UNSTEADY MHD FLOW OF SOME NANOFLUIDS PAST AN ACCELERATED VERTICAL PLATE EMBEDDED IN A POROUS MEDIUM

2016 ◽  
Vol 78 (2) ◽  
Author(s):  
Abid Hussanan ◽  
Ilyas Khan ◽  
Hasmawani Hashim ◽  
Muhammad Khairul Anuar ◽  
Nazila Ishak ◽  
...  
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Vertical Plate ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Transform Method ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
The Laplace Transform ◽  
Infinite Vertical Plate

The present paper deals with the unsteady magnetohydrodynamics (MHD) flow and heat transfer of some nanofluids past an accelerating infinite vertical plate in a porous medium. Water as conventional base fluid containing three different types of nanoparticles such as copper (Cu), aluminum oxide (Al2O3) and titanium oxide (TiO2) are considered. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy are converted into linear ordinary differential equations. Exact solutions of these equations are obtained with the Laplace Transform method. The influence of pertinent parameters on the fluid motion is graphically underlined. It is found that the temperature of Cu-water is higher than those of Al2O3-water and TiO2-water nanofluids.   

scholarly journals MHD Flow of Micropolar Fluid over an Oscillating Vertical Plate Embedded in Porous Media with Constant Temperature and Concentration

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Nadeem Ahmad Sheikh ◽  
Farhad Ali ◽  
Ilyas Khan ◽  
Muhammad Saqib ◽  
Arshad Khan
Keyword(s):  
Porous Media ◽  
Micropolar Fluid ◽  
Vertical Plate ◽  
Flow Behavior ◽  
Mathematical Formulation ◽  
Mhd Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Graphical Illustration ◽  
Infinite Vertical Plate

The present analysis represents the MHD flow of micropolar fluid past an oscillating infinite vertical plate embedded in porous media. At the plate, free convections are caused due to the differences in temperature and concentration. Therefore, the combined effect of radiative heat and mass transfer is taken into account. Partial differential equations are used in the mathematical formulation of a micropolar fluid. The system of dimensional governing equations is reduced to dimensionless form by means of dimensional analysis. The Laplace transform technique is applied to obtain the exact solutions for velocity, temperature, and concentration. In order to highlight the flow behavior, numerical computation and graphical illustration are carried out. Furthermore, the corresponding skin friction and wall couple stress are calculated.

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 General Solution of Linear Fractional Neutral Differential Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hai Zhang ◽  
Jinde Cao ◽  
Wei Jiang
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Difference Equations ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Linear Ordinary Differential Equations ◽  
Exponential Estimates ◽  
The Laplace Transform ◽  
Gronwall Integral Inequality ◽  
Delay Differential

This paper is concerned with the general solution of linear fractional neutral differential difference equations. The exponential estimates of the solution and the variation of constant formula for linear fractional neutral differential difference equations are derived by using the Gronwall integral inequality and the Laplace transform method, respectively. The obtained results extend the corresponding ones of integer order linear ordinary differential equations and delay differential equations.

scholarly journals Convection heat mass transfer and MHD flow over a vertical plate with chemical reaction, arbitrary shear stress and exponential heating

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sehra ◽  
Sami Ul Haq ◽  
Syed Inayat Ali Shah ◽  
Kottakkaran Sooppy Nisar ◽  
Saeed Ullah Jan ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Vertical Plate ◽  
Mhd Flow ◽  
Convection Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Transform Method ◽  
Molecular Diffusivity ◽  
Special Cases ◽  
Infinite Vertical Plate

AbstractThe present research article is directed to study the heat and mass transference analysis of an incompressible Newtonian viscous fluid. The unsteady MHD natural convection flow over an infinite vertical plate with time dependent arbitrary shear stresses has been investigated. In heat and mass transfer analysis the chemical molecular diffusivity effects have been studied. Moreover, the infinite vertical plate is subjected to the phenomenon of exponential heating. For this study, we formulated the problem into three governing equations along with their corresponding initial and boundary conditions. The Laplace transform method has been used to gain the exact analytical solutions to the problem. Special cases of the obtained solutions are investigated. It is noticed that some well-known results from the published literature are achieved from these special cases. Finally, different physical parameters’ responses are investigated graphically through Mathcad software.

scholarly journals Flow of Brinkman Fluid with Heat Generation and Chemical Reaction

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
M. Ramzan ◽  
Zaib Un Nisa ◽  
M. Ahmad ◽  
M. Nazar
Keyword(s):  
Chemical Reaction ◽  
Heat Generation ◽  
Vertical Plate ◽  
Magnetic Parameter ◽  
Mhd Flow ◽  
Velocity Fields ◽  
Temperature Profiles ◽  
Laplace Transform Method ◽  
Transform Method ◽  
The Laplace Transform

Unsteady magnetohydrodynamics (MHD) flow of fractionalized Brinkman-type fluid over a vertical plate is discussed. In the model of problem, additional effects such as heat generation/absorption and chemical reaction are also considered. The model is solved by using the Caputo fractional derivative. The governing dimensionless equations for velocity, concentration, and temperature profiles are solved using the Laplace transform method and compared graphically. The effects of different parameters like fractional parameter, heat generation/absorption Q , chemical reaction R, and magnetic parameter M are discussed through numerous graphs. Furthermore, comparison among ordinary and fractionalized velocity fields are also drawn. From the figures, it is observed that chemical reaction and magnetic field have decreasing effect on velocity profile, whereas thermal radiation and mass Grashof numbers have increasing effect on the velocity of the fluid.

scholarly journals Bioconvection of Nanofluid Past Stretching Sheet in a Porous Medium in Presence of Gyrotactic Microorganisms with Newtonian Heating

2018 ◽  
Vol 220 ◽  
pp. 01004
Author(s):  
Rashid Pourrajab ◽  
Aminreza Noghrehabadi
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Boussinesq Approximation ◽  
Newtonian Heating ◽  
Gyrotactic Microorganisms ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
Layer Flow

In this study, the effect of Newtonian heating on the boundary layer flow and heat transfer over a stretching surface in a porous medium in the presence of gyrotactic microorganisms and nanoparticle fractions are analysed. The governing equations are reduced to a system of couple non-linear ordinary differential equations, subjected to the Boussinesq approximation and asymmetric heat conditions. The reduced governing ordinary differential equations are then solved numerically. The solutions obtained are graphically represented. The effects of the controlling parameters on the flow, heat, nanoparticle concentration and the density of motile microorganisms have been examined. The results of the present study show the flow velocity, heat and mass transfer and motile microorganism characteristics on the stretching sheet are strongly influenced by the bioconvection parameters and Newtonian.

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