Spectral Relaxation Method for Powell-Eyring Fluid Flow Past a Radially Stretching Heated Disk Surface in a Porous Medium

2018 ◽  
Vol 387 ◽  
pp. 575-586 ◽  
Author(s):  
K. Gangadhar ◽  
P.R. Sobhana Babu ◽  
Oluwole Daniel Makinde
Keyword(s):  
Porous Medium ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Slip Flow ◽  
Relaxation Method ◽  
Disk Surface ◽  
Skin Friction Coefficient ◽  
Nonlinear Boundary Value Problems ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

In this study we use a spectral relaxation method to investigate heat transfer in axisymmetric slip flow of a MHD Powell-Eyring fluid over a radially stretching surface embedded in porous medium with viscous dissipation. The transformed governing system of nonlinear differential equations was solved numerically using the spectral relaxation method that has been proposed for the solution of nonlinear boundary layer equations. Results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for the same values of the governing physical and fluid parameters. Validation of the results was reached by the comparison with limiting cases from previous studies in the literature. We show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to common numerical methods for solving nonlinear boundary value problems. We show that the convergence rate of the spectral relaxation method is significant improved by using the method in conjunction with the successive over - relaxation method.

On Spectral Relaxation Approach to Radiating Powell-Eyring Fluid Flow over a Stretching Disk with Newtonian Heating

2018 ◽  
Vol 387 ◽  
pp. 461-473 ◽  
Author(s):  
K. Gangadhar ◽  
D. Vijaya Kumar ◽  
S. Mohammed Ibrahim ◽  
Oluwole Daniel Makinde
Keyword(s):  
Boundary Layer ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Relaxation Method ◽  
Newtonian Heating ◽  
Nonlinear Boundary Value Problems ◽  
Local Skin ◽  
Boundary Layer Equations ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

In this study we use a new spectral relaxation method to investigate an axisymmetric law laminar boundary layer flow of a viscous incompressible non-Newtonian Eyring-Powell fluid and heat transfer over a heated disk with thermal radiation and Newtonian heating. The transformed boundary layer equations are solved numerically using the spectral relaxation method that has been proposed for the solution of nonlinear boundary layer equations. Numerical solutions are obtained for the local wall temperature, the local skin friction coefficient, as well as the velocity and temperature profiles. We show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to common numerical methods for solving nonlinear boundary value problems. We show that the convergence rate of the spectral relaxation method is significantly improved by using method in conjunction with the successive over-relaxation method. It is observed that CPU time is reduced in SOR method compare with SRM method.

Thermal Slip Flow of a Three-Dimensional Casson Fluid Embedded in a Porous Medium with Internal Heat Generation

2021 ◽  
Vol 10 (1) ◽  
pp. 58-66
Author(s):  
K. Gangadhar ◽  
M. Venkata Subba Rao ◽  
K. Venkata Ramana ◽  
Ch. Suresh Kumar ◽  
Ali J. Chamkha
Keyword(s):  
Skin Friction ◽  
Slip Flow ◽  
Three Dimensional ◽  
Internal Heat ◽  
Relaxation Method ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Newtonian Case ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

Present assessment is considered to analysis flow as well as heat characteristics of steady, thermal slip flow of three-dimensional Casson fluid embedded in a porous medium with internal heat generation. Geometry of the present analysis is linearly stretched surface. Later, all the PDEs corresponding to the study are altered to set of nonlinear equations ODEs by means of appropriate similarity transformations. An efficient numerical scheme of spectral relaxation method (SRM) is applied to solve the nonlinear ordinary system. Variations of Nusselt number, temperature, velocity, and local skin friction coefficient with fluid parameters exhibited by graphs and tables. Spectral relaxation method gives an exact convergence to the nonlinear boundary value problems compare with general methods. In this study, to improve the precision and accuracy of the SRM successive over-relaxation (SOR) strategy is utilized. Proposed method as well as outcomes is checked with the comparison. A sensible connection is acquired between the current outcomes and accessible outcomes in writing. Some of the observations are skin friction coefficient raises and velocities decreases by the magnetic field strength. Skin friction and Local Nusselt number at the surface is more pronounced for non-Newtonian case than that of Newtonian case.

scholarly journals Unsteady mixed convection flow through a permeable stretching flat surface with partial slip effects through MHD nanofluid using spectral relaxation method

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 323-334 ◽  
Author(s):  
Sami M. Ahamed ◽  
Sabyasachi Mondal ◽  
Precious Sibanda
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Flat Surface ◽  
Internal Heat ◽  
Relaxation Method ◽  
Skin Friction Coefficient ◽  
Partial Slip ◽  
Spectral Relaxation Method ◽  
Flow Through ◽  
Spectral Relaxation

AbstractAn unsteady, laminar, mixed convective stagnation point nanofluid flow through a permeable stretching flat surface using internal heat source or sink and partial slip is investigated. The effects of thermophoresis and Brownian motion parameters are revised on the traditional model of nanofluid for which nanofluid particle volume fraction is passively controlled on the boundary. Spectral relaxation method is applied here to solve the non-dimensional conservation equations. The results show the illustration of the impact of skin friction coefficient, different physical parameters, and the heat transfer rate. The nanofluid motion is enhanced with increase in the value of the internal heat sink or source. On the other hand, the rate of heat transfer on the stretching sheet and the skin friction coefficient are reduced by an increase in internal heat generation. This study further shows that the velocity slip increases with decrease in the rate of heat transfer. The outcome results are benchmarked with previously published results.

scholarly journals Hydromagnetic Stagnation-Point Flow towards a Radially Stretching Convectively Heated Disk

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
S. Shateyi ◽  
O. D. Makinde
Keyword(s):  
Stagnation Point ◽  
Numerical Solutions ◽  
Relaxation Method ◽  
Disk Surface ◽  
Stagnation Point Flow ◽  
Temperature Fields ◽  
Physical Parameters ◽  
Local Skin ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

The steady stagnation-point flow and heat transfer of an electrically conducted incompressible viscous fluid are extended to the case where the disk surface is convectively heated and radially stretching. The fluid is subjected to an external uniform magnetic field perpendicular to the plane of the disk. The governing momentum and energy balance equations give rise to nonlinear boundary value problem. Using a spectral relaxation method with a Chebyshev spectral collocation method, the numerical solutions are obtained over the entire range of the physical parameters. Emphasis has been laid to study the effects of viscous dissipation and Joule heating on the thermal boundary layer. Pertinent results on the effects of various thermophysical parameters on the velocity and temperature fields as well as local skin friction and local Nusselt number are discussed in detail and shown graphically and/or in tabular form.

scholarly journals Numerical Analysis of MHD Stagnation Point Flow Towards a Radially Stretching Convectively Heated Disk

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Stagnation Point ◽  
Numerical Solutions ◽  
Relaxation Method ◽  
Disk Surface ◽  
Stagnation Point Flow ◽  
Temperature Fields ◽  
Physical Parameters ◽  
Local Skin ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

The steady stagnation point flow and heat transferof an electrically conducting incompressible viscous fluid isextended to the case where the disk surface is convectivelyheated and radially stretching. The fluid is subjected to anexternal uniform magnetic field perpendicular to the planeof the disk. The governing momentum and energy balanceequations give rise to non-linear boundary value problem.Using a spectral relaxation method with a Chebyshev spectralcollocation method, the numerical solutions are obtained overthe entire range of the physical parameters. Emphasis hasbeen laid to study the effects of viscous dissipation and Jouleheating on the thermal boundary layer. Pertinent results on theeffects of various thermophysical parameters on the velocityand temperature fields as well as local skin friction and localNusselt number are discussed in detail and shown graphicallyand/or in tabular form.

scholarly journals A Spectral Relaxation Approach for Unsteady Boundary-Layer Flow and Heat Transfer of a Nanofluid over a Permeable Stretching/Shrinking Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
S. S. Motsa ◽  
P. Sibanda ◽  
J. M. Ngnotchouye ◽  
G. T. Marewo
Keyword(s):  
Numerical Algorithms ◽  
Relaxation Method ◽  
Coupled Systems ◽  
Shrinking Sheet ◽  
Nonlinear Boundary Value Problems ◽  
Flow And Heat Transfer ◽  
Highly Nonlinear ◽  
Spectral Relaxation Method ◽  
Layer Flow ◽  
Spectral Relaxation

This paper introduces two novel numerical algorithms for the efficient solution of coupled systems of nonlinear boundary value problems. The methods are benchmarked against existing methods by finding dual solutions of the highly nonlinear system of equations that model the flow of a viscoelastic liquid of Oldroyd-B type in a channel of infinite extent. The methods discussed here are the spectral relaxation method and spectral quasi-linearisation method. To verify the accuracy and efficiency of the proposed methods a comparative evaluation of the performance of the methods against established numerical techniques is given.

scholarly journals Numerical Analysis for the Synthesis of Biodiesel Using Spectral Relaxation Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Z. G. Makukula ◽  
S. S. Motsa ◽  
S. Shateyi
Keyword(s):  
Vegetable Oils ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Relaxation Method ◽  
Numerical Results ◽  
Reaction Rate Constants ◽  
Animal Fats ◽  
Alternative Diesel Fuel ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

Biodiesel is an alternative diesel fuel chemically defined as the mono-alkyl esters of long chain fatty acids derived from vegetable oils or animal fat. It is becoming more attractive as an alternative fuel due to the depleting fossil fuel resources. A mathematical model for the synthesis of biodiesel from vegetable oils and animal fats is presented in this study. Numerical solutions of the model are found using a spectral relaxation method. The method, originally developed for boundary value problems, is an iterative scheme based on the Chebyshev spectral collocation method developed by decoupling systems of equations using Gauss-Seidel type of techniques. The effects of the reaction rate constants and initial concentrations of the reactants on the amount of the final product are being investigated. The accuracy of the numerical results is validated by comparison with known analytical results and numerical results obtained usingode45, an efficient explicit 4th and 5th order Runge-Kutta method used to integrate both linear and nonlinear differential equations.

scholarly journals A Numerical Examination of an Unsteady Nonlinear MHD Flow in the Presence of Thermal Radiation and Heat Generation

2021 ◽  
Vol 26 (1) ◽  
pp. 1-17
Author(s):  
T.M. Agbaje ◽  
P.G.L. Leach
Keyword(s):  
Thermal Radiation ◽  
Perturbation Method ◽  
Heat Generation ◽  
Nonlinear Differential Equations ◽  
Mhd Flow ◽  
Relaxation Method ◽  
Generating Series ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation ◽  
Spectral Perturbation

AbstractIn this study, the spectral perturbation method and the spectral relaxation method are used to solve the nonlinear differential equations of an unsteady nonlinear MHD flow in the presence of thermal radiation and heat generation. The SPM is mainly based on series expansion, generating series approximation coupled with the Chebyshev spectral method. The numerical results generated using the spectral perturbation method were compared with those found in the literature, and the two results were in good agreement.

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