scholarly journals Darcy–Brinkman–Forchheimer Model for Nano-Bioconvection Stratified MHD Flow through an Elastic Surface: A Successive Relaxation Approach

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2514
Author(s):  
Anwar Shahid ◽  
Mohamed S. Mohamed ◽  
Muhammad Mubashir Bhatti ◽  
Mohammad Hossein Doranehgard
Keyword(s):  
Differential Equations ◽  
Mhd Flow ◽  
Coupled System ◽  
Relaxation Method ◽  
Numerical Comparison ◽  
System Of Equations ◽  
Nanofluid Flow ◽  
Elastic Surface ◽  
Flow Through ◽  
Forchheimer Model

The present study deals with the Darcy–Brinkman–Forchheimer model for bioconvection-stratified nanofluid flow through a porous elastic surface. The mathematical modeling for MHD nanofluid flow with motile gyrotactic microorganisms is formulated under the influence of an inclined magnetic field, Brownian motion, thermophoresis, viscous dissipation, Joule heating, and stratifi-cation. In addition, the momentum equation is formulated using the Darcy–Brinkman–Forchheimer model. Using similarity transforms, governing partial differential equations are reconstructed into ordinary differential equations. The spectral relaxation method (SRM) is used to solve the nonlinear coupled differential equations. The SRM is a straightforward technique to develop, because it is based on decoupling the system of equations and then integrating the coupled system using the Chebyshev pseudo-spectral method to obtain the required results. The numerical interpretation of SRM is admirable because it establishes a system of equations that sequentially solve by providing the results of the first equation into the next equation. The numerical results of temperature, velocity, concentration, and motile microorganism density profiles are presented with graphical curves and tables for all the governing parametric quantities. A numerical comparison of the SRM with the previously investigated work is also shown in tables, which demonstrate excellent agreement.

scholarly journals On Numerical Analysis of Carreau–Yasuda Nanofluid Flow over a Non-Linearly Stretching Sheet under Viscous Dissipation and Chemical Reaction Effects

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1148
Author(s):  
Stanford Shateyi ◽  
Hillary Muzara
Keyword(s):  
Differential Equations ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Coupled System ◽  
Linear Differential Equations ◽  
Nanofluid Flow ◽  
Linear Differential

This work reports the Carreau–Yasuda nanofluid flow over a non-linearly stretching sheet viscous dissipation and chemical reaction effects. The coupled system of non-linear partial differential equations are changed into a system of linear differential equations employing similarity equations. The spectral quasi-linearization method was used to solve the linear differential equations numerically. Error norms were used to authenticate the accuracy and convergence of the numerical method. The effects of some thermophysical parameters of interest in this current study on the non-dimensional fluid velocity, concentration and temperature, the skin friction, local Nusselt and Sherwood numbers are presented graphically. Tables were used to depict the effects of selected parameters on the skin friction and the Nusselt number.

Effects of Variable Fluid Properties on MHD Non-Darcy Convective Flow from Vertical Plate with Heat Generation and Chemical Reaction

2018 ◽  
Vol 388 ◽  
pp. 190-203
Author(s):  
R. Suresh Babu ◽  
B. Rushi Kumar ◽  
B. Mallikarjuna ◽  
P.A. Dinesh
Keyword(s):  
Differential Equations ◽  
Numerical Computation ◽  
Chemical Reaction ◽  
Vertical Plate ◽  
Mhd Flow ◽  
Numerical Comparison ◽  
Linear Partial Differential Equations ◽  
Similarity Transformations ◽  
Fluid Properties ◽  
First Order Chemical Reaction

A numerical computation has been carried out to study, MHD flow of an electrically conducting viscous fluid from a semi-infinite vertical plate in a porous medium in the presence of heat source and homogeneous first order chemical reaction. The fluid and porous properties, thermal and solutal diffusivity, permeability and porosity are considered to be varied. The governing non-linear partial differential equations for the fluid flow are derived and transformed into a system of ordinary differential equations using a suitable similarity transformations. A numerical computation of shooting technique is employed along Runge Kutta method of fourth order with the help of Newton-Raphson algorithm to compute the solution and analyze the behavior of velocity, temperature, concentration, skin friction, heat and mass transfer rates graphically for various non-dimensional parameters which are controlling the flow of the physical system. The results of the numerical scheme are validated and a numerical comparison has been made with the available literature in the absence of some parameters and it is found to be in good agreement.

Construction of metric and vector potential perturbations of a Reissner–Nordström black hole

1979 ◽  
Vol 369 (1736) ◽  
pp. 67-81 ◽  
Keyword(s):  
Black Hole ◽  
Partial Differential Equations ◽  
Linear System ◽  
Differential Equations ◽  
Vector Potential ◽  
Maxwell Equations ◽  
Coupled System ◽  
System Of Equations ◽  
Partial Differential ◽  
Explicit Formulae

When an appropriate decoupling of variables in a coupled linear system of partial differential equations is obtained, a recently described procedure enables one to construct solutions to the full coupled system of equations. We employ this procedure here to generate solutions of the linearized Einstein–Maxwell equations describing perturbations of a Reissner–Nordström black hole, using Chandrasekhar’s recent decoupling of these equations. Explicit formulae are given for the metric and vector potential perturbations for each parity type.

scholarly journals An uncoupling procedure for a class of coupled linear partial differential equations

1985 ◽  
Vol 26 (4) ◽  
pp. 503-516 ◽  
Author(s):  
A. McNabb
Keyword(s):  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Large Class ◽  
Partial Differential Operator ◽  
Coupled System ◽  
System Of Equations ◽  
Partial Differential ◽  
Similar System ◽  
Linear Partial Differential Equations

AbstractA Fredholm operator exists which maps the solutions of a system of linear partial differential equations of the form ∂u/∂t = DLu + Au coupled by a matrix A onto those solutions of a similar system coupled by a matrix B which have the same initial values. The kernels of this operator satisfy a hyperbolic system of equations. Since these equations are independent of the linear partial differential operator L, the same operator serves as a mapping for a large class of equations. If B is chosen diagonal, the solutions of a coupled system with matrix A may be obtained from the uncoupled system with matrix B.

scholarly journals A New Numerical Approach of MHD Flow with Heat and Mass Transfer for the UCM Fluid over a Stretching Surface in the Presence of Thermal Radiation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
S. Shateyi ◽  
G. T. Marewo
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Heat And Mass Transfer ◽  
Mhd Flow ◽  
Relaxation Method ◽  
Maxwell Fluid ◽  
Numerical Approach ◽  
Highly Nonlinear

This paper numerically investigates the magnetohydrodynamic boundary layer flow with heat and mass transfer of an incompressible upper-convected Maxwell fluid over a stretching sheet in the presence of viscous dissipation and thermal radiation as well as chemical reaction. The governing partial differential equations are transformed into a system of ordinary differential equations by using suitable similarity transformations. The resultant highly nonlinear ordinary differential equations are then solved using spectral relaxation method. The results are obtained for velocity, temperature, concentration, skin friction, and Nusselt number. The effects of various material parameters on the flow with heat and mass transfer and the dimensionless variables are illustrated graphically and briefly discussed.

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.

scholarly journals Impact of autocatalytic chemical reaction in an Ostwald-de-Waele nanofluid flow past a rotating disk with heterogeneous catalysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bai Yu ◽  
Muhammad Ramzan ◽  
Saima Riasat ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Power Law ◽  
Variable Thickness ◽  
Rotating Disk ◽  
Thermal Profile ◽  
Nanofluid Flow ◽  
Power Law Index

AbstractThe nanofluids owing to their alluring attributes like enhanced thermal conductivity and better heat transfer characteristics have a vast variety of applications ranging from space technology to nuclear reactors etc. The present study highlights the Ostwald-de-Waele nanofluid flow past a rotating disk of variable thickness in a porous medium with a melting heat transfer phenomenon. The surface catalyzed reaction is added to the homogeneous-heterogeneous reaction that triggers the rate of the chemical reaction. The added feature of the variable thermal conductivity and the viscosity instead of their constant values also boosts the novelty of the undertaken problem. The modeled problem is erected in the form of a system of partial differential equations. Engaging similarity transformation, the set of ordinary differential equations are obtained. The coupled equations are numerically solved by using the bvp4c built-in MATLAB function. The drag coefficient and Nusselt number are plotted for arising parameters. The results revealed that increasing surface catalyzed parameter causes a decline in thermal profile more efficiently. Further, the power-law index is more influential than the variable thickness disk index. The numerical results show that variations in dimensionless thickness coefficient do not make any effect. However, increasing power-law index causing an upsurge in radial, axial, tangential, velocities, and thermal profile.

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