scholarly journals Dufour Effect with Ramped Wall Temperature and Specie Concentration on Natural Convection Flow Through A Channel

Physics ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 111-130 ◽  
Author(s):  
Jha ◽  
Gambo
Keyword(s):  
Wall Temperature ◽  
Numerical Solutions ◽  
Vertical Channel ◽  
Convection Flow ◽  
Physical Situation ◽  
Dimensionless Time ◽  
Dufour Effect ◽  
Laplace Transform Technique ◽  
Flow Through ◽  
The Mathematical Model

In this paper, we have obtained an analytical solution to the problem of unsteady free convection and mass transfer flow of an incompressible fluid through a vertical channel in the presence of Dufour effect (or diffusion thermo). The bounding plates are assumed to have ramped wall temperature as well as specie concentration. The mathematical model responsible for the physical situation is presented in dimensionless form and solved analytically using the powerful Laplace Transform Technique (LTT) under relevant initial and boundary conditions. In order to cross check the accuracy of the analytical results, numerical solutions are obtained using PDEPE solver in MATLAB. The expressions for temperature, concentration, and velocity are obtained. The effects of Dufour parameter, Prandtl number (Pr), Schmidt number (Sc), and dimensionless time are described during the course of these discussions. The temperature, concentration, and velocity profiles are graphically presented for some realistic values of Pr=0.025, 0.71, 7.0, 11.62, 100.0 and Sc=0.22, 0.60, 1.00, 2.62, while the values of all other parameters are arbitrarily taken.

scholarly journals Influence of Thermal Radiation on Unsteady MHD Free Convection Flow of Jeffrey Fluid over a Vertical Plate with Ramped Wall Temperature

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Nor Athirah Mohd Zin ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Free Convection ◽  
Thermal Radiation ◽  
Wall Temperature ◽  
Vertical Plate ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Dimensionless Time ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform

Influence of thermal radiation on unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid over a vertical plate with ramped wall temperature is studied. The Laplace transform technique is used to obtain the analytical solutions. Expressions for skin friction and Nusselt number are also obtained. Results of velocity and temperature distributions are shown graphically for embedded parameters such as Jeffrey fluid parameterλ, Prandtl numberPr, Grashof numberGr, Hartmann numberHa, radiation parameterRd, and dimensionless timeτ. It is observed that the amplitude of velocity and temperature profile for isothermal are always higher than ramped wall temperature.

scholarly journals Unsteady/Steady Hydromagnetic Convective Flow between Two Vertical Walls in the Presence of Variable Thermal Conductivity

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
M. M. Hamza ◽  
I. G. Usman ◽  
A. Sule
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Approximate Solutions ◽  
Variable Thermal Conductivity ◽  
Convection Flow

Unsteady as well as steady natural convection flow in a vertical channel in the presence of uniform magnetic field applied normal to the flow region and temperature dependent variable thermal conductivity is studied. The nonlinear partial differential equations governing the flow have been solved numerically using unconditionally stable and convergent semi-implicit finite difference scheme. For steady case, approximate solutions have been derived for velocity, temperature, skin friction, and the rate of heat transfer using perturbation series method. Results of the computations for velocity, temperature, skin friction, and the rate of heat transfer are presented graphically and discussed quantitatively for various parameters embedded in the problem. An excellent agreement was found during the numerical computations between the steady-state approximate solutions and unsteady numerical solutions at steady-state time. In addition, comparison with previously published work is performed and the results agree well.

scholarly journals Porosity effect on unsteady MHD free convection flow of Jeffrey fluid past an oscillating vertical plate with ramped wall temperature

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Nor Athirah Mohd Zin ◽  
Ahmad Qushairi Mohamad ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Free Convection ◽  
Wall Temperature ◽  
Vertical Plate ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Dimensionless Time ◽  
Governing Equations ◽  
Free Convection Flow ◽  
Permeability Parameter ◽  
The Impact

The unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid embedded in porous medium past an oscillating vertical plate generated by thermal radiation with ramped wall temperature is investigated. The incompressible fluid is taken electrically conducting under the action of transverse magnetic field towards the flow. Constitutive relation of Jeffrey fluid is employed to model the governing equations in terms of partial differential equations with some physical conditions. The transformed dimensionless governing equations are solved analytically using Laplace transform technique. The impact of various pertinent parameters namely material parameter of Jeffrey fluid , dimensionless parameter of Jeffrey fluid , phase angle , Hartmann number , permeability parameter , Grashof number , Prandtl number , radiation parameter  and dimensionless time  on velocity and temperature distributions are presented graphically and discussed in details. It is observed that, the permeability parameter tend to retard the fluid velocity for ramped wall temperature but enhance the velocity for an isothermal plate. Besides that, this study shows, the amplitude of velocity and temperature fields for ramped wall temperature are always lower than isothermal plate. A comparison with the existing published work is also provided to confirm the validity of the present results and an excellent agreement are found. 

MHD Free Convection Flow Through Porous Medium in a Vertical Channel

2014 ◽  
Vol 3 (3) ◽  
pp. 21-33
Author(s):  
Hari Priya.G ◽  
◽  
Bhuvana Vijaya.R ◽  
Siva Prasad.R ◽  
◽  
...  
Keyword(s):  
Porous Medium ◽  
Free Convection ◽  
Vertical Channel ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Flow Through

Magnetohydrodynamics Free Convection Flow of a Radiating and Chemically Reacting Fluid Past an Impulsively Moving Plate With Ramped Wall Temperature

2012 ◽  
Vol 79 (6) ◽  
Author(s):  
Kalidas Das
Keyword(s):  
Mass Transfer ◽  
Free Convection ◽  
Chemical Reaction ◽  
Wall Temperature ◽  
Fluid Velocity ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Moving Plate ◽  
Laplace Transform Technique ◽  
Chemically Reacting

In the present study, the effects of radiation and chemical reaction on unsteady free convection flow and mass transfer of a viscous, electrically conducting incompressible fluid near an impulsively moving vertical flat plate with ramped wall temperature is studied. The primary purpose of this study is to characterize the effects of ramped wall temperature, radiation parameter, chemical reaction parameter, Schmidt number etc., on the flow properties. Exact solutions of the present problem are obtained in closed form by Laplace transform technique. The variations in fluid velocity, temperature and concentration are shown graphically whereas numerical values of skin friction, rate of heat and mass transfer are presented in tabular form to observe the effects of various parameters.

A Note on Exact Solutions for the Unsteady Free Convection Flow of a Jeffrey Fluid

2015 ◽  
Vol 70 (6) ◽  
pp. 397-401 ◽  
Author(s):  
Ilyas Khan
Keyword(s):  
Shear Stress ◽  
Free Convection ◽  
Exact Solutions ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform

AbstractIn this note, we investigate the unsteady free convection flow of a Jeffrey fluid past an infinite isothermal vertical plate. Exact solutions are obtained using the Laplace transform technique. These solutions are expressed in terms of exponential and complementary error functions, and satisfy all imposed initial and boundary conditions as well as the governing equations. The expression for the shear stress is also evaluated. The corresponding solutions for a Newtonian fluid can be easily obtained as a special case. It is found from the velocity and shear stress solutions that they strongly depend on the material parameters of a Jeffrey fluid. The exact solutions obtained here can be used as a benchmark for checking the correctness of other approximate or numerical solutions. In addition, this note will help in understanding the characteristics of non-Newtonian fluid flows that are subject to free convection due to buoyancy force.

Heat Transfer in Eccentric-Concentric Rotation of a Disk and Fluid at Infinity

2016 ◽  
Vol 13 (10) ◽  
pp. 6482-6487
Author(s):  
Ilyas Khan ◽  
Tarek Nabil Ahmed Abdelhameed ◽  
L. C. C Dennis
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Strong Influence ◽  
Fluid Velocity ◽  
Convection Flow ◽  
Dimensionless Time ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Convection Parameter

Heat transfer due to free convection flow in eccentric-concentric rotation of a disk and fluid at infinity is studied in this work Exact solutions for velocity and temperature are obtained by using the Laplace transform technique. The performed calculations disclose that the free convection parameter, Prandtl number, radiation parameter, and dimensionless time have strong influence on fluid velocity and temperature. The graphs are presented for such influence and examined carefully.

Natural Convection Flow in Vertical Channel Due to Ramped Wall Temperature at One Boundary

2009 ◽  
Author(s):  
Narahari Marneni ◽  
Vijay R. Raghavan
Keyword(s):  
Natural Convection ◽  
Volume Flow Rate ◽  
Vertical Channel ◽  
The Other ◽  
Temperature Fields ◽  
Convection Flow ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
Laplace Transform Technique ◽  
The Laplace Transform

An exact solution to the problem of unsteady natural convective flow of a viscous and incompressible fluid in a vertical parallel plate channel due to ramp heating at one boundary is presented. The temperature at one of the channel plates increases linearly over a certain time period and then remains constant while that at the other plate is maintained at the initial fluid temperature. The Laplace transform technique has been used to obtain the expressions for the velocity and temperature fields by solving the dimensionless governing partial differential equations under appropriate boundary conditions. The influence of the physical parameters on the velocity field, the temperature field, rate of heat transfer, skin-friction and volume flow rate of the fluid are analyzed systematically. The shear stress at the plate with ramped temperature boundary condition is significantly higher than that at the other plate because of the steeper velocity profiles in the vicinity. The Nusselt number at the plate with ramped temperature is much higher than that at the other plate indicating that much of the energy released from the plate because of its increasing temperature with time is convected out by the fluid before it reaches the second plate. The natural convection due to ramp heating has also been compared with the baseline case of flow with constant temperature.

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