Conjugate unsteady heat transfer from a droplet in creeping flow

Abstract

NOTATION C = dimensionless velocities of the dispersion waves = area available for heat transfer between gas and solid = concentration (normalized with respect to unit con-= heat capacities of fluid and solid, respectively = particle diameter = dispersion coefficient = axial and radial dispersion coefficients, respectively = Peclet number = ud/D = time variable = temperature = interstitial velocity = heat transfer coefficient between gas and solid = volume of a cell (in cell model) = distance coordinate = dimensionless distance coordinate = dimensionless time coordinate phases in a packed bed centration) Greek Letters € = voidage of the packed bed 7 , A, p = see Equations (5) and (6) Y = length of a cell pf, ps = densities of fluid and solid, respectively e = residence time in a cell 7 = fraction of the total residence time which the fluid spends in the plug flow section of a cell

Advanced models of fuel droplet heating and evaporation

“…Abramzon and Borde [111] presented the results of numerical analysis of transient heat transfer to slowly moving droplets (Stokesian approximation) in a wide range of Peclet numbers 0%Pe%1000. They studied the conjugate problem so that the heat transfer processes in gas and droplets were taken into account.…”

Interphase Mass Transfer from Bubbles, Drops, and Solid Spheres: Diffusional Transport Enhanced by External Chemical Reaction

“…Most of the published research, however, has been restricted to cases in which the resistance to mass transfer occurs in one of the phases, while that in the other phase is negligible. Exceptions are the computationally intensive investigations of Chung and his co-workers Chung, 1986,1990;Nguyen et al, 1993), as well as of Abramzon and Borde (1980). If there is a chemical reaction present, then the problem is even more computationally intensive than that for connective diffusion, for which only the role of the Peclet number Pe has been studied extensively (Abramzon and Borde, 1980;Chung, 1986, 1990), although a rather wide range of the diffusivity ratio D has been considered (Jungu and Mihail, 1986).…”

“…Exceptions are the computationally intensive investigations of Chung and his co-workers Chung, 1986,1990;Nguyen et al, 1993), as well as of Abramzon and Borde (1980). If there is a chemical reaction present, then the problem is even more computationally intensive than that for connective diffusion, for which only the role of the Peclet number Pe has been studied extensively (Abramzon and Borde, 1980;Chung, 1986, 1990), although a rather wide range of the diffusivity ratio D has been considered (Jungu and Mihail, 1986). To our knowledge the only comparable coupled convective diffusion-reaction research on interphase mass transfer is our own Reed, 1992, 1994).…”

Streamline-averaged mass transfer in a circulating drop

“…A way to understand liquid-liquid extraction in circulating drops has been considered by Ubal et al (2010) based on ideas originally proposed by Kronig and Brink (1950) and by Abramzon and Borde (1980); Brignell (1975); Oliver et al (1985); Prakash and Sirignano (1978). Convection is, by definition, along streamlines, so that (at least in a system with steady and laminar fluid flow) the only way to transport material across streamlines is via diffusion, no matter how fast the flow.…”