Erratum: State space formulation for boundary-layer magneto-hydrodynamic free convection flow with one relaxation time

2002 ◽  
Vol 80 (10) ◽  
pp. 1185
Author(s):  
M A Ezzat ◽  
A A Samaan ◽  
A Abd-El Bary
Keyword(s):  
Boundary Layer ◽  
Relaxation Time ◽  
Free Convection ◽  
State Space ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Space Formulation

State space formulation for boundary-layer magneto-hydrodynamic free convection flow with one relaxation time

2002 ◽  
Vol 80 (10) ◽  
pp. 1157-1174 ◽  
Author(s):  
M A Ezzat ◽  
A A Samaan ◽  
A Abd-El Bary
Keyword(s):  
Boundary Layer ◽  
Relaxation Time ◽  
State Space ◽  
Boundary Layer Equation ◽  
Convection Flow ◽  
Heat Sources ◽  
Space Problem ◽  
Whole Space ◽  
Space Formulation ◽  
Plane Distribution

We introduce a magnetohydrodynamic model of a boundary-layer equation for a conducting viscous fluid. The state space approach is adopted for one-dimensional problems including heat sources with one relaxation time. The resulting formulation is applied to a problem for the whole space with a plane distribution of heat sources. The reflection method together with the solution obtained for the whole space is applied to a semi-space problem with a plane distribution of heat sources located inside the fluid. Numerical results for the velocity, temperature, and induced-magnetic- and induced-electric-field distributions are given and illustrated graphically for both problems. PACS No.: 47.65+a

Instability in Boundary-Layer Free Convection along an inclined Plate

1972 ◽  
Vol 1 (4) ◽  
pp. 197-204 ◽  
Author(s):  
J.B. Lee ◽  
G.S.H. Lock
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Plane Surface ◽  
Convection Flow ◽  
Neutral Stability ◽  
Inclined Plate ◽  
Free Convection Flow ◽  
Roll Vortices ◽  
The Stability ◽  
Rayleigh Numbers

This paper gives theoretical consideration to the problem of the stability of laminar, boundary-layer, free-convection flow of air along a long, inclined plane surface heated isothermally. The analysis considers two forms of small disturbance: a two-dimensional wave disturbance, and a set of longitudinal roll vortices. Development of the appropriate disturbance equations is followed by their numerical solution. The effect of inclination on the neutral stability curves for both disturbance forms is presented graphically along with a comparison of the critical Rayleigh numbers obtained from both disturbance forms.

scholarly journals The Effect of Plate Oscillations on Horizontal Free Convection Flow

1977 ◽  
Vol 30 (3) ◽  
pp. 335 ◽  
Author(s):  
RL Verma ◽  
Punyatma Singh
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Convection ◽  
Skin Friction ◽  
Low Frequency ◽  
Convection Flow ◽  
Phase Lag ◽  
Mean Flow ◽  
Free Convection Flow ◽  
Boundary Layer Equations

The free convection flow along a semi-infinite horizontal plate oscillating in its own plane is analysed The basic flow is purely buoyancy induced, while the oscillations in the plate cause a time-dependent boundary layer flow and heat transfer. The boundary layer equations are linearized and the first two approximations are considered. Two separate solutions valid for high and low frequency ranges are obtained by a series expansion in terms of frequency parameters. The skin friction and the rate of heat transfer are studied for both frequency ranges. For very high frequencies, the oscillatory flow pattern is of a 'shear-wave' type, unaffected by the mean flow. It is found that the phase of the skin friction at the plate lags that of the plate oscillations by in and the rate of heat transfer has a phase lag of 1/2n.

Developing Laminar Free Convection in an Open Ended Vertical Annulus with a Rotating Inner Cylinder

1981 ◽  
Vol 103 (3) ◽  
pp. 552-558 ◽  
Author(s):  
M. A. I. El-Shaarawi ◽  
A. Sarhan
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Free Convection ◽  
Outer Cylinder ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Boundary Layer Equations ◽  
Thermal Boundary Conditions ◽  
Displacement Thickness ◽  
Vertical Annulus

A finite-difference scheme is developed for solving the boundary layer equations governing the laminar free convection flow in open ended vertical concentric annuli with rotating inner walls. Numerical results are presented for a fluid of Pr = 0.7 in an annulus of radius ratio 0.5 under the thermal boundary conditions of one wall being isothermal and the opposite wall adiabatic. Comparing the present results for the development of δθ (tangential boundary layer displacement thickness) with those corresponding results of forced flows shows that heating the inner cylinder has always stabilizing effects while heating the outer cylinder has either destabilizing or stabilizing effects.

Laminar Boundary∼Layer Free Convection along an Inclined, Isothermal Surface

1972 ◽  
Vol 1 (4) ◽  
pp. 189-196 ◽  
Author(s):  
J.B. Lee ◽  
G.S.H. Lock
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Convection ◽  
Laminar Boundary Layer ◽  
Theoretical Consideration ◽  
Plane Surface ◽  
Convection Flow ◽  
Inclined Plane ◽  
Free Convection Flow ◽  
Boundary Layer Equations

This paper gives theoretical consideration to the problem of laminar, boundary-layer, free convection flow along a long, inclined, plane surface heated isothermally. Development of the appropriate boundary-layer equations is followed by their numerical solution for air. The effects of inclination and position on heat transfer and the temperature, pressure and velocity profiles are presented graphically for RaL ≤ 106.

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