Inertia and Energy Effects in the Developing Gas Film Between Two Parallel Flat Plates

Inertia and temperature effects in entrance flow between parallel flat plates are investigated with the use of boundary-layer theory. In addition, an approximate theory is developed which is implemented by a “gas table” similar to that employed for conventional Fanno-line computations.

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Experiments on Transient Thermal Convection With Internal Heating—Large Time Results

Journal of Heat Transfer ◽

10.1115/1.3245572 ◽

1983 ◽

Vol 105 (2) ◽

pp. 261-266 ◽

Cited By ~ 3

Author(s):

M. Keyhani ◽

F. A. Kulacki

Keyword(s):

Boundary Layer ◽

Thermal Convection ◽

Lower Boundary ◽

Horizontal Layer ◽

Step Change ◽

Boundary Layer Theory ◽

Approximate Theory ◽

Fourier Number ◽

Final State ◽

Volumetric Heating

Experimental data and correlations are presented for the time scales of developing and decaying thermal convection with volumetric heating in a horizontal layer. The layer is bounded by rigid surfaces, with an insulated lower boundary and an isothermal upper boundary. The time for complete flow development/decay, as a result of a step change in volumetric heat generation, is simply parameterized in terms of the Fourier number for the layer, the step change in Rayleigh number, ΔRa, and the initial/final dimensionless maximum core temperature. For developing flows, ΔRa > 0, results are in good agreement with existing experiments and an approximate boundary layer theory. In decaying flows, Fourier numbers are larger than those of previously reported experiments for a motionless final state. Data for turbulent-to-turbulent transitions when ΔRa < 0 suggests that the approximate boundary layer theory underestimates the Fourier number. Experimental uncertainties on measured Fourier numbers are generally well within the limits of uncertainty allowed by the approximate theory.

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The Boundary Layer and Recent Developments

Journal of the Royal Aeronautical Society ◽

10.1017/s0368393100104109 ◽

1936 ◽

Vol 40 (309) ◽

pp. 563-585 ◽

Cited By ~ 1

Author(s):

L. Bairstow

Keyword(s):

Boundary Layer ◽

National Physical Laboratory ◽

Boundary Layer Theory ◽

Compressed Air ◽

Flat Plates ◽

Physical Laboratory ◽

Recent Developments

As time passes more and more knowledge of the flow of fluids past bodies accumulates and of this increase some becomes applied to the problems of the day. Boundary layer theory is being applied at the present time to the problem of the degree of polish which should be given to a wing in order to reduce its profile drag to a minimum. Tests in the compressed air tunnel at the National Physical Laboratory and in flight at Cambridge and Farnborough have recently been directed to this point and give quantitative assurance of the correctness of theory. In what follows, a survey is made of a group of theorems relating to the resistance of various bodies such as aerofoils and flat plates and more generally to streamline forms. The theorems are partly physical and partly mathematical and approximations are numerous and of very different degrees of validity.

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An approximate theory for incompressible viscous flow past two-dimensional bluff bodies in the intermediate Reynolds number regime O(1) < Re < O(102)

Journal of Fluid Mechanics ◽

10.1017/s002211207600116x ◽

1976 ◽

Vol 77 (1) ◽

pp. 129-152 ◽

Cited By ~ 2

Author(s):

Sheldon Weinbaum ◽

Michael S. Kolansky ◽

Michael J. Gluckman ◽

Robert Pfeffer

Keyword(s):

Boundary Layer ◽

Reynolds Number ◽

Pressure Gradient ◽

Boundary Layer Theory ◽

Navier Stokes ◽

Bluff Bodies ◽

Approximate Theory ◽

Two Dimensional ◽

First Order ◽

Flow Past

A new approximate theory is proposed for treating the flow past smoothly contoured two-dimensional bluff bodies in the intermediate Reynolds number rangeO(1) <Re< 0(102), where the displacement effect of the thick viscous layer near the surface of the body is large and a steady laminar wake is present. The theory is based on a new pressure hypothesis which enables one to take account of the displacement interaction and centrifugal effects in thick viscous layers using conventional first-order boundary-layer equations. The basic question asked is how the wall pressure gradient in ordinary boundary -layer theory must be modified if the pressure gradient along the displacement surface using the Prandtl pressure hypothesis is to be equal to the pressure gradient along this surface using a higher-order approximation to the Navier-Stokes equation in which centrifugal forces are considered. The inclusion of the normal pressure field with displacement interaction is shown to be equivalent to stretching the streamwise body co-ordinate in first-order boundary-layer theory such that the streamwise pressure gradient as a function of distance along the original and displacement body surfaces are equal.While the new theory is of a non-rigorous nature, it yields results for the location of separation and detailed surface pressure and vorticity distribution which are in remarkably good agreement with the large body of available numerical Navier-Stokes solutions. A novel feature of the new boundary-value problem is the development of a simple but accurate approximate method for determining the inviscid flow past an arbitrary two-dimensional displacement body with its wake.

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