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.

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.

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.

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.

Keller-Box Scheme to Mixed Convection Flow Over a Solid Sphere with the Effect of MHD

2021 ◽  
Vol 6 (1) ◽  
pp. 97
Author(s):  
Mohammad Ghani ◽  
Wayan Rumite
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Mixed Convection ◽  
Numerical Solutions ◽  
Solid Sphere ◽  
Convection Flow ◽  
Boundary Layer Equations ◽  
Buoyancy Forces ◽  
Dimensional Boundary ◽  
External Forces

Mixed convection is the combination of a free convection caused by the buoyancy forces due to the different density and a forced convection due to external forces that increase the heat exchange rate. This means that, in free convection, the effect of external forces is significant besides buoyancy forces. In this study the fluid type with viscoelastic effect is non-Newtonian. The viscoelastic fluids that pass over a surface of a sphere form a thin layer, which due to their dominant viscosity is called by the border layer. The obtained limiting layer is analyzed with the thickness of the boundary layer-  near the lower stagnating point, then obtained dimensional boundary layer equations, continuity, momentum, and energy equations. These dimensional boundary layer equations are then transformed into non-dimensional boundary layer equations by using non-dimensional variables. Further, the non-dimensional boundary layer equations are transformed into ordinary differential equations by using stream function, so that obtained the non-similar boundary layer equations. These non-similar boundary layer equations are solved numerically by using finite difference method of Keller-Box. The discretization results are non-linear and it should be linearized using newton linearization technique. The numerical solutions are analyzed the effect of Prandtl number, viscoelastic, mixed convection, and MHD parameters towards velocity profile, temperature profile, and wall temperature.

scholarly journals Finite difference solution of radiation effects on MHD unsteady free-convection flow over vertical plate with variable surface temperature

2003 ◽  
Vol 2003 (2) ◽  
pp. 65-86 ◽  
Author(s):  
M. A. Abd El-Naby ◽  
Elsayed M. E. Elbarbary ◽  
Nader Y. Abdelazem
Keyword(s):  
Finite Difference ◽  
Free Convection ◽  
Radiation Effects ◽  
Vertical Plate ◽  
Convection Flow ◽  
Temperature Profiles ◽  
Radiation Parameter ◽  
Free Convection Flow ◽  
Variable Surface ◽  
Variable Surface Temperature

An analysis is performed to study radiation effects on magnetohydrodynamic (MHD) unsteady free-convection flow past a semi-infinite vertical plate with variable surface temperature in the presence of transversal uniform magnetic field. The boundary layer equations are transformed into a linear algebraic system by an implicit finite-difference method. A parametric study is performed to illustrate the influence of radiation parameter, magnetic parameter, and Prandtl number on the velocity and temperature profiles. The numerical results reveal that the radiation has significant influences on the velocity and temperature profiles, skin friction, and Nusselt number. The results indicate that the velocity, temperature, and local and average skin friction increase as the radiation parameter increases, while the local and average Nusselt numbers decrease as the radiation parameter increases.

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