Theoretical and numerical analysis of large-scale heat transfer problems with temperature-dependent pore-fluid densities

Purpose - In many scientific and engineering fields, large-scale heat transfer problems with temperature-dependent pore-fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large-scale heat transfer problems with temperature-dependent pore-fluid densities in the lithosphere and crust scales. Design/methodology/approach - The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts. Findings - From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive-and-advective lithosphere with variable pore-fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere. Originality/value - The present analytical solutions can be used to: validate numerical methods for solving large-scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large-scale heat transfer problems with temperature-dependent fluid densities.

Numerical analysis of gas and micro-particle interactions in a hand-held shock-tube device

A unique hand-held gene gun is employed for ballistically delivering biomolecules to key cells in the skin and mucosa in the treatment of the major diseases. One of these types of devices, called the Contoured Shock Tube (CST), delivers powdered micro-particles to the skin with a narrow and highly controllable velocity distribution and a nominally uniform spatial distribution. In this paper, we apply a numerical approach to gain new insights in to the behavior of the CST prototype device. The drag correlations proposed by Henderson (1976), Igra and Takayama (1993) and Kurian and Das (1997) were applied to predict the micro-particle transport in a numerically simulated gas flow. Simulated pressure histories agree well with the corresponding static and Pitot pressure measurements, validating the CFD approach. The calculated velocity distributions show a good agreement, with the best prediction from Igra & Takayama correlation (maximum discrepancy of 5%). Key features of the gas dynamics and gas-particle interaction are discussed. Statistic analyses show a tight free-jet particle velocity distribution is achieved (570 +/- 14.7 m/s) for polystyrene particles (39 +/- 1 mu m), representative of a drug payload.

Numerical analysis of capacities for two-qubit unitary operations

We present numerical results on the capacities of two-qubit unitary operations for performing communication and creating entanglement. The capacities for communication considered are based upon the increase in Holevo information of an ensemble. Our results indicate that the capacity may be accurately estimated using ensemble sizes and ancilla dimensions of 4. In addition, the calculated values of these capacities were close to, and in some cases equal to, the similarly defined entangling capacities; this result indicates connections between these capacities.

Atmospheric boundary layer development over a narrow coastal plain during onshore flow

A study of the structure of the daytime atmospheric boundary layer during onshore flow over a narrow coastal plain is presented. The main emphasis of the study is on the nature and causes of heating and cooling observed in the boundary layer temperature profiles. Measurements included vertical temperature profiles above at least two sites derived from radiosondes and aircraft, as well as surface estimates of radiative and sensible heat fluxes. Surface meteorological and pilot balloon data were also available, providing further evidence of short-term changes in atmospheric boundary layer structure. The Manawatu case was representative of autumnal anticyclonic conditions with weak pressure gradients, and illustrated typical diurnal development of a convective boundary layer over a coastal plain bordered by mountain ranges, with a transition from a stable nocturnal situation to a well-mixed profile in the afternoon. The profiles show surface input of heat propagating upwards through the boundary layer during the day, as well as entrainment of heat at the top associated with shear induced turbulence and/or penetrative convection. Applying a one-dimensional model, estimates of boundary layer heat budget components were obtained for four time periods during the day. Later periods were affected by cumulus cloud development at the top of the boundary layer, resulting in significant changes in individual components. Input of sensible heat from the surface decreased, while the addition of heat to the boundary layer from both cloud condensation and advection increased.

A note on the Balanced method

Recently the Balanced method was introduced as a class of quasi-implicit methods for solving stiff stochastic differential equations. We examine asymptotic and mean-square stability for several implementations of the Balanced method and give a generalized result for the mean-square stability region of any Balanced method. We also investigate the optimal implementation of the Balanced method with respect to strong convergence.