The stability of the laminar natural convection boundary layer

1968 ◽  
Vol 34 (4) ◽  
pp. 657-686 ◽  
Author(s):  
C. P. Knowles ◽  
B. Gebhart
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Three Dimensional ◽  
Thermal Capacity ◽  
Wave Number ◽  
Convection Boundary Layer ◽  
Grashof Number ◽  
Convection Boundary ◽  
Laminar Natural Convection ◽  
The Stability

This paper concerns the stability characteristics of laminar natural convection in external flows. Until recently, very little was known about such stability because of the inherent complexity of temperature-coupled flows and because of the complicated mechanisms of disturbance propagation. In this work the stability of the laminar natural convection boundary layer is examined more closely in an attempt to predict the experimental results recently obtained. In particular, it is shown that an important thermal capacity coupling exists between the fluid and the wall which generates the flow. This thermal capacity coupling is shown to have a first-order effect for particular Grashof-number wave-number products. Solutions are obtained for a Prandtl number of 0·733 and several values of relative wall thermal capacity. These solutions indicate the important role of this wall coupling. In particular, the results predict the experimental data previously obtained.In addition, solutions with ‘zero wall storage’ are obtained for a range of Prandtl numbers from 0·733 to 6·9. The relative disturbance u-velocity and temperature amplitudes and their phases are shown for Pr = 0·733 and several wall-storage parameters, and for Pr = 6·9 with zero wall storage. A comparison between the disturbance temperature distribution and the data obtained from a recent experimental investigation shows close agreement when the thermal capacity of the wall is taken into account.In the appendix, it is shown that for temperature-coupled flows and wall-coupled boundary conditions the flow is unstable at a lower Grashof number for two-dimensional disturbances than it is for three-dimensional disturbances. This result has been supported by the recent experimental observations.

Stress work effects in laminar flat-plate natural convection

1974 ◽  
Vol 62 (4) ◽  
pp. 677-695 ◽  
Author(s):  
J. A. D. Ackroyd
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Convection Boundary Layer ◽  
Pressure Work ◽  
Flat Surfaces ◽  
Convection Boundary ◽  
Laminar Natural Convection ◽  
Temperature And Pressure ◽  
Pressure Stress ◽  
Stress Work

The effects of both viscous and pressure stress work are considered in laminar natural convection on flat surfaces. Whereas in previous investigations only viscous stress work effects were studied, it is established here that pressure work effects are generally rather more important both for gases and liquids. Variations in the properties of the fluid outside the natural convection boundary layer are shown to occur inevitably in this problem and are found to lead to effects comparable with those produced by pressure work. Property variations in the boundary layer itself are also found to be of importance. Such variations, both inside and outside the boundary layer, have been ignored in previous studies. Examples of flows are discussed in which the fluids are either perfect gases or fluids undergoing small changes in temperature and pressure. For both of these fluids, the effects of conditions of either constant temperature or constant entropy in the fluid outside the boundary layer are examined.

Stability of a temporally evolving natural convection boundary layer on an isothermal wall

2019 ◽  
Vol 877 ◽  
pp. 1163-1185 ◽  
Author(s):  
Junhao Ke ◽  
N. Williamson ◽  
S. W. Armfield ◽  
G. D. McBain ◽  
S. E. Norris
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Linear Stability ◽  
Transition Point ◽  
Three Dimensional ◽  
Base Flow ◽  
Convection Boundary Layer ◽  
Two Dimensional ◽  
Integral Boundary ◽  
Convection Boundary

The stability properties of a natural convection boundary layer adjacent to an isothermally heated vertical wall, with Prandtl number 0.71, are numerically investigated in the configuration of a temporally evolving parallel flow. The instantaneous linear stability of the flow is first investigated by solving the eigenvalue problem with a quasi-steady assumption, whereby the unsteady base flow is frozen in time. Temporal responses of the discrete perturbation modes are numerically obtained by solving the two-dimensional linearized disturbance equations using a ‘frozen’ base flow as an initial-value problem at various $Gr_{\unicode[STIX]{x1D6FF}}$, where $Gr_{\unicode[STIX]{x1D6FF}}$ is the Grashof number based on the velocity integral boundary layer thickness $\unicode[STIX]{x1D6FF}$. The resultant amplification rates of the discrete modes are compared with the quasi-steady eigenvalue analysis, and both two-dimensional and three-dimensional direct numerical simulations (DNS) of the temporally evolving flow. The amplification rate predicted by the linear theory compares well with the result of direct numerical simulation up to a transition point. The extent of the linear regime where the perturbations linearly interact with the base flow is thus identified. The value of the transition $Gr_{\unicode[STIX]{x1D6FF}}$, according to the three-dimensional DNS results, is dependent on the initial perturbation amplitude. Beyond the transition point, the DNS results diverge from the linear stability predictions as nonlinear mechanisms become important.

Instability of Laminar Natural Convection Boundary Layer Flow on a Vertical Porous Flat Plate

1996 ◽  
Vol 63 (2) ◽  
pp. 404-410 ◽  
Author(s):  
T. Watanabe ◽  
H. Taniguchi ◽  
I. Pop
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Boundary Layer Flow ◽  
Convection Boundary Layer ◽  
Injection Parameter ◽  
Convection Boundary ◽  
Porous Flat Plate ◽  
Suction Or Injection ◽  
Laminar Natural Convection ◽  
Layer Flow

The effects of uniform suction and injection on the linear stability theory of laminar natural convection boundary layer flow along a vertical porous flat plate which is maintained at a constant temperature are studied. The nonsimilar boundary layer equations for the basic steady flow have been solved numerically employing a very efficient finite difference scheme in combination with an iterative method for solving the resulting ordinary differential equations. The temporal neutral stability theory for wavelike disturbances of Tollmien-Schlichting type are then presented for the velocity and temperature functions. The corresponding eigenvalue problem for the disturbance amplitude functions is also solved numerically using a very accurate method. Results are presented graphically for both the basic and disturbance velocity and temperature profiles for some values of the modified local Grashof number G and suction or injection parameter X. The Prandtl number Pr is taken to be 0.73 (air) throughout this paper. The results show clearly the important role that suction or injection parameter X may have on the basic and disturbance flow characteristics in this problem.

Sign in / Sign up

Export Citation Format

Share Document