A conducting paper technique for the analogue solution of the biharmonic equation

Curtis, A. R.; Sherry, N P R

doi:10.1088/0022-3727/3/7/419

Cited by 4 publications

(8 citation statements)

References 5 publications

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“…This is done by drawing a normal to the boundary of the cylinder on the $ layer at points corresponding to the centre of each segment on the $ layer. The t,b values at small distances 1 and 21 from the boundary along the normal are required to be in proportion $z=4$1 (Curtis and Sherry 1970).…”

Section: Experimental Methodsmentioning

confidence: 99%

“…These analogues consist of two plane meshes each composed of a rectangular array of equal resistors, linked at corresponding points by resistors of higher resistance. Curtis and Sherry (1970) gave details of an analogue comprising two sheets of conducting paper linked at corresponding points by resistors of resistance higher than the resistance per square of the paper. A useful advantage of this method is that problems with curved boundaries may be readily solved.…”

Section: Introductionmentioning

confidence: 99%

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The viscous drag on cylinders falling symmetrically between parallel walls

Curtis¹,

Marr²

1978

J. Phys. D: Appl. Phys.

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An analogue technique for the approximate solution of the biharmonic equation is used to determine the viscous drag at Reynolds number approaching zero for cylinders falling symmetrically in a liquid between parallel walls. Results obtained show good agreement with numerical solutions, with results by direct experiment and with the work of other authors. Streamlines are obtained with a maximum error of 2% and vorticities and viscous drag forces with a maximum error of approximately 10%. Symbols viscosity kinematic viscosity x and y components qf velocity velocity of cylinder stream function vorticity viscous drag force surface resistance resistance mesh element voltages corresponding to and $ ratio of cylinder diameter to wall separation.

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Section: Experimental Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The viscous drag on cylinders falling symmetrically between parallel walls

Curtis¹,

Marr²

1978

J. Phys. D: Appl. Phys.

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“…Hence, the strength in the direction of orientation is greater than that of the orientation-free structures. On the other hand, the strength perpendicular to the orientation is much less than that of the orientation-free polymers, since the deformation along this direction occurs when the weak intermolecular bonds break (1).…”

Section: Effect Of Molecular Orientationmentioning

confidence: 99%

Performance prediction of weldline structure in amorphous polymers

Kim

Suh

1986

Polymer Engineering & Sci

108

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The presence of a weldline generally reduces the mechanical strength of injection molded parts. A typical remedy to eliminate the problem of weak weldline structure has been to increase the melt temperature. This, however, is not an acceptable solution in some situations. A general solution to the weak weldline problem requires an in-depth understanding of the thermomechanical history of the injection molding process. A theoretical model for the strength of weldlines is presented that provides a comprehensive physical insight of the bonding process at the weldline interface. The model is based on the self-diffusion of molecular chains across the polymer-polymer interface and the frozen-in orientation that remains parallel to the interface. Both factors are analyzed separately and then superimposed to predict the strength of weldlines from known processing conditions and geometry. Experimental results show good correlation with predictions.

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“…The double-field analogue previously described (Curtis and Sherry 1970) is then used in the x, y plane after the problem has been transformed to this plane by the relationships…”

Section: Theorymentioning

confidence: 99%

“…The analogue problem is now solved in the x , y plane as in the two-dimension case previously described (Curtis and Sherry 1970). The following boundary conditions must be simulated.…”

Section: Applicationsmentioning

confidence: 99%

An approximate analogue solution for the axially symmetrical form of the biharmonic equation

Curtis

Sherry

1977

J. Phys. D: Appl. Phys.

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A novel electrical analogue technique is described for the approximate solution of problems that have axial symmetry and are governed by the biharmonic equation. The approximation is good for problems where the radius of curvature of strealmines and vorticities is not too small. The technique uses two plane sheets of conducting paper linked by an array of resistors whose resistance is proportional to the distance from the axis of symmetry. The method has been satisfactorily applied to the flow of fluids at Reynold's number below 0.1 and it is shown how values of fluid velocity components and vorticity can be readily determined from the analogue. The flow of fluid parallel to a uniformly spaced array of fibres has been studied, and the Kozeny coefficient deduced shows good agreement with other theoretical and experimental values.

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A conducting paper technique for the analogue solution of the biharmonic equation

Cited by 4 publications

References 5 publications

The viscous drag on cylinders falling symmetrically between parallel walls

The viscous drag on cylinders falling symmetrically between parallel walls

Performance prediction of weldline structure in amorphous polymers

An approximate analogue solution for the axially symmetrical form of the biharmonic equation

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