A spectral relaxation method for linear and non-linear stratification effects on mixed convection in a porous medium

2015 ◽  
Vol 268 ◽  
pp. 991-1000 ◽  
Author(s):  
Ch. RamReddy ◽  
P.A. Lakshmi Narayana ◽  
S.S. Motsa
Keyword(s):  
Porous Medium ◽  
Mixed Convection ◽  
Relaxation Method ◽  
Non Linear ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

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 Mixed convection flow of nanofluid with Hall and ion-slip effects using spectral relaxation method

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Wubshet Ibrahim ◽  
Temesgen Anbessa
Keyword(s):  
Mixed Convection ◽  
Relaxation Method ◽  
Convection Flow ◽  
Mixed Convection Parameter ◽  
Slip Effects ◽  
Spectral Relaxation Method ◽  
Ion Slip ◽  
Spectral Relaxation ◽  
Convection Parameter ◽  
Buoyancy Ratio

AbstractIn this article, the Hall and ion-slip effects on a mixed convection flow of an electrically conducting nanofluid over a stretching sheet in a permeable medium have been discussed. Using the similarity transformations, the partial differential equations corresponding to the momentum, energy, and concentration equations are transformed to a system of nonlinear ordinary differential equations which are solved numerically using a spectral relaxation method (SRM). The effects of significant parameters on the velocities, temperature, and concentration profiles are analyzed graphically. Moreover, the results of the skin friction coefficients, local Nusselt number, and Sherwood number are determined numerically. The results of the analysis showed that the velocity profile in the flow direction increases with an increase in mixed convection parameter λ, Hall parameter βh, and ion-slip parameter βi, and it decreases with an increase in the magnetic parameter M. Furthermore, temperature and concentration profiles decrease as the mixed convection parameter λ and buoyancy ratio Nr increase. It is also observed that the skin friction coefficients, local Nusselt number, and Sherwood number increase with an increase in the Hall parameter βh, mixed convection parameter λ, and buoyancy ratio Nr.

Hydromagnetic Nanofluids Flow through a Porous Medium with Thermal Radiation, Chemical Reaction and Viscous Dissipation using the Spectral Relaxation Method

2019 ◽  
Vol 16 (06) ◽  
pp. 1840020
Author(s):  
Nageeb A. H. Haroun ◽  
Sabyasachi Mondal ◽  
Precious Sibanda
Keyword(s):  
Porous Medium ◽  
Thermal Radiation ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Heat Generation ◽  
Relaxation Method ◽  
Spectral Relaxation Method ◽  
Flow Through ◽  
Spectral Relaxation ◽  
The Impact

We investigate the convective heat and mass transfer in a magnetohydrodynamic nanofluid flow through a porous medium over a stretching sheet subject to heat generation, thermal radiation, viscous dissipation and chemical reaction effects. We have assumed that the nanoparticle volume fraction at the wall may be actively controlled. Two types of nanofluids, namely Cu-water and Al2O3-water are studied. The physical problem is modeled using systems of nonlinear differential equations which have been solved numerically using the spectral relaxation method. Comparing the results with those previously published results in the literature shows excellent agreement. The impact of porosity, heat generation, thermal radiation, magnetic field, viscous dissipation and chemical reaction on the flow field is evaluated and explained.

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