scholarly journals Numerical simulation of the motion of a micropolar Casson fluid through a porous medium over a stretching surface

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1285-1297 ◽  
Author(s):  
Nabil El-Dabe ◽  
Galal Moatimid ◽  
Abd-Elhafez Elshekhipy ◽  
Naglaa Aballah
Keyword(s):  
Porous Medium ◽  
Casson Fluid ◽  
Similarity Solutions ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Transform Method ◽  
Differential Transform ◽  
Non Linear ◽  
Linear Differential ◽  
External Uniform Magnetic Field

The present study examines the motion of a micropolar non-Newtonian Casson fluid through a porous medium over a stretching surface. The system is pervaded by an external uniform magnetic field. The heat transfer and heat generation are taken into consideration. The problem is modulated mathematically by a system of non-linear PDE which describe the equations of continuity, momentum, and energy. Suitable similarity solutions are utilized to transform the system of equation ordinary non-linear differential equations. In accordance with the appropriate boundary conditions, are numerically solved by means of the finite difference technique. Also, the system is solved by using multistep differential transform method. The effects of the various physical parameters, of the problem at hand, are illustrated through a set of diagrams.

scholarly journals Solution of Non-Linear Differential Equations by Using Differential Transform Method

2014 ◽  
Vol 10 (2) ◽  
pp. 14-18
Author(s):  
Saurabh Dilip Moon ◽  
◽  
Akshay Bhagwat Bhosale ◽  
Prashikdivya Prabhudas Gajbhiye
Keyword(s):  
Differential Equations ◽  
Differential Transform Method ◽  
Linear Differential Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Non Linear ◽  
Linear Differential

scholarly journals Casson fluid flow with heat and mass transfer in a channel using the differential transform method

2021 ◽  
Vol 49 (1) ◽  
Author(s):  
Asia Yasmin ◽  
◽  
Kashif Ali ◽  
Muhammad Ashraf ◽  
◽  
...  
Keyword(s):  
Mass Transfer ◽  
Fluid Flow ◽  
Heat And Mass Transfer ◽  
Casson Fluid ◽  
Differential Transform Method ◽  
Temperature Fields ◽  
Transform Method ◽  
Differential Transform ◽  
Non Linear ◽  
Linear Odes

In the present investigation, we consider the heat and mass transfer characteristics of steady, incompressible and electrically conducting Casson fluid flow in a channel. The effect of chemical reactions have also been considered. The differential transform method (DTM) is applied to a system of non-linear ODEs, and the results are obtained in the form of DTM series. The principal gain of this approach is that it applies to the non-linear ODEs without requiring any discretization, linearization or perturbation. The velocity, mass and heat transfer profiles thus obtained are in good agreement with those provided by the quasi-linearization method (QLM). Graphical results for velocity, concentration and temperature fields are presented for a certain range of values of the governing parameters.

Entropy Generation on Maxwell Fluid Flow Past an Inclined Stretching Plate with Slip and Convective Surface Conditon: Darcy-Forchheimer Model

2019 ◽  
Vol 26 ◽  
pp. 62-83
Author(s):  
Tunde Abdulkadir Yusuf ◽  
Jacob Abiodun Gbadeyan
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Entropy Generation ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study the effect of entropy generation on two dimensional magnetohydrodynamic (MHD) flow of a Maxwell fluid over an inclined stretching sheet embedded in a non-Darcian porous medium with velocity slip and convective boundary condition is investigated. Darcy-Forchheimer based model was employed to describe the flow in the porous medium. The non-linear thermal radiation is also taken into account. Similarity transformation is used to convert the non-linear partial differential equations to a system of non-linear ordinary differential equations. The resulting transformed equations are then solved using the Homotopy analysis method (HAM). Influence of various physical parameters on the dimensionless velocity profile, temperature profile and entropy generation are shown graphically and discussed in detail while the effects of these physical parameters on velocity gradient and temperature gradient are aided with the help of Table. Furthermore, comparison of some limiting cases of this model was made with existing results. The results obtained are found to be in good agreement with previously published results. Moreover, increase in local inertial coefficient parameter is found to decrease the entropy generation rate.

scholarly journals MHD Slip Flow of Casson Fluid along a Nonlinear Permeable Stretching Cylinder Saturated in a Porous Medium with Chemical Reaction, Viscous Dissipation, and Heat Generation/Absorption

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 531 ◽  
Author(s):  
Ullah ◽  
Abdullah Alkanhal ◽  
Shafie ◽  
Nisar ◽  
Khan ◽  
...  
Keyword(s):  
Porous Medium ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Heat Generation ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Casson Fluid ◽  
Similarity Solutions ◽  
Local Similarity ◽  
The Impact

The aim of the present analysis is to provide local similarity solutions of Casson fluid over a non-isothermal cylinder subject to suction/blowing. The cylinder is placed inside a porous medium and stretched in a nonlinear way. Further, the impact of chemical reaction, viscous dissipation, and heat generation/absorption on flow fields is also investigated. Similarity transformations are employed to convert the nonlinear governing equations to nonlinear ordinary differential equations, and then solved via the Keller box method. Findings demonstrate that the magnitude of the friction factor and mass transfer rate are suppressed with increment in Casson parameter, whereas heat transfer rate is found to be intensified. Increase in the curvature parameter enhanced the flow field distributions. The magnitude of wall shear stress is noticed to be higher with an increase in porosity and suction/blowing parameters.

scholarly journals Mixed Convective Fully Developed Flow in a Vertical Channel in the Presence of Thermal Radiation and Viscous Dissipation

2017 ◽  
Vol 22 (1) ◽  
pp. 123-144 ◽  
Author(s):  
K.V. Prasad ◽  
P. Mallikarjun ◽  
H. Vaidya
Keyword(s):  
Thermal Radiation ◽  
Perturbation Method ◽  
Viscous Dissipation ◽  
Vertical Channel ◽  
Differential Transform Method ◽  
Physical Parameters ◽  
Regular Perturbation ◽  
Transform Method ◽  
Fully Developed Flow ◽  
Differential Transform

Abstract The effect of thermal radiation and viscous dissipation on a combined free and forced convective flow in a vertical channel is investigated for a fully developed flow regime. Boussinesq and Roseseland approximations are considered in the modeling of the conduction radiation heat transfer with thermal boundary conditions (isothermal-thermal, isoflux-thermal, and isothermal-flux). The coupled nonlinear governing equations are also solved analytically using the Differential Transform Method (DTM) and regular perturbation method (PM). The results are analyzed graphically for various governing parameters such as the mixed convection parameter, radiation parameter, Brinkman number and perturbation parameter for equal and different wall temperatures. It is found that the viscous dissipation enhances the flow reversal in the case of a downward flow while it counters the flow in the case of an upward flow. A comparison of the Differential Transform Method (DTM) and regular perturbation method (PM) methods shows the versatility of the Differential Transform Method (DTM). The skin friction and the wall temperature gradient are presented for different values of the physical parameters and the salient features are analyzed.

scholarly journals An Axisymmetric Squeezing Fluid Flow between the Two Infinite Parallel Plates in a Porous Medium Channel

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
S. Islam ◽  
Hamid Khan ◽  
Inayat Ali Shah ◽  
Gul Zaman
Keyword(s):  
Differential Equation ◽  
Porous Medium ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Differential Transform ◽  
Fluid Parameters

The flow between two large parallel plates approaching each other symmetrically in a porous medium is studied. The Navier-Stokes equations have been transformed into an ordinary nonlinear differential equation using a transformationψ(r,z)=r2F(z). Solution to the problem is obtained by using differential transform method (DTM) by varying different Newtonian fluid parameters and permeability of the porous medium. Result for the stream function is presented. Validity of the solutions is confirmed by evaluating the residual in each case, and the proposed scheme gives excellent and reliable results. The influence of different parameters on the flow has been discussed and presented through graphs.

scholarly journals Using the Differential Transform Method to Solve Non-Linear Partial Differential Equations

2020 ◽  
pp. 34-43
Author(s):  
Fadwa A. M. Madi ◽  
Fawzi Abdelwahid
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Variable Coefficients ◽  
Differential Transform Method ◽  
Partial Differential ◽  
Transform Method ◽  
Linear Partial Differential Equations ◽  
Differential Transform ◽  
Non Linear

In this work, we reviewed the two-dimensional differential transform, and introduced the differential transform method (DTM). As an application, we used this technique to find approximate and exact solutions of selected non-linear partial differential equations, with constant or variable coefficients and compared our results with the exact solutions. This shows that the introduced method is very effective, simple to apply to linear and nonlinear problems and it reduces the size of computational work comparing with other methods.

scholarly journals Differential Transform Technique on the Effect of Baffle Convective Nanofluid Flow in Saturated Porous Channel

2019 ◽  
Vol 8 (4) ◽  
pp. 10349-10360
Keyword(s):  
Porous Medium ◽  
Perturbation Method ◽  
Vertical Channel ◽  
Differential Transform Method ◽  
Regular Perturbation ◽  
Nanofluid Flow ◽  
Transform Method ◽  
Differential Transform ◽  
Perturbation Parameters ◽  
Energy Equations

Simulations are shown for steady nanofluid saturated with porous medium in a vertical channel divided into two way by placing a thin baffle. Tiwari and Das model applied for continuity, momentum and energy equations are written using to define the nanofluid and non-Darcy model used for porous medium. The nonlinear equations are solved analytically using regular perturbation method and by semi analytical method using differential transform method. The validity of the solutions obtained by perturbation method and differential transform method are compared and found that they agree very well for small values of perturbation parameters. The numerical values of the velocity and temperature are shown graphically at different baffle positions for all the pertinent parameters. The Nusselt number for both regular and nanofluids are evaluated and tabulated.

scholarly journals Numerical Analysis of the Flow of a Casson Fluid in Magnetic Field over an Inclined Nonlinearly Stretching Surface with Velocity Slip in a Forchheimer Porous Medium

2020 ◽  
pp. 34-58
Author(s):  
Bhim Sen Kala ◽  
Madan Singh Rawat ◽  
Ajay Kumar
Keyword(s):  
Porous Medium ◽  
Velocity Slip ◽  
Casson Fluid ◽  
Momentum Equation ◽  
Stretching Surface ◽  
Local Skin ◽  
Local Skin Friction ◽  
Nonlinearly Stretching Surface ◽  
The Mathematical Model ◽  
Local Sherwood Number

In this work, we have studied a magnetohydrodynamic, Casson fluid flow with velocity slip over an inclined nonlinearly stretching surface in Non-Darcy porous medium, numerically. In the mathematical model, we have transformed the momentum equation, energy equation and mass concentration equations to non-dimensional ordinary differential equations using similarity variables. We have solved the equations numerically by bvp4c using MATLAB for the numerical computation, and took  and axes so that figures are clearly visible. We have discussed and analysed the magnitude of the velocity, temperature, concentration, Local Skin friction, Local Nusselt number and Local Sherwood number using their representative parameters and the effects of these parameters on the respective boundary layer regions using graphs, figures and tables.

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