Steady rotation of a body of revolution in a conducting fluid

1969 ◽  
Vol 65 (1) ◽  
pp. 329-350 ◽  
Author(s):  
R. T. Waechter
Keyword(s):  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Body Of Revolution ◽  
Bodies Of Revolution ◽  
Electrically Conducting ◽  
Reduced Equations ◽  
Electrically Conducting Fluid ◽  
Weakly Conducting ◽  
Steady Rotation ◽  
Inertia Forces

We investigate the steady rotation of an insulating body of revolution in an unbounded electrically conducting fluid permeated by a uniform axial applied magnetic field. The assumptions of a small magnetic Reynolds number (Rm ≪ 1, i.e. the weakly conducting situation) and negligible inertia forces compared with the magnetic forces (R/M2 ≪ 1) permit us to suppress the inflow at the poles and outflow at the equator, which normally occurs for a non-conducting viscous fluid ((12), pp. 436–439). Thus in the case of the sphere, we find an exact solution of the reduced equations in terms of an infinite series of Legendre polynomials of order 1 with coefficients which are the ratios of modified spherical Bessel functions. This is the canonical problem by which results for arbitrary bodies of revolution are obtained.

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.

Investigation of the Influence of Inertia Forces on the Adhesion of the Coating to the Outer Surface of Bodies of Revolution during Thermal Spraying

2021 ◽  
Vol 316 ◽  
pp. 726-731
Author(s):  
Alexey Yu. Rodichev ◽  
Roman N. Polyakov ◽  
Andrey V. Gorin
Keyword(s):  
Adhesion Strength ◽  
Outer Surface ◽  
External Surface ◽  
Thermal Spraying ◽  
Inertial Forces ◽  
Body Of Revolution ◽  
Mathematical Apparatus ◽  
Bodies Of Revolution ◽  
Steel Base ◽  
Inertia Forces

The article presents the results of a study of the influence of inertial forces on the adhesion of the coating to the external surface of a body of revolution during thermal spraying. A mathematical apparatus is proposed for calculating the inertia forces, acting on a particle of coating, applied to the outer surface of the bodies of revolution. As a result, dependencies have been revealed that allow predicting the adhesion strength of the coating with the steel base during thermal spraying.

scholarly journals Span-Wise Fluctuating MHD Convective Flow of a Viscoelastic Fluid through a Porous Medium in a Hot Vertical Channel with Thermal Radiation

2016 ◽  
Vol 21 (3) ◽  
pp. 667-681 ◽  
Author(s):  
K.D. Singh
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Vertical Channel ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Temperature Fields ◽  
Convection Flow ◽  
Electrically Conducting ◽  
Unsteady Mixed Convection ◽  
Phase Angles

Abstract An unsteady mixed convection flow of a visco-elastic, incompressible and electrically conducting fluid in a hot vertical channel is analyzed. The vertical channel is filled with a porous medium. The temperature of one of the channel plates is considered to be fluctuating span-wise cosinusoidally, i.e., $T^* \left( {y^* ,z^* ,t^* } \right) = T_1 + \left( {T_2} - {T_ 1} \right)\cos \left( {{{\pi z^* } \over d} - \omega ^* t^* } \right)$ . A magnetic field of uniform strength is applied perpendicular to the planes of the plates. The magnetic Reynolds number is assumed very small so that the induced magnetic field is neglected. It is also assumed that the conducting fluid is gray, absorbing/emitting radiation and non-scattering. Governing equations are solved exactly for the velocity and the temperature fields. The effects of various flow parameters on the velocity, temperature and the skin friction and the Nusselt number in terms of their amplitudes and phase angles are discussed with the help of figures.

Sign in / Sign up

Export Citation Format

Share Document