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## Optimal convective heating of a hollow cylinder with temperature dependent thermal conductivity

### Applied Scientific Research (1994-01-01) 52: 67-79 , January 01, 1994

An infinitely long hollow cylinder with temperature dependent thermal conductivity is heated optimally by controlling the ambient temperature,*T*_{a}(*t*), such that at the final specified time*t*_{f}, the final temperature distribution*T*_{f}(*r*) of the hollow cylinder approximates a desired uniform temperature*T*_{d} as closely as possible with a minimum amount of energy spent for the heating.

## The inductive iris double discontinuity

### Applied Scientific Research (1969-01-01) 20: 61-76 , January 01, 1969

### Summary

The reflection coefficient of a double discontinuity consisting of two closely spaced inductive irises in a rectangular waveguide is found. Standard transmission line techniques are no longer valid when the irises lie close together. Instead, the solution must include effects of interaction of the higher order modes excited by each iris. A variational expression for the reflection coefficient including the effects of the higher order modes is derived in terms of integrals of the induced current on one of the irises. The solution shows how more higher order mode terms become significant in determining the reflection coefficient as the iris spacing decreases. A numerical example is presented using only a few of the higher order mode factors. The results follow measured values of the reflection coefficient with spacings as close as 1/32 of a waveguide wavelength. More terms in the solution are required for closer spacings. The numerical example correctly predicts the spacing (3/16 of a waveguide wavelength) at which the higher order mode interaction becomes significant and the transmission line solution deteriorates.

## Diffraction by a double grating

### Applied Scientific Research (1972-12-01) 26: 389-397 , December 01, 1972

The reflection and transmission of a plane electromagnetic wave by a double grating is investigated. The double grating consists of two mutually parallel, planar arrays of perfectly conducting strips of vanishing thickness. Two types of polarization are investigated, viz.*E- and H-polarization*. For both types, integral equations for the unknown current densities in the two strips belonging to a single period of the grating, are derived. Subsequently, these integral equations are solved numerically, whereupon the reflection and transmission factors for the different spectral orders are computed.

## Forthcoming articles

### Applied Scientific Research (1969-01-01) 21: 85-86 , January 01, 1969

## Internal and inertial waves in a viscous rotating stratified fluid

### Applied Scientific Research (1977-12-01) 33: 481-499 , December 01, 1977

The effects of viscosity on the propagation of a St. Andrew's cross wave which is generated by a simple-harmonic localized disturbance in a rotating stratified fluid are considered. A similarity solution of the linearised equations shows that the velocities decay and that the wave width increases away from the disturbance. Previous solutions in a stratified non-rotating fluid are recovered by letting the rotation tend to zero. The solutions are also valid in the limit of a homogeneous rotating fluid. Further solutions for waves in a realistic ocean and in an isothermal atmosphere on a rotating Earth are also included.

## Rayleigh problem in slip flow with transverse magnetic field

### Applied Scientific Research (1971-01-01) 23: 315-323 , January 01, 1971

An analytical continuum solution of the Rayleigh problem in slip flow with applied magnetic field is obtained using a modified initial condition and slip boundary conditions. The results are uniformly valid for all times and show that the velocity slip and the local skin friction coefficient remain almost unaffected by the imposition of the magnetic field for small times. They increase however with the magnetic field for large times. The present results reduce to the corresponding results of the hydrodynamic case when there is no magnetic field.

## Similarity rules and degrees of thermodynamic coupling in flowing systems

### Applied Scientific Research (1974-11-01) 30: 17-31 , November 01, 1974

Thermodynamic coupling due to thermal diffusion, diffusion-thermo, and *ob aliam* diffusion effects in boundary layers is considered. Decoupling of the set of conservation equations is achieved by diagonalisation of the phenomenological coefficients matrix. A new Peclet number for coupled transfer is defined in terms of the eigenvalues of the diagonal matrix. The specific and overall degrees of thermodynamic coupling are shown to depend both on the values of the coupling coefficients and on the magnitude and direction of the gradients across the boundary layers. The application of the theory is illustrated for coupled transfer in two-phase particulate systems.

The practical advantages of the present method lie in the possibilities to: (*a*) employ available solutions for (uncoupled) thermal or diffusion boundary layers to analogous cases of coupled transfer using specific degrees of coupling and the newly defined Peclet number; and (*b*) to estimate the overall degree of thermodynamic coupling for a given flow regime from a known overall degree of coupling for another regime.

The present method establishes similarity rules for thermodynamic coupling in flow systems which enable one to evaluate the overall degree of thermodynamic coupling for a given system from available data on a different system (e.g., from liquid to gaseous system, or vice versa).

## Coherent structures and riblets

### Applied Scientific Research (1995-06-01) 54: 349-385 , June 01, 1995

This work deals with the effect of the riblets on the coherent structures near the wall. The emphasis is put on the genesis of the quasi-streamwise vortices in the presence of the riblets. The quasi-streamwise vortices regenerate by the tilting of wall normal vorticity induced by prevailing structures. This requires a mechanism which leads to a temporal streamwise dependence near the elongated flow structures and to a subsequent formation of new wall normal vorticity. It is suggested here that the action of existing quasi-streamwise vortices on the sidewalls of wall normal vorticity may create a local, streamwise dependent spanwise velocity and therefore, a secondary wall normal vorticity field. A preliminary analysis of the set-up and the time and space development of this secondary three-dimensional flow associated with the regeneration mechanism, is given. An attempt is made, in order to explain the drag reduction performed by the riblets through an intermittent model, based on the protrusion height. Logical estimates of the amount of drag reduction are obtained. The differences between the mechanism suggested here and those based on forced control experiments are also discussed.

## Ion-molecule reactions in Geiger-Mueller discharges

### Applied Scientific Research (1971-12-01) 24: 209-212 , December 01, 1971

In exploring the nature of a GM discharge a small amount of tritium is mixed with commercial Q-gas (1.3% n-butane and 98.7% helium). After operation the counter is found to be badly contaminated. Attempts to remove the activity fail to yield satisfactory results. An analysis of the gas mixture reveals that tritium activity is present in n-butane, with none being found in the expected decomposition products. An ion-molecule reaction involving n-butane is proposed to explain the results.