Soret and Dufour effects on unsteady Casson magneto-nanofluid flow over an inclined plate embedded in a porous medium

2019 ◽  
Vol 16 (2) ◽  
pp. 260-274 ◽  
Author(s):  
Olumide Falodun Bidemi ◽  
M.S. Sami Ahamed
Keyword(s):  
Porous Medium ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Relaxation Method ◽  
Inclined Plate ◽  
Nanofluid Flow ◽  
Content Type ◽  
Non Linear ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

PurposeThe purpose of this paper is to consider a two-dimensional unsteady Casson magneto-nanfluid flow over an inclined plate embedded in a porous medium. The novelty of the present study is to investigate the effects of Soret–Dufour on unsteady magneto-nanofluid flow.Design/methodology/approachAppropriate similarity transformations are used to convert the governing non-linear partial differential equations into coupled non-linear dimensionless partial differential equations. The transformed equations are then solved using spectral relaxation method.FindingsThe effects of controlling parameters on flow profiles is discussed and depicted with the aid of graphs. Results show that as the non-Newtonian Casson nanofluid parameter increases, the fluid velocity decreases. It is found that the Soret parameter enhance the temperature profile, while Dufour parameter decreases the concentration profile close to the wall.Originality/valueThe novelty of this paper is to consider the combined effects of both Soret and Dufour on unsteady Casson magneto-nanofluid flow. The present model is in an inclined plate embedded in a porous medium which to the best of our knowledge has not been considered in the past. The applied magnetic field gives rise to an opposing force which slows the motion of the fluid. A newly developed spectral method known as spectral relaxation method (SRM) is used in solving the modeled equations. SRM is an iterative method that employ the Gauss–Seidel approach in solving both linear and non-linear differential equations. SRM is found to be effective and accurate.

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.

scholarly journals Slip Velocity and Temperature Jump on Dissipative CASSON Fluid with CATTANEO-CHRISTOV Heat Flux Model: Spectral Relaxation Method

2018 ◽  
Vol 7 (4.10) ◽  
pp. 240
Author(s):  
K. Gangadhar ◽  
K. V. Ramana ◽  
T. Kannan ◽  
B. Rushi Kumar
Keyword(s):  
Heat Flux ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Thermal Relaxation ◽  
Relaxation Method ◽  
Casson Fluid ◽  
Fluid Temperature ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

A numerical analysis is performed for investigating the slip flow of a viscous dissipative Casson fluid towards a stretching sheet with Cattaneo-Christov heat flux and variable viscosity. The nonlinear partial differential equations are transformed with appropriate similarity variables into a system of nonlinear ordinary differential equations. Numerical solutions are carried out by using efficient Spectral relaxation method. Notable accuracy of the present results has been obtained with previous results in a limiting sense from the literature. It is found that thermal relaxation time has an inverse relationship with the fluid temperature. Interestingly, the fluid velocity is gradually decreasing with higher values of slip factor.   

A modified method for solving non-linear time and space fractional partial differential equations

2019 ◽  
Vol 36 (7) ◽  
pp. 2162-2178
Author(s):  
Umer Saeed ◽  
Muhammad Umair
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Linear Time ◽  
Differential Quadrature Method ◽  
Fractional Partial Differential Equations ◽  
Lagrange Polynomial ◽  
Time And Space ◽  
Partial Differential ◽  
Content Type ◽  
Non Linear

Purpose The purpose of the paper is to extend the differential quadrature method (DQM) for solving time and space fractional non-linear partial differential equations on a semi-infinite domain. Design/methodology/approach The proposed method is the combination of the Legendre polynomials and differential quadrature method. The authors derived and constructed the new operational matrices for the fractional derivatives, which are used for the solutions of non-linear time and space fractional partial differential equations. Findings The fractional derivative of Lagrange polynomial is a big hurdle in classical DQM. To overcome this problem, the authors represent the Lagrange polynomial in terms of shifted Legendre polynomial. They construct a transformation matrix which transforms the Lagrange polynomial into shifted Legendre polynomial of arbitrary order. Then, they obtain the new weighting coefficients matrices for space fractional derivatives by shifted Legendre polynomials and use these in conversion of a non-linear fractional partial differential equation into a system of fractional ordinary differential equations. Convergence analysis for the proposed method is also discussed. Originality/value Many engineers can use the presented method for solving their time and space fractional non-linear partial differential equation models. To the best of the authors’ knowledge, the differential quadrature method has never been extended or implemented for non-linear time and space fractional partial differential equations.

Investigation of nanoparticles shape effects on MHD nanofluid flow and heat transfer over a rotating stretching disk through porous medium

2020 ◽  
Vol 30 (12) ◽  
pp. 5169-5189 ◽  
Author(s):  
Umair Rashid ◽  
Haiyi Liang
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Titanium Oxide ◽  
Shape Effect ◽  
Nanofluid Flow ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Rotating Stretchable Disk ◽  
The Impact

Purpose In this article, we consider the magnetohydrodynamic (MHD) nanofluid flow over a rotating stretchable disk through porous medium. For porous medium, Darcy’s relation is used. It also encompassed the impact of nanoparticles shape on MHD nanofluid flow and heat transfer. The effect of thermal radiation and Joule heating is also being considered. Design/methodology/approach Three categories of nanoparticles are taken into deliberation, i.e. copper, silver and titanium oxide. The nanofluid is made of pure water and various types of sphere- and lamina-shaped nanoparticles. By using appropriate similarity transformation, the governing partial differential equations are transformed to ordinary one. The coupled ordinary differential equations system is tackled numerically by bvp4c method. Findings The impact of various pertinent parameters, i.e. solid volume fraction, Hartman number, thermal radiations parameter, Reynolds number, Eckert number, porosity parameter and ratio parameter, on flow and Nusselt number with a fixed value of Prandtl number at 6.2 is discussed in details. The obtained results are presented in the concluding section. The lamina shape of nanoparticles in silver-water performed an excellent role on temperature distribution. The heat transfer rate of lamina shape in copper-water was found to be greater in the system of flow regime. Originality/value The authors have discussed the shape effect of nanoparticles on MHD nanofluid flow over a rotating stretchable disk through porous medium using three categories of nanoparticles, such as copper, silver and titanium oxide. To the best of the authors’ knowledge, this is the first study on mass and heat transfer nanofluid flow and no such study is yet published in literature. A detailed mathematical analysis has also to be carried out to prove the regularity of model. The authors believe that the numerical results are original and have not been copied from any other sources.

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