NUMERICAL SOLUTION OF UNSTEADY FREE CONVECTION FLOW IN A SECOND GRADE FLUID

2016 ◽  
Vol 78 (3-2) ◽  
Author(s):  
Nor Athirah Mohd Zin ◽  
Noraihan Afiqah Rawi ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Free Convection ◽  
Prandtl Number ◽  
Vertical Plate ◽  
Second Grade ◽  
Convection Flow ◽  
Second Grade Fluid ◽  
Free Convection Flow ◽  
Viscoelastic Parameter ◽  
Grashof Number ◽  
Grade Fluid

In this paper, the problem of unsteady free convection flow moves along a vertical plate in a second grade fluid is studied. The vertical plate with constant temperature is considered. The dimensional governing equations are transformed into non dimensional equations using appropriate dimensionless variables and solved numerically using Finite Difference Method. Numerical results for velocity and temperature profiles are displayed graphically for viscoelastic parameter, Grashof number and Prandtl number and discussed in details. It is found that, increasing the values of Grashof number and time leads to increase in the velocity profiles. Increasing the values of the Prandtl number and viscoelastic parameter is found to decrease the velocity profile. It is further found that, increasing the values of Prandtl number tends to decrease the thermal boundary layer thickness. 

THE UNSTEADY FREE CONVECTION FLOW OF ROTATING SECOND GRADE FLUID OVER AN OSCILLATING VERTICAL PLATE

2016 ◽  
Vol 78 (3-2) ◽  
Author(s):  
Ahmad Qushairi Mohamad ◽  
Ilyas Khan ◽  
Zulkhibri Ismail ◽  
Sharidan Shafie
Keyword(s):  
Free Convection ◽  
Exact Solutions ◽  
Vertical Plate ◽  
Second Grade ◽  
Convection Flow ◽  
Second Grade Fluid ◽  
Free Convection Flow ◽  
Energy Profiles ◽  
Laplace Transform Technique ◽  
Grade Fluid

In this paper, the exact solutions for unsteady free convection flow of rotating second grade fluid over an isothermal oscillating vertical plate are investigated. This phenomenon is modeled in the form of partial differential equations with initial and boundary conditions. Some suitable non dimensional variables are introduced. The corresponding non-dimensional equations with conditions are solved using Laplace transform technique. Exact solutions for velocity and energy profiles are obtained. They are expressed in simple forms in terms of exponential and complementary error functions of Gauss. It is found that they satisfy governing equations and conditions imposed. Computations are carried out and the results are analyzed for various emerging parameters.

scholarly journals Unsteady Magnetohydrodynamic Free Convection Flow of a Second Grade Fluid in a Porous Medium with Ramped Wall Temperature

PLoS ONE ◽  
2014 ◽  
Vol 9 (5) ◽  
pp. e88766 ◽  
Author(s):  
Samiulhaq ◽  
Sohail Ahmad ◽  
Dumitru Vieru ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Porous Medium ◽  
Free Convection ◽  
Wall Temperature ◽  
Second Grade ◽  
Convection Flow ◽  
Second Grade Fluid ◽  
Free Convection Flow ◽  
Grade Fluid

FREE CONVECTION FLOW OF A SECOND-GRADE FLUID WITH RAMPED WALL TEMPERATURE

2014 ◽  
Vol 45 (7) ◽  
pp. 579-588 ◽  
Author(s):  
Samiulhaq ◽  
Ilyas Khan ◽  
Farhad Ali ◽  
Sharidan Shafie
Keyword(s):  
Free Convection ◽  
Wall Temperature ◽  
Second Grade ◽  
Convection Flow ◽  
Second Grade Fluid ◽  
Free Convection Flow ◽  
Grade Fluid

Free convection flow with chemical reaction effect between oscillating parallel plates

2021 ◽  
Vol 2 (2) ◽  
pp. 52-59
Author(s):  
F. Zulkiflee ◽  
S. Shafie ◽  
A. Ali ◽  
A.Q. Mohamad
Keyword(s):  
Free Convection ◽  
Prandtl Number ◽  
Skin Friction ◽  
Chemical Reaction ◽  
Schmidt Number ◽  
Convection Flow ◽  
Parallel Plates ◽  
Free Convection Flow ◽  
Transform Method ◽  
Grashof Number

This research purpose is to investigate the exact solutions for unsteady free convection flow between oscillating parallel plates with mass diffusion and chemical reaction. The governing equations are modelled and reduced using non-dimensional variables. The method used is Laplace transform method. Solutions for velocity, temperature, and concentration fields as well as skin friction, Nusselt and Sherwood number are obtained. For physical understanding, analytical results for velocity, temperature and concentration profile are plotted graphically with respect to the Schmidt number, Prandtl number, oscillating parameter, Grashof number, mass Grashof number and chemical reaction parameter. Increasing Prandtl number and Schmidt number decreases the concentration, velocity, temperature, and skin friction but increases the Sherwood and Nusselt numbers.

scholarly journals Magnetohydrodynamic Fluctuating Free Convection Flow of Second-Grade Fluid Flow in a Porous Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Farhad Ali ◽  
Momin Khan ◽  
Madeha Gohar
Keyword(s):  
Porous Medium ◽  
Free Convection ◽  
Fluid Motion ◽  
Second Grade ◽  
Convection Flow ◽  
Stream Velocity ◽  
Parallel Plates ◽  
Free Convection Flow ◽  
Viscoelastic Parameter ◽  
Electrically Conducting

The article’s objective is to study the magnetohydrodynamic fluctuating free convection flow of incompressible electrically conducting viscoelastic fluid in a porous medium in the presence of a pressure gradient. The flow is between two parallel plates; the lower plate is at rest, while the upper plate moves with a free stream velocity U t . A uniform magnetic field of strength B0 is applied transversely to the fluid motion. The dimensional governing equations and physical initial and boundary conditions are nondimensionalized by inserting appropriate dimensionless variables. Furthermore, Lighthill’s method is used to obtain exact analytical solutions for the velocity, temperature, and concentration distributions. Finally, the influences of inserted parameters are studied through plots and discussed physically. The numerical results are calculated and presented in tabular form for skin friction. It is worth mentioning that when the viscoelastic parameter α 1 tends to zero, the obtained general solution is reduced to Newtonian fluid, which shows the validity and correctness of our obtained exact solutions.

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