scholarly journals On the existence of solution of the Greenspan-Carrier equation

1973 ◽  
Vol 15 (3) ◽  
pp. 373-384
Author(s):  
H. P. Heinig ◽  
K. Kuen Tam
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Existence Of Solution ◽  
Conducting Fluid ◽  
Rigid Plate ◽  
Different Boundary Conditions ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Electrically Conducting Fluid

We are concerned with the flow of a viscous incompressible electrically conducting fluid of constant properties past a semi-infinite rigid plate. The governing boundary layer equations were derived by Greenspan and Carrier [2] in 1959. Numerical solutions of these equations subject to different boundary conditions have been considered by Stewartson and Wilson [5], Wilson [8], and recently by Bramley [1].

Mixed Convection Cooling of a Stretching Sheet in the Presence of a Magnetic Field for Manufacturing Processes

2009 ◽  
Vol 419-420 ◽  
pp. 353-356 ◽  
Author(s):  
Chien Hsin Chen
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Numerical Solutions ◽  
Conducting Fluid ◽  
Manufacturing Processes ◽  
Stretching Surface ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Electrically Conducting Fluid ◽  
Rate Of Cooling

The problem of flow and heat transfer over a continuously stretching surface finds applications in many manufacturing processes, such as polymer extrusion, wire drawing, continuous casting, glass fiber production, and metallurgical processes. It is known that the properties of the final product depend considerably on the rate of cooling during the manufacturing processes. The rate of cooling can be controlled by drawing the strips in an electrically conducting fluid subject to a magnetic field, so that a final product of desired characteristics can be achieved. In this study, the problem of magneto-hydrodynamic (MHD) mixed convective flow and heat transfer of an electrically conducting fluid past a stretching surface under the influence of an applied magnetic field is analyzed. After transforming the governing equations with suitable dimensionless variables, numerical solutions are generated by an implicit finite-difference technique for the non-similar, coupled flow. To reveal the tendency of the solutions, typical results for the velocity and temperature profiles, the skin-friction coefficient, and the local Nusselt number are presented for different parameters.

scholarly journals Effect of variable viscosity on laminar convection flow of an electrically conducting fluid in uniform magnetic field

2002 ◽  
pp. 49-62 ◽  
Author(s):  
S. Chakraborty ◽  
A.K. Borkakati
Keyword(s):  
Magnetic Field ◽  
Flat Plate ◽  
Uniform Magnetic Field ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Conducting Fluid ◽  
Fluid Viscosity ◽  
Electrically Conducting ◽  
Viscosity Parameter ◽  
Electrically Conducting Fluid

The flow of a viscous incompressible electrically conducting fluid on a continuous moving flat plate in presence of uniform transverse magnetic field, is studied. The flat plate which is continuously moving in its own plane with a constant speed is considered to be isothermally heated. Assuming the fluid viscosity as an inverse linear function of temperature, the nature of fluid velocity and temperature in presence of uniform magnetic field are shown for changing viscosity parameter at different layers of the medium. Numerical solutions are obtained by using Runge-Kutta and Shooting method. The coefficient of skin friction and the rate of heat transfer are calculated at different viscosity parameter and Prandt l number. .

Numerical Treatment of the MHD Convective Heat and Mass Transfer in an Electrically Conducting Fluid over an Infinite Solid Surface in Presence of the Internal Heat Generation

2003 ◽  
Vol 58 (11) ◽  
pp. 601-611 ◽  
Author(s):  
N. T. Eldabe ◽  
A. G. El-Sakka ◽  
Ashraf Fouad
Keyword(s):  
Mass Transfer ◽  
Heat Generation ◽  
Solid Surface ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Conducting Fluid ◽  
Electrically Conducting ◽  
Linear Partial Differential Equations ◽  
Electrically Conducting Fluid

Numerical solutions of a set of non-linear partial differential equations are investigated. We obtained the velocity distribution of a conducting fluid flowing over an infinite solid surface in the presence of an uniform magnetic field and internal heat generation. The temperature and concentration distributions of the fluid are studied as well as the skin-friction, rate of mass transfer and local wall heat flux. The effect of the parameters of the problem on these distributions is illustrated graphically.

scholarly journals Non-Newtonian conducting fluid flow and heat transfer due to a rotating disk

2004 ◽  
Vol 46 (2) ◽  
pp. 237-248 ◽  
Author(s):  
Hazem A. Attia ◽  
Mohamed E. S. Ahmed
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Hall Current ◽  
Rotating Disk ◽  
Conducting Fluid ◽  
Physical Parameters ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Electrically Conducting Fluid ◽  
Fluid Characteristics

AbstractThe steady flow of an incompressible viscous non-Newtonian electrically conducting fluid and heat transfer due to the rotation of an infinite disk are studied considering the Hall effect. The effects of an externally applied uniform magnetic field, the Hall current, and the non-Newtonian fluid characteristics on the velocity and temperature distributions as well as the heat transfer are considered. Numerical solutions of the nonlinear equations which govern the magnetohydrodynamics (MHD) and energy transfer are obtained over the entire range of the physical parameters.

Mixed convection flow of an electrically conducting fluid in a vertical channel with boundary conditions of the third kind

2014 ◽  
Vol 92 (11) ◽  
pp. 1387-1396 ◽  
Author(s):  
J.C. Umavathi ◽  
A.J. Chamkha
Keyword(s):  
Mixed Convection ◽  
Average Velocity ◽  
Vertical Channel ◽  
Perturbation Parameter ◽  
Conducting Fluid ◽  
Integration Scheme ◽  
Electrically Conducting ◽  
Nusselt Numbers ◽  
Electrically Conducting Fluid ◽  
External Fluid

In this study, the effects of viscous and Ohmic dissipation in steady, laminar, mixed, convection heat transfer for an electrically conducting fluid flowing through a vertical channel is investigated in both aiding and opposing buoyancy situations. The plates exchange heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. First, the simpler cases of either negligible Brinkman number or negligible Grashof number are addressed with the help of analytical solutions. The combined effects of buoyancy forces and viscous dissipation are analyzed using a perturbation series method valid for small values of the perturbation parameter. To relax the conditions on the perturbation parameter, the governing equations are also evaluated numerically by a shooting technique that uses the classical explicit Runge–Kutta method of four slopes as an integration scheme and the Newton–Raphson method as a correction scheme. In the examined cases of velocity and temperature fields, the Nusselt numbers at both the walls and the average velocity are explored. It is found that the velocity profiles for an open circuit (E > 0 or E < 0) lie in between the short circuit (E = 0). The graphical results illustrating the effects of various parameters on the flow as well as the average velocity and Nusselt numbers are presented for open and short circuits. In the absence of electric field load parameter and Hartmann number, the results agree with Zanchini (Int. J. Heat Mass Transfer, 41, 3949 (1998)). Further, the analytical and numerical solutions agree very well for small values of the perturbation parameter.

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