D.L.R. Oliver

Conjugate unsteady heat transfer from a spherical droplet at low Reynolds numbers

Abstract The phenomena of conjugate unsteady heat transfer from a spherical droplet or particle moving in a continuous fluid medium is numerically investigated. The energy equation is solved for a spherical droplet using the implicit, finite-difference method of alternating directions (ADI). In this study, the volumetric heat capacities of the two phases are of comparable magnitude but not necessarily equal to each other and the value of the thermal diffusivities of the two phases are set equal to each other. The range of Peclet numbers investigated are : 50⩽ Pe ⩽ 1000, with ratios of volumetric heat capacities, (interior to exterior) varying between 0.333 and 3.0. The velocities used in the convective terms are those corresponding to low Reynolds number flow. It was found that the dimensionless temperature profile asymptotically approaches a steady-state value that is independent of the initial profile in the droplet.

Unsteady conjugate heat transfer from a translating fluid sphere at moderate Reynolds numbers

Abstract The conjugate unsteady heat transfer between a translating droplet and its surrounding fluid at moderate Reynolds number is numerically investigated. The energy equation is solved by the ADI finite difference method with fluid motions inside and outside the droplet simulated by a series-truncation spectral method. The range of Reynolds numbers investigated is between 0 and 50. The ratios of viscosity and thermal conductivity between a droplet and its ambient flow range from 0 to 10 7 and 0.01 to 3, respectively. It was found that by increasing the Reynolds number, the predicted rate of heat transfer is significantly increased for fluid spheres as a result of increased fluid motions both inside and outside the droplet. On the other hand, the transfer rate for a solid sphere is much less sensitive to the Reynolds number than are the fluid spheres. For a gas bubble, any increase in the Reynolds number only increases the amplitude and frequency of the fluctuations in the Nusselt number and the steady-state Nusselt number is nearly independent of the Reynolds number.

A phase change problem with temperature-dependent thermal conductivity and specific heat

Abstract A semi-analytic solution is obtained to model conduction heat transfer with phase change into a semi-infinite slab, where the thermal conductivities and specific heats of both phases are a linear function of the temperature. This model extends the model of a previous work to include temperature-dependent specific heats.

Heat Transfer From a Translating Droplet at High Peclet Numbers: Revisiting the Classic Solution of Kronig & Brink

More than five decades ago Kronig and Brink published a classic analysis of transport from translating droplets. Their analysis assumed that the bulk of the resistance to transfer was in the droplet phase. It considered the limiting solution as the Peclet number became very large. Their work has been cited in many subsequent studies of droplet transfer. The present work revisits their solution using numerical techniques that were not then available. It was found that only the first mode of their solution is mathematically accurate. Hence, their solution is accurate only at large times.

Transfer From a Droplet at High Peclet Numbers With Heat Generation: Interior Problem

Transient heat transfer from a droplet with heat generation is investigated. It is assumed that the bulk of the thermal resistance resides in the droplet. Two cases were investigated: low Peclet flows and very high Peclet flows. As expected, it was found that the temperature rise due to the heat generation was less for high Peclet flows. In addition, the temperature profile responds more quickly for high Peclet flows. This analysis is also applicable for mass transfer with a zero-order reaction.

Effects of thermal osmosis near a buried isolated heat sphere

Abstract The effects of thermal osmosis in a homogeneous porous medium are analytically investigated near a heated spherical container. It was demonstrated that accurate estimations of the effects of thermal osmosis must account for physical constraints such as continuity of mass. This work has application in predicting release from a radioactive waste site.

A Project to Develop Initiative and Innovation through Laboratory Improvement

In an effort to cultivate initiative and innovative spirit, a new project was introduced in an undergraduate mechanical engineering laboratory, exemplified here by the Thermal Sciences Laboratory. In this project, each student lab group (typically a group of four) had to suggest improvements to a specific laboratory. There were no other imposed restrictions; improvements could be in any area, such as hardware, software, work procedure, technical presentation, and so on. By having the project run in parallel with the typical labs, several objectives were attained. First, students were exposed to the ideas of continuous innovation and product or process improvement. Second, being a group project, students were exposed to the practical aspects and important advantages of teamwork and brainstorming. Third, due to the latest innovations in technology and education, laboratory-based work is always in need of enhancement; students engaged in performing lab work are well positioned to understand the possible shortcomings, and thus propose improvements; each student should be able to have at least one contribution, ranging from very small to significant. Lastly, some of the best solutions can be followed by senior design projects in which the proposed improvements are further developed and implemented in the laboratory. This paper shows how the project was organized, and also presents results obtained during its first year of implementation.

MASS TRANSFER TO A DROPLET WITH A FIRST-ORDER CHEMICAL REACTION

The steady-state mass transfer to a droplet with a first-order chemical reaction is i nvestigated as a function of the Damkohler number (Da11) for the special case of very high Peclet number flow. The flow field in the droplet employed in this work is Hills spherical vortex. The resistance to mass transfer is assumed to occur inside the droplet with negligible resistance to mass transfer in the continuous phase.

Experimental demonstration of diffusocapillary flow in an oil droplet

Abstract The phenomenon of diffusocapillary flow is demonstrated utilizing a vegetable oil droplet suspended in a host medium composed of Dow Corning 200 silicone fluids. The host fluid was prepared in such a way that the average polymer length was varied across the surface of the droplet, thus creating an interfacial tension gradient with concomitant Marangoni flow.

Nusselt number of a sphere in creeping flow

Abstract Rates of heat or mass transfer from a spherical droplet translating in a field under creeping flow conditions are examined. The existing expressions for Nusselt numbers are evaluated via an independent numerical analysis.