scholarly journals Multiple Solutions of Mixed Convective MHD Casson Fluid Flow in a Channel

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Jawad Raza ◽  
Azizah Mohd Rohni ◽  
Zurni Omar
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fluid Flow ◽  
Multiple Solutions ◽  
Shooting Method ◽  
Similarity Transformation ◽  
Numerical Technique ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Nonlinear Ordinary Differential Equations

A numerical investigation is made to determine the occurrence of the multiple solutions of MHD Casson fluid in a porous channel. Governing partial differential equation of the proposed problem converted into nonlinear ordinary differential equations by using similarity transformation. Numerical technique known as shooting method is used to investigate the existence of the multiple solutions for the variations of different parameters. Effects of physical parameters on velocity profile, temperature, concentration, and skin friction are presented in pictorial and tabulation representation.

Effects of Inclination angle and Free Convection on Velocity Profile for a Steady 2-Dimensional Magnetohydrodynamic Fluid Flow in an Inclined Cylindrical Pipe

2021 ◽  
Vol 6 (7) ◽  
pp. 114-117
Author(s):  
B. Odongo ◽  
R. Opiyo ◽  
A. Manyonge
Keyword(s):  
Differential Equation ◽  
Fluid Flow ◽  
Velocity Profile ◽  
Free Convection ◽  
Shooting Method ◽  
Hartmann Number ◽  
Similarity Transformation ◽  
Cylindrical Pipe ◽  
Order Scheme ◽  
Magnetohydrodynamic Fluid

Effects of inclination and free convection on velocity profile for magnetohydrodynamic (MHD) fluid flow in an inclined cylindrical pipe has been investigated. The governing partial differential equations are the equations of continuity, momentum and energy which are converted into ordinary differential equation by employing similarity transformation and solved numerically by the Runge- Kutta fourth order scheme with shooting method. The findings, which are presented in the form of tables and graphs reveal that; when Hartmann number, Grashoff number and Gamma are decreased, the velocity of the fluid increases. The results of the study may be useful for the different model investigations, especially, in various areas of science and technology in which optimal inclination and free convection are utilized.

Implementation of DTM as a numerical study for the Casson fluid flow past an exponentially variable stretching sheet with thermal radiation

2021 ◽  
pp. 2150111
Author(s):  
Khadijah M. Abualnaja
Keyword(s):  
Fluid Flow ◽  
Thermal Radiation ◽  
Numerical Method ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Transformation Method ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Special Cases

This paper introduces a theoretical and numerical study for the problem of Casson fluid flow and heat transfer over an exponentially variable stretching sheet. Our contribution in this work can be observed in the presence of thermal radiation and the assumption of dependence of the fluid thermal conductivity on the heat. This physical problem is governed by a system of ordinary differential equations (ODEs), which is solved numerically by using the differential transformation method (DTM). This numerical method enables us to plot figures of the velocity and temperature distribution through the boundary layer region for different physical parameters. Apart from numerical solutions with the DTM, solutions to our proposed problem are also connected with studying the skin-friction coefficient. Estimates for the local Nusselt number are studied as well. The comparison of our numerical method with previously published results on similar special cases shows excellent agreement.

Numerical Study of Micropolar Fluid Flow Past an Impervious Sphere

2018 ◽  
Vol 388 ◽  
pp. 344-349
Author(s):  
D.V. Jayalakshmamma ◽  
P.A. Dinesh ◽  
D.V. Chandrashekhar
Keyword(s):  
Differential Equation ◽  
Fluid Flow ◽  
Micropolar Fluid ◽  
Similarity Transformation ◽  
Numerical Study ◽  
Transformation Method ◽  
Governing Equations ◽  
Shooting Technique ◽  
Micropolar Fluid Flow ◽  
Incompressible Micropolar Fluid

The numerical study of axi-symmetric, steady flow of an incompressible micropolar fluid past an impervious sphere is presented by assuming uniform flow far away from the sphere. The continuity, linear and angular momentum equations are considered for incompressible micropolar fluid in accordance with Eringen. The governing equations of the physical problem are transformed to ordinary differential equation with variable co-efficient by using similarity transformation method. The obtained differential equation is then solved numerically by assuming the shooting technique. The effect of coupling and coupling stress parameter on the properties of the fluid flow is studied and demonstrated by graphs.

scholarly journals The Effects of Chemical Reaction, Hall, and Ion-Slip Currents on MHD Micropolar Fluid Flow with Thermal Diffusivity Using a Novel Numerical Technique

2012 ◽  
Vol 2012 ◽  
pp. 1-30 ◽  
Author(s):  
S. S. Motsa ◽  
S. Shateyi
Keyword(s):  
Fluid Flow ◽  
Thermal Diffusivity ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Chemical Reaction ◽  
Numerical Technique ◽  
Linearization Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Successive Linearization Method ◽  
Ion Slip

The problem of magnetomicropolar fluid flow, heat, and mass transfer with suction through a porous medium is numerically analyzed. The problem was studied under the effects of chemical reaction, Hall, ion-slip currents, and variable thermal diffusivity. The governing fundamental conservation equations of mass, momentum, angular momentum, energy, and concentration are converted into a system of nonlinear ordinary differential equations by means of similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is the then solved using a fairly new technique known as the successive linearization method together with the Chebyshev collocation method. A parametric study illustrating the influence of the magnetic strength, Hall and ion-slip currents, Eckert number, chemical reaction and permeability on the Nusselt and Sherwood numbers, skin friction coefficients, velocities, temperature, and concentration was carried out.

Unsteady Chemically Reacting Casson Fluid Flow in an Irregular Channel with Convective Boundary

2015 ◽  
Vol 70 (8) ◽  
pp. 583-591
Author(s):  
Muhammad Nasir ◽  
Adnan Saeed Butt ◽  
Asif Ali
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Mass Concentration ◽  
Perturbation Technique ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Wavy Wall ◽  
Convective Boundary ◽  
Grashof Number ◽  
Chemically Reacting

AbstractA mathematical model has been performed for momentum, temperature, and mass concentration of a time-dependent Casson fluid flow between a long vertical wavy wall and a parallel wavy wall subject to convective boundary conditions. Perturbation technique is used to convert the coupled partial differential equations for velocity, temperature, and mass concentration to systems of ordinary differential equations. Analytical results for these differential equations are computed. The effects of various physical parameters such as thermal conductivity, thermal Grashof number, solutal Grashof number, heat absorption parameter, and Biot number are analysed graphically.

Heat generating/absorbing and chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium

2017 ◽  
Vol 27 (1) ◽  
pp. 156-173 ◽  
Author(s):  
Mythili Durairaj ◽  
Sivaraj Ramachandran ◽  
Rashidi Mohammad Mehdi
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Flat Plate ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Vertical Cone ◽  
Soret And Dufour Effects ◽  
Content Type ◽  
Chemically Reacting

Purpose The present investigation aims to deal with the study of unsteady, heat-generating/-absorbing and chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium in the presence of cross-diffusion effects. Design/methodology/approach A numerical computation for the governing equations has been performed using implicit finite difference method of Crank–Nicolson type. Findings The influence of various physical parameters on velocity, temperature and concentration distributions is illustrated graphically, and the physical aspects are discussed in detail. Numerical results for average skin-friction, Nusselt number and Sherwood number are tabulated for the pertaining physical parameters. Results indicate that Soret and Dufour effects have notable influence on heat and mass transfer characteristics of the fluid when the temperature and concentration gradients are high. It is also observed that the consideration of heat generation/absorption plays a vital role in predicting the heat transfer characteristics of moving fluids. Research limitations/implications Consider a two-dimensional, unsteady, free convective flow of an incompressible Casson fluid over a vertical cone and a flat plate saturated with non-Darcy porous medium. The fluid properties are assumed to be constant except for density variations in the buoyancy force term. The fluid flow is moderate and the permeability of the medium is assumed to be low, so that the Forchheimer flow model is applicable. Practical implications The flow of Casson fluids (such as drilling muds, clay coatings and other suspensions, certain oils and greases, polymer melts and many emulsions), in the presence of heat transfer, is an important research area because of its relevance in the optimized processing of chocolate, toffee and other foodstuffs. Social implications In the heat and mass transfer investigations, the Casson fluid model is found to be accurately applicable in many practical situations in the wings of polymer processing industries and biomechanics, etc.; some prominent examples are silicon suspensions, suspensions of bentonite in water and lithographic varnishes used for printing inks. Originality/value The motivation of the present study is to bring out the effects of heat source/sink, Soret and Dufour effects on chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium. The flow of Casson fluids (such as certain oils and greases, polymer melts and many emulsions) in the presence of heat transfer is an important research area because of its relevance in the optimized processing of chocolate, toffee and other foodstuffs. A numerical computation for the governing equations has been performed using implicit finite difference method of the Crank–Nicolson type.

scholarly journals The Inclined Factors of Magnetic Field and Shrinking Sheet in Casson Fluid Flow, Heat and Mass Transfer

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 373
Author(s):  
Shahanaz Parvin ◽  
Siti Suzilliana Putri Mohamed Isa ◽  
Norihan Md Arifin ◽  
Fadzilah Md Ali
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Fluid Model ◽  
Casson Fluid ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Flow Heat

The development of the mathematical modeling of Casson fluid flow and heat and mass transfer is presented in this paper. The model is subjected to the following physical parameters: shrinking parameter, mixed convection, concentration buoyancy ratio parameter, Soret number, and Dufour number. This model is also subjected to the inclined magnetic field and shrinking sheet at a certain angle projected from the y- and x-axes, respectively. The MATLAB bvp4c program is the main mathematical program that was used to obtain the final numerical solutions for the reduced ordinary differential equations (ODEs). These ODEs originate from the governing partial differential equations (PDEs), where the transformation can be achieved by applying similarity transformations. The MATLAB bvp4c program was also implemented to develop stability analysis, where this calculation was executed to recognize the most stable numerical solution. Numerical graphics were made for the skin friction coefficient, local Nusselt number, local Sherwood number, velocity profile, temperature profile, and concentration profile for certain values of the physical parameters. It is found that all the governed parameters affected the variations of the Casson fluid flow, heat transfer, mass transfer, and the profiles of velocity, temperature, and concentration. In addition, a stable solution can be applied to predict the impact of physical parameters on the actual fluid model by using a mathematical fluid model.

scholarly journals THE MATHEMATICAL MODELLING OF THE NONLINEAR HEAT TRANSPORT IN THIN PLATE

1999 ◽  
Vol 4 (1) ◽  
pp. 44-50
Author(s):  
A. Buikis
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Mathematical Modelling ◽  
Heat Transport ◽  
Initial Value Problem ◽  
Nonlinear Ordinary Differential Equations ◽  
Algebraic Equations ◽  
Initial Value ◽  
First Order ◽  
Nonlinear Algebraic Equations

The approximations of the nonlinear heat transport problem are based on the finite volume (FM) and averaging (AM) methods [1,2]. This procedures allows reduce the nonlinear 2‐D problem for partial differential equation (PDE) to a initial‐value problem for a system of 2 nonlinear ordinary differential equations(ODE) of first order in the time t or to a initial‐value problem for one nonlinear ODE of first order with two nonlinear algebraic equations.

A note on some solutions of micropolar fluid in a channel with permeable walls

2018 ◽  
Vol 14 (1) ◽  
pp. 91-101 ◽  
Author(s):  
Jawad Raza ◽  
Azizah M. Rohni ◽  
Zurni Omar
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Micropolar Fluid ◽  
Design Methodology ◽  
Shooting Method ◽  
Similarity Transformation ◽  
Physical Parameters ◽  
Content Type ◽  
Single Solution ◽  
Permeable Walls

Purpose The purpose of this paper is to investigate different branches of the solution of micropolar fluid in a channel with permeable walls. Moreover, the intention of the study is to examine the effect of different physical parameters on fluid flow. Design/methodology/approach The mathematical modeling is performed on the basis of law of conservation of mass, momentum and angular momentum. The governing partial differential equations were transformed into ordinary differential equations by applying suitable similarity transformation. Afterwards, the set of nonlinear ordinary differential equations was solved numerically by a shooting method. Findings The study reveals that various branches of the solution of the proposed problem exist only in the case of strong suction. Originality/value The investigation of new branches of the solution of non-Newtonian micropolar fluid is relatively difficult as far as the single solution is concern. This study explores the new branches of the solution of a micropolar fluid in a channel with suction/injection. Simultaneous effect of suction Reynolds number and vortex viscosity parameter on velocity and micro-rotation profile is examined for different branches of solution in order to make the analysis more interesting.

Sign in / Sign up

Export Citation Format

Share Document