Skin-Friction and Heat-Transfer Characteristics of a Laminar Boundary Layer on a Cylinder in Axial Incompressible Flow

Seban, R. A.; Bond, Ryan B.

doi:10.2514/8.2076

Cited by 128 publications

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“…Skin-friction coefficient (C f ) as a function of non-dimensional parameter νx U a 2 (a), where results for radius based Reynolds number Rea = 500, 1000 and 10000 are shown along with solutions of Seban-Bond-Kelly(Seban & Bond 1951;Kelly 1954)( ) andGlauert-Lighthill (Glauert & Lighthill 1955)( ). The present result (eq.…”

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confidence: 99%

Analysis of axisymmetric boundary layers

Kumar

Mahesh

2018

J. Fluid Mech.

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Axisymmetric boundary layers are studied using integral analysis of the governing equations for axial flow over a circular cylinder. The analysis includes the effect of pressure gradient and focuses on the effect of transverse curvature on boundary layer parameters such as shape factor (H) and skin-friction coefficient (C f ), defined as H = δ * /θ and) respectively, where δ * is displacement thickness, θ is momentum thickness, τ w is the shear stress at the wall, ρ is density and U e is the streamwise velocity at the edge of the boundary layer. Relations are obtained relating the mean wall-normal velocity at the edge of the boundary layer (V e ) and C f to the boundary layer and pressure gradient parameters. The analytical relations reduce to established results for planar boundary layers in the limit of infinite radius of curvature. The relations are used to obtain C f which shows good agreement with the data reported in the literature. The analytical results are used to discuss different flow regimes of axisymmetric boundary layers in the presence of pressure gradients. †

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confidence: 99%

Analysis of axisymmetric boundary layers

Kumar

Mahesh

2018

J. Fluid Mech.

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“…Shear stress on the surface of a circular cylinder at rest in a moving fluid in axially symmetric flow using the Padé approximation technique Following the asymptotic series solution of Seban & Bond [1], this paper evaluates the shear stress on the surface of a circular cylinder of radius a at rest in a fluid moving with steady velocity U 0 parallel to the axis of the cylinder. The boundary layer builds up from the front of the cylinder and its thickness increases with increasing ξ, where ξ is a non-dimensional variable representing axial distance from the front of the cylinder.…”

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Shear stress on the surface of a circular cylinder at rest in a moving fluid in axially symmetric flow using the Padé approximation technique

Redmond¹,

Spillane²

2003

Proc Appl Math and Mech

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Following the asymptotic series solution of Seban & Bond [1], this paper evaluates the shear stress on the surface of a circular cylinder of radius a at rest in a fluid moving with steady velocity U0 parallel to the axis of the cylinder. The boundary layer builds up from the front of the cylinder and its thickness increases with increasing ξ, where ξ is a non‐dimensional variable representing axial distance from the front of the cylinder. The Seban & Bond solution is valid for small ξ only, near the front of the cylinder where the boundary layer thickness is small compared with a. Curle [2] extended the Seban & Bond results, thus making them valid for larger ξ. Glauert & Lighthill [3] used an asymptotic series to solve the problem in the region where ξ is large. They also used an approximate Pohlhausen method valid for small and large ξ. It is the purpose of this paper to extend the results given by the exact asymptotic series of Seban & Bond so that they are valid for both small and large ξ. This will be done using a Padé approximation technique, which will be compared with the historical results above. It will be seen that the region of validity of the series solution is extended without the need for Curle's extensive analysis and interpolation as in the other cases.

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“…Sakiadis modified the profile to account for different boundary conditions. Middleman and Vasudevan (1970) claimed to have obtained a similarity solution for this problem; however, as was pointed out by Fox and Hagen (1971), a similarity solution does not exist for this flow.A common method for transforming the boundary layer equations written in cylindrical coordinates was suggested first by Seban and Bond (1951). A drawback of this transformation is the large streamwise variations of the velocity profiles and boundary layer thickness that result.…”

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“…A common method for transforming the boundary layer equations written in cylindrical coordinates was suggested first by Seban and Bond (1951). A drawback of this transformation is the large streamwise variations of the velocity profiles and boundary layer thickness that result.…”

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Approximate solution for the viscous boundary layer on a continuous cylinder

Sayles

1990

AIChE Journal

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The boundary layer flow on a continuous flat surface issuing from a slot in a wall into an infinite still fluid was analyzed first by Sakiadis (1961a). His solution consisted of solving the well-known Blasius equation for two-dimensional boundary layer flow (for example, White, 1974) subject to different boundary conditions. The resulting solution is truly a similarity solution for the two-dimensional problem and provides the necessary solution for the early development of the boundary layer on a continuous cylinder upstream of any location where the transverse curvature becomes significant. Sakiadis (1961 b) then solved the problem of boundary layer flow on a continuous cylinder issuing from a wall. This was a momentum integral solution incorporating a logarithmic velocity profile that was suggested first by Glauert and Lighthill (1954). Sakiadis modified the profile to account for different boundary conditions. Middleman and Vasudevan (1970) claimed to have obtained a similarity solution for this problem; however, as was pointed out by Fox and Hagen (1971), a similarity solution does not exist for this flow.A common method for transforming the boundary layer equations written in cylindrical coordinates was suggested first by Seban and Bond (1951). A drawback of this transformation is the large streamwise variations of the velocity profiles and boundary layer thickness that result. Wanous and Sparrow (1965) used this transformation with great success in their perturbation series solution for laminar flow longitudinal to a stationary circular cylinder with surface mass transfer. From their solutions, the dimensionless boundary layer thickness varied by a multiplicative factor of 15 over the entire solution domain. This was not a drawback for their method, but it is for other approximate methods that seek to neglect the prior development of the boundary layer flow. Sparrow et al. (1970) incorporated the transformation used both by Gortler (1957) and Meksyn (1 96 1 ) very successfully in the development of their multiple-equation boundary layer theory. Their choice of a suitable transformation was based on a desire to reduce streamwise variation in the solution, which accomplished the goal better than the previously mentioned transformation. Their three-equation local similarity model yielded solutions of high precision a t the expense of some calculational complexities. The results presented here represent the extension of the theory of Sayles (1984) for the viscous boundary layer flow over semiinfinite cylinders. The first term on the righthand side of Eq. 2 introduces the transverse curvature effect that precludes the possibility of obtaining a similarity solution for this boundary layer flow. The radial velocity component, u, can be expressed in terms of the axial velocity component, w, as (3)A dimensionless axial velocity component can then be defined as:where wo is the velocity of the translating cylinder. Also, dimensionless independent variables q and s are defined as:

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Skin-Friction and Heat-Transfer Characteristics of a Laminar Boundary Layer on a Cylinder in Axial Incompressible Flow

Cited by 128 publications

References 1 publication

Analysis of axisymmetric boundary layers

Analysis of axisymmetric boundary layers

Shear stress on the surface of a circular cylinder at rest in a moving fluid in axially symmetric flow using the Padé approximation technique

Approximate solution for the viscous boundary layer on a continuous cylinder

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