be treated as variable throughout the boundary layer. Results also show that the slip factor significantly controls the flow and heat transfer characteristics.  

Thermal Diffusion and Diffusion Thermo Effects on Peristaltic Flow of Sisko Fluid in Nonuniform Channel With Dissipative Heating

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Sharidan Shafie ◽  
Obaid Ullah Mehmood ◽  
Norzieha Mustapha
Keyword(s):  
Thermal Diffusion ◽  
Perturbation Technique ◽  
Shear Thickening ◽  
Dissipative Heating ◽  
Peristaltic Flow ◽  
Sisko Fluid ◽  
Dissipative Heat ◽  
Highly Nonlinear ◽  
Axial Pressure Gradient ◽  
And Diffusion

This investigation deals with thermal diffusion and diffusion thermo effects on the peristaltic flow of a Sisko fluid in an asymmetric channel. The mode of dissipative heat transfer is taken into account with nonuniform wall temperatures. Long wavelength approximation is utilized. Solutions for the highly nonlinear coupled governing equations involving power law index as an exponent are derived by employing the perturbation technique in a Sisko fluid parameter. Closed form solutions for the stream function, the axial pressure gradient, the skin friction, the temperature, the concentration, and the Nusselt number are presented. Effects of various interesting parameters are graphically interpreted. A comparative study between Newtonian, shear thinning, and shear thickening fluids is also presented. Comparison with published results for the case of viscous fluid is observed in good agreement.

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