The laminar boundary layer with arbitrarily distributed mass transfer

Libby, Paul A.

doi:10.1016/0017-9310(66)90034-2

Cited by 13 publications

(3 citation statements)

References 7 publications

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“…Taking the derivative of that sum with respect to AX, equating to zero, and solving for AX we find ZZ X Z'Z\ (Z\) 2 (A6)…”

Section: Discussionmentioning

confidence: 99%

“…The coordinates x and y are along and normal to the surface, and u and v are the respective velocity components. If the tracer is introduced as an impurity in the ablation material over the interva Xi < x < x h as a constant mass fraction </> of the ablating material, the conservation of species at the solid surface gives as the boundary conditions = (C -<t>)(pv) w , y = 0, Xi < x < x h (2) and P D(<)C/<)y) = C(pv) v , y = 0, x h < x (3) The remaining initial and boundary conditions imposed on the solution are that there is no seedant upstream of Xi; hence C(x,y) = 0 i < X (4) and at the outer edge of the boundary layer the concentration also vanishes, C(*,co) = 0 (5) The quantity (pv) w is the mass transfer rate on the surface y = 0 and this is considered to be known.…”

Section: The Diffusion Equation For a Chemically Inert Species Ismentioning

confidence: 99%

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Distribution of a trace element in a boundary layer with mass transfer

Kemp¹,

Wallace²

1970

AIAA Journal

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A theory is presented for the downstream distribution of a tracer injected into a boundary layer of a flat plate or cone with self-similar mass transfer. The tracer, which is injected over a finite length of the surface, is assumed to be chemically inert. Its behavior is controlled by a frozen diffusion equation. The assumption of constant density-viscosity product, and unit Schmidt number results in a linear partial differential equation for the seed mass fraction. This is solved analytically in series form by separation of variables, and numerically by a finite difference technique. It is shown that far downstream of the tracer injection region the analytical results reduce to a simple form; namely, the mass concentration profile is proportional to the local shear even in the presence of mass transfer. However, near the tracer injection region, even the first ten terms are insufficient to yield profiles comparable to those produced by the numerical integration scheme. NomenclatureC = trace species D = diffusion coefficient / = Blasius function with mass transfer M = total mass rate of injection of trace species N = eigenfunction with mass transfer u,v = velocity components along and normal to the surface x,y = Cartesian coordinates along and normal to the surface z = transformed similarity variable £,17 = similarity variables X = eigenvalue 0 = mass fraction of tracer in ablating material p = density IJL = coefficient of viscosity (pv) w ~ mass transfer at solid surface Subscripts e = outer edge of boundary layer h = trailing edge of injection region Received May 12, 1969.

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“…Taking the derivative of that sum with respect to AX, equating to zero, and solving for AX we find ZZ X Z'Z\ (Z\) 2 (A6)…”

Section: Discussionmentioning

confidence: 99%

Section: The Diffusion Equation For a Chemically Inert Species Ismentioning

confidence: 99%

Distribution of a trace element in a boundary layer with mass transfer

Kemp¹,

Wallace²

1970

AIAA Journal

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“…The present analysis adopts the Blasius-perturbation approach developed by Libby and Fox E5J, which has been successfully applied to a variety of laminar boundary layer problems with surface chemical reactions or ablations [6,7,8]. One of the characteristics of the present problem is that the Schmidt number involved is very large.…”

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confidence: 99%

Perturbation analysis of a continuous system for desalination by reverse osmosis

Liu

1972

Appl. Sci. Res.

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Blasius perturbation solutions are developed for the incompressible laminar boundary layer at high Schmidt numbers. The eigenvalues have been found to be multiples of { and the eigenfunctions can be expressed as confluent hypergeometric functions. The eigenfunctions are employed in analyzing a continuous desalination system. Tile reverse-osmosis boundary condition leads to all integral equation which is, in turn, solved by iterative techniques. The first-order calculations show that the results are most accurate for large ratios of osmotic to applied pressures. For medium ratios, the results are reasonably good.The present analysis should be useful, in general, for high Schmidt number flows with linear or nonlinear surface conditions provided that the transverse wall velocity is vanishingly small.

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Generalizing the meaning of ‘heat’

Tribus

1968

International Journal of Heat and Mass Transfer

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The laminar boundary layer with arbitrarily distributed mass transfer

Cited by 13 publications

References 7 publications

Distribution of a trace element in a boundary layer with mass transfer

Distribution of a trace element in a boundary layer with mass transfer

Perturbation analysis of a continuous system for desalination by reverse osmosis

Generalizing the meaning of ‘heat’

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