Overall heat transfer and mean temperature distribution measurements have been made of turbulent thermal convection in horizontal water layers heated from below. The Nusselt number is found to be proportional to Ra0·278 in the range 2·76 × 105 < Ra < 1·05 × 108. Eight discrete heat flux transitions are found in this Rayleigh number range. An interferometric method is used to measure the mean temperature distribution for Rayleigh numbers between 3·11 × 105 and 1·86 × 107. Direct visual and photographic observations of the fluctuating interferogram patterns show that the main heat transfer mechanism is the release of thermals from the boundary layers. For relatively low Rayleigh numbers (up to 5 × 105) many of the thermals reach the opposite surface and coalesce to form large masses of relatively warm fluid near the cold surface and masses of cold fluid near the warm surface, resulting in a temperature-gradient reversal. With increasing Rayleigh numbers, fewer and fewer thermals reach the opposite bounding surface and the thermals show persistent horizontal movements near the bounding surfaces. The central region of the layer becomes an isothermal core. The mean temperature distributions for the high Rayleigh number range are found to follow a Z−2 power law over a considerable range, where Z is the distance from the bounding surface. A very limited agreement with the theoretically predicted Z−1 power law is also found.

The decomposition of ,unconfined rigid polyurethane foam has been modeled by a kinetic bond-breaking scheme describing degradation of a primary polymer and formation of a thermally stable secondary polymer. The bond-breaking scheme is resolved using percolation theory to describe evolving polymer fragments. The polymer fragments vaporize according to individual vapor pressures. Kinetic parameters for the model were obtained from Thermal Gravimetric Analysis (TGA). The chemical structure of the foam was determined from the preparation techniques and ingredients used to synthesize the foam. Scale-up effects were investigated by simulating the response of an incident heat flux of 25 W/cm2 on a partially confined 8.8-cm diameter by 15-cm long right circular cylinder of foam that contained an encapsulated component. Predictions of center, midradial, and component temperatures, as well as regression of the foam surface, were in agreement with measurements using thermocouples and X-ray imaging.

The stability of a gas bearing is treated by a new procedure in which the bearing film is characterised by its responses to step-jump displacements. Duhamel’s theorem is invoked to generalize these step responses in a system of dynamical equations. Stability is determined by calculation of a “growth factor” for each degree of freedom. Results are presented for the infinitely long self-acting sleeve bearing and for a finite length two-bearing system.

The present study is undertaken in order to gain an understanding of certain aspects of convective transport in a magma chamber. We have chosen to represent the chamber by an enclosure with localized heating from below. Results of both laboratory experiments and computer modeling are reported. The experimental apparatus consists of a transparent enclosure with a square planform. An electrically heated strip, with a width equal to 1/4 of the length of a side of the enclosure, is centered on the lower inside surface of the enclosure. For the experiments reported here, the top of the fluid layer is maintained at a constant temperature and the depth of the layer is equal to the width of the heated strip. The large viscosity variation characteristic of magma convection is simulated by using corn syrup as the working fluid. Measured velocity and temperature distributions as well as overall heat transfer rates are presented. The experiment is numerically simulated through use of a finite element computer program. Numerically predicted steamlines, isotherms, and velocity distributions are presented for the transverse vertical midplane of the enclosure. Good agreement is demonstrated between predictions and measurements.

Direct and incremental variational formulations for the steady-state compressible Reynolds’ equation are given. Finite element equations for these are derived and sample solutions are presented.