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

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.

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

Jurnal Teknologi ◽

10.11113/jt.v78.7819 ◽

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.

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SLIP EFFECT ON FREE CONVECTION FLOW OF SECOND GRADE FLUIDS WITH RAMPED WALL TEMPERATURE

Heat Transfer Research ◽

10.1615/heattransres.2015007464 ◽

2015 ◽

Vol 46 (8) ◽

pp. 713-724 ◽

Cited By ~ 5

Author(s):

Dumitru Vieru ◽

M. A. Imran ◽

A. Rauf

Keyword(s):

Free Convection ◽

Wall Temperature ◽

Second Grade ◽

Convection Flow ◽

Slip Effect ◽

Free Convection Flow ◽

Second Grade Fluids

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The unsteady mixed convection flow of rotating second grade fluid in porous medium with ramped wall temperature

Malaysian Journal of Fundamental and Applied Sciences ◽

10.11113/mjfas.v13n4.747 ◽

2017 ◽

Vol 13 (4) ◽

pp. 798-802

Author(s):

Ahmad Qushairi Mohamad ◽

Ilyas Khan ◽

Nor Athirah Mohd Zin ◽

Zulkhibri Ismail ◽

Sharidan Shafie

Keyword(s):

Mixed Convection ◽

Wall Temperature ◽

Fluid Velocity ◽

Second Grade ◽

Convection Flow ◽

Mixed Convection Flow ◽

Second Grade Fluid ◽

Porosity Parameter ◽

Unsteady Mixed Convection ◽

Grade Fluid

The effects of ramped wall temperature, rotation and porosity on mixed convection flow of incompressible second grade fluid are studied. The momentum equation is modelled in a problem of rotating fluid with constant angular velocity subjected to initial and oscillating boundary conditions. The energy equation is also introduced. Some suitable non-dimensional variables are used to write equations into non-dimensional form. Laplace transform method is used to solve these equations in order to obtain the analytical solutions of velocity and temperature profiles. Computations are carried out and presented graphically to analyse the effect of second grade fluid parameter, rotation parameter, porosity parameter, Prandtl number and Grashof number on the profiles. It is found that, for larger values of porosity parameter, the fluid velocity will increase for both primary and secondary velocities. The results also show that, velocity for ramped wall temperature is lower compared to isothermal temperature. It is worth to mention that, the exact solutions obtained in this study can be used to check correctness of the results obtained through numerical schemes.

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