Two-dimensional heat conduction with phase change in a semi-infinite mould

Analytical solution of a 2-dimensional problem of solidification of a superheated liquid in a semi-infinite mould has been studied in this paper. On the boundary, the prescribed temperature is such that the solidification starts simultaneously at all points of the boundary. Results are also given for the 2-dimensional ablation problem. The solution of the heat conduction equation has been obtained in terms of multiple Laplace integrals involving suitable unknown fictitious initial temperatures. These fictitious initial temperatures have interesting physical interpretations. By choosing suitable series expansions for fictitious initial temperatures and moving interface boundary, the unknown quantities can be determined. Solidification thickness has been calculated for short time and effect of parameters on the solidification thickness has been shown with the help of graphs.

Time-domain criteria for theL_{2}-stability of nonstationary feedback systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

The heat capacity of liquid carbon disulfide + acetonitrile, especially near the upper critical solution temperature

The heat capacity Cp of the binary liquid system CS2 + CH3CN has been studied. This system has an upper critical solution temperature To ≈ 323.4 K and a critical mole fraction of CS2xo ≈ 0.5920. Measurements were made both for mixtures close to and far away from the critical region. The heat capacity of the mixture with x = xo exhibits a symmetric logarithmic anomaly around Tc, which is apparently preserved even for compositions in the immediate vicinity of xc. For compositions far away from xc, only a normal rise in Cp over the covered temperature range is observed.

Stability of large flexible damped spacecraft modeled as elastic continua

Vibrational stability of a large flexible, structurally damped spacecraft subject to large rigid body rotations is analysed modelling the system as an elastic continuum. Using solution of rigid body attitude motion under torque free conditions and modal analysis, the vibrational equations are reduced to ordinary differential equations with time-varying coefficients. Stability analysis is carried out using Floquet theory and Sonin-Polya theorem. The cases of spinning and non-spinning spacecraft idealized as a flexible beam plate undergoing simple structural vibration are analysed in detail. The critical damping required for stabilization is shown to be a function of the spacecraft's inertia ratio and the level of disturbance.

Storage stability of solid rocket fuels. 2. Effect of oxidizer loadings

Ageing behaviour, leading to ballistic changes, has been studied as a function of oxidizer loading in polystyrene/ammonium perchlorate solid-propellants. The ageing studies were carried out at 100 °C in air. Change in burning rate decreased as the oxidizer loading increased from 75 to 80%. The change in thermal decomposition rates both at 230 and 260 °C also decreased as the oxidizer loading in the propellants increased. The shapes of the plots of the changes in burning rate and thermal decomposition rate (230 and 260 °C) at different storage times for different oxidizer-loaded propellants seem to be exactly similar. These results lead to the conclusion that the thermal decomposition of the propellant may be responsible for bringing about the ballistic changes during the ageing process. Infrared studies of the binder portion of the aged propellant indicate that peroxide formation takes place during the course of ageing and that peroxide formation for a particular storage time and temperature increases as the loading decreases.

L_{2}- stability of a class of nonstationary feedback systems with dynamical nonlinear subsystems

A class of feedback systems, consisting of dynamical non-linear subsystems which arise in many diverse control applications, is analyzed for L2-stability. It is shown that, although a transformation of these systems to the familiar Lur'e configuration does not seem to be possible, a one-to-one correspondence may be effected between the stability properties of these and the Lur'e systems. Interesting stability criteria are developed by exploiting this characteristic.

Construction of stability multipliers for non-linear feedback systems

This paper is concerned with the analysis of the absolute stability of a non-linear autonomous system which consists of a single non-linearity belonging to a particular class, in an otherwise linear feedback loop. It is motivated from the earlier Popovlike frequency-domain criteria using the ' multiplier ' eoncept and involves the construction of ' stability multipliers' with prescribed phase characteristics. A few computer-based methods by which this problem can be solved are indicated and it is shown that this constitutes a stop-by-step procedure for testing the stability properties of a given system.

An exponential stability criterion for certain nonlinear systems

Improved sufficient conditions are derived for the exponential stability of a nonlinear time varying feedback system having a time invariant blockG in the forward path and a nonlinear time varying gain ϕ(.)k(t) in the feedback path. φ(.) being an odd monotone nondecreasing function. The resulting bound on $$\left( {{{\frac{{dk}}{{dt}}} \mathord{\left/ {\vphantom {{\frac{{dk}}{{dt}}} k}} \right. \kern-\nulldelimiterspace} k}} \right)$$ is less restrictive than earlier criteria.

Numerical study of heat transfer in laminar film boiling by the finite-difference method

The finite-difference form of the basic conservation equations in laminar film boiling have been solved by the false-transient method. By a judicious choice of the coordinate system the vapour-liquid interface is fitted to the grid system. Central differencing is used for diffusion terms, upwind differencing for convection terms, and explicit differencing for transient terms. Since an explicit method is used the time step used in the false-transient method is constrained by numerical instability. In the present problem the limits on the time step are imposed by conditions in the vapour region. On the other hand the rate of convergence of finite-difference equations is dependent on the conditions in the liquid region. The rate of convergence was accelerated by using the over-relaxation technique in the liquid region. The results obtained compare well with previous work and experimental data available in the literature.

On the positivity and stability of non-stationary systems

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequency- domain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.

On the computation of two-dimensional compressible flow fields by the modified local stability scheme

The modified local stability scheme is applied to several two-dimensional problems—blunt body flow, regular reflection of a shock and lambda shock. The resolution of the flow features obtained by the modified local stability scheme is found to be better than that achieved by the other first order schemes and almost identical to that achieved by the second order schemes incorporating artificial viscosity. The scheme is easy for coding, consumes moderate amount of computer storage and time. The scheme can be advantageously used in place of second order schemes.

Storage stability of solid rocket fuel. 1. Effect of temperature

Ageing behaviour of polystyrene (PS)/ammonium perchlorate (AP) propellent leading to ballistic changes has been studied. It follows a zero-order kinetic law. Ageing behaviour leading to change in burning rate ( ) in the temperature range of 60–200 ° C was found to remain the same. The dependence of the change of the average thermal decomposition (TD) rate at 230 and 260°C on the change in burning rate for the propellant aged at 100 ° C in air suggests that the slow TD of the propellant is the cause of ageing. The safe-life (for a pre-assigned burning-rate change limit) at 25 ° C in air has been calculated as a function of the rate of change.

On the stability of a nonlinear system with periodic coefficients

A quasi-geometric stability criterion for feedback systems with a linear time invariant forward block and a periodically time varying nonlinear gain in the feedback loop is developed.