Transient Convection

The important reason for the quasi-steady-state approach arises from the difficulty in obtaining a solution to the transient convection problem for two-phase situations. 

This chapter complements Refs. 21 and 22 in reviewing the progresses made on the transient, convective, multicomponent droplet vaporization, with particular emphasis on the internal transport processes and their influences on the bulk vaporization characteristics. The interest and importance in stressing these particular features of droplet vaporization arise from the fact that most of the practical fuels used are blends of many chemical compounds with widely different chemical and physical properties. The approximation of such a complex mixture by a single compound, as is frequently assumed, not only may result in grossly inaccurate estimates of the quantitative vaporization characteristics but also may not account for such potentially important phenomena as soot formation when the droplet becomes more concentrated with high-boiling point compounds towards the end of its lifetime. Furthermore, multi-... 

The present lecture summarizes some of tiie most recent joint research results from tiie cooperation between the Federal University of Rio de Janeiro, Brasil, and tiie University of Miami, USA, on tiie fransient analysis of both fluid flow and heat transfer within microchannels. This collaborative link is a natural extension of a long term cooperation between the two groups, in the context of fimdamental work on transient forced convection, aimed at tiie development of hybrid numerical-analytical techniques and tiie experimental validation of proposed models md methodologies [1- 9]. The motivation of this new phase of tiie cooperation was thus to extend the previously developed hybrid tools to handle both transient flow and transient convection problems in microchannels within the slip flow regime. 

As an illustration of the formal integral transform procedure, a transient convection-diffusion problem of n coupled potentials (velocity, temperature or concentration) is considered. These parameters are defined in tiie region V with boundary surface S and including non-linear effects in the convective and source terms as follows ... 

Cotta, R.M. (1996) Integral Transforms in Transient Convection - Benchmarks and Engineering Simulations, Invited Keynote Lecture, ICHMT International Symposium on Transient Convective Heat Transfer, Turkey, pp.433-453, August. 

The transient, convective and diffusive terms are discretized just like the corresponding terms in the liquid phase (i.e., see sect C.4.4). 

Statement of the problem. Preliminary remarks. Let us consider the transient convective mass and heat transfer between a spherical drop of radius a and a translational Stokes flow where the resistance to the transfer exists only in the disperse phase. We assume that at the initial time t = 0 the concentration inside the drop is constant and equal to Co, whereas for t > 0 the concentration on the interface is maintained constant and equal to Cs. 

Polyanin, A. D., Qualitative features of internal problems of transient convective mass and heat exchange at large Peclet numbers, Theor. Found. Chem. Eng., Vol. 18, No. 3, pp. 171-181, 1984. 

The first section presents some fundamental ideas that are frequently referred to in the remainder of the chapter. The next three sections deal with the major topics in natural convection. The first of these addresses problems of heat exchange between a body and an extensive quiescent ambient fluid, such as that depicted in Fig. 4.1a. Open cavity problems, such as natural convection in fin arrays or through cooling slots (Fig. 4.1fe), are considered next. The last major section deals with natural convection in enclosures, such as in the annulus between cylinders (Fig. 4.1c). The remaining sections present results for special topics including transient convection, natural convection with internal heat generation, mixed convection, and natural convection in porous media. 

Nisancioglu K, Newman J (1974) Transient convective diffusion to a disk electrode. J Electroanal Chem 50 23. 

Currently, analytical approaches are still the most preferred tools for model reduction in microfluidic research community. While it is impossible to enumerate all of them in this chapter, we will discuss one particular technique - the Method of Moments, which has been systematically investigated for species dispersion modeling [9, 10]. The Method of Moments was originally proposed to study Taylor dispersion in a circular tube under hydrodynamic flow. Later it was successfully applied to investigate the analyte band dispersion in microfluidic chips (in particular electrophoresis chip). Essentially, the Method of Moments is employed to reduce the transient convection-diffusion equation that contains non-uniform transverse species velocity into a system of simple PDEs governing the spatial moments of the species concentration. Such moments are capable of describing typical characteristics of the species band (such as transverse mass distribution, skew, and variance). 

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