A spectral relaxation method for three-dimensional MHD flow of nanofluid flow over an exponentially stretching sheet due to convective heating: an application to solar energy

2018 ◽  
Vol 92 (12) ◽  
pp. 1577-1588 ◽  
Author(s):  
M. Venkata Subba Rao ◽  
K. Gangadhar ◽  
P. L. N. Varma
Keyword(s):  
Solar Energy ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Mhd Flow ◽  
Relaxation Method ◽  
Convective Heating ◽  
Nanofluid Flow ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation ◽  
Exponentially Stretching

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 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.

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.

MHD Flow of a Carreau Fluid Past a Stretching Cylinder with Cattaneo-Christov Heat Flux Using Spectral Relaxation Method

2018 ◽  
Vol 387 ◽  
pp. 91-105 ◽  
Author(s):  
K. Gangadhar ◽  
K.V. Ramana ◽  
Oluwole Daniel Makinde ◽  
B. Rushi Kumar
Keyword(s):  
Heat Flux ◽  
Temperature Jump ◽  
Thermal Relaxation ◽  
Mhd Flow ◽  
Relaxation Method ◽  
Stretching Cylinder ◽  
Carreau Fluid ◽  
Highly Nonlinear ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

A theoretical investigation of a hydromagnetic boundary layer flow of Carreau fluid over a stretching cylinder with surface slippage and temperature jump is presented in this paper. It is assumed that heat transfer characteristics of the flow follows Cattaneo-Christov heat flux model base on conventional Fourier’s law with thermal relaxation time. The spectral relaxation method (SRM) is being utilized to provide the solution of highly nonlinear system of coupled partial differential equations converted into dimensionless governing equations. The behaviour of flow parameters on velocity, temperature distributions are sketched as well as analyzed physically. The result indicates that the temperature distribution decay for higher temperature jump and thermal relaxation parameters respectively.

scholarly journals MHD stagnation point transient flow of a nanofluid past a stretching sheet: SRM approach

2019 ◽  
Vol 49 (3) ◽  
pp. 205-211
Author(s):  
Bhuvaneshvar Kumar ◽  
G. S. Seth
Keyword(s):  
Stagnation Point ◽  
Stretching Sheet ◽  
Transient Flow ◽  
Fluid Velocity ◽  
Velocity Slip ◽  
Relaxation Method ◽  
Opposite Case ◽  
Boundary Layer Equations ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

Stagnation point nanofluid flow over a stretching sheet embedded in a porous medium is investigated in the present model by taking Navier’s velocity sip into account. The spectral relaxation method (SRM) is utilized to solve boundary layer equations. The variation of nanofluid velocity, concentration and temperature corresponding to some dominant flow parameters is displayed via graphs. The findings reveal that when stretching sheet is moving faster than free stream then porous permeability, unsteadiness, velocity slip and magnetic parameters have tendency to reduce fluid velocity but in opposite case, they behave as an assisting parameters for flow field.

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