Unsteady forced convection heat/mass transfer around two spheres in tandem at low Reynolds numbers

Juncu, Gheorghe

doi:10.1016/j.ijthermalsci.2006.12.008

Cited by 12 publications

(15 citation statements)

References 19 publications

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“…Below, we compare the output of the model with a number of numerical simulation studies [3,8,14,16,17]. Interpretation and discussion of the results is postponed to section 4.2.1 below.…”

Section: 2mentioning

confidence: 99%

“…z 12 = variable (in units of sphere radii). The J data refer to [8], the EL data to the current model. Juncu [8] studied the temporal evolution of the heat flow rate to two spheres aligned along the flow direction.…”

Section: 2mentioning

confidence: 99%

“…The J data refer to [8], the EL data to the current model. Juncu [8] studied the temporal evolution of the heat flow rate to two spheres aligned along the flow direction. The flow was assumed to be laminar; the StimsonJeffery [15] flow field was used.…”

Section: 2mentioning

confidence: 99%

“…In section 4.1, the model is compared against singlesphere numerical data, obtained by use of a commercial, finite-element, general PDE solver (Comsol). In section 4.2, the model is compared against previously published numerical simulation studies of heat or mass transfer to a multiplicity of spheres in a convective flow field [3,8,14,16,17].…”

mentioning

confidence: 99%

“…An appreciable part of this discrepancy stems from the original Levich model itself, rather than from our method of extending the Levich model. For multisphere problems, the model was compared against previously published numerical simulation studies [3,8,14,16,17]. In these comparisons, the discrepancies were found to be < 30%.…”

mentioning

confidence: 99%

See 4 more Smart Citations

The Steady-State Convection-Diffusion Equation at High Péclet Numbers for a Cluster of Spheres: An Extension of Levich's Theory

Biello¹,

Samson²,

Sigal³

2016

SIAM J. Appl. Math.

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Abstract. This paper describes an approximate analytical model of competitive effects between members of a dense cluster of absorbing objects, which are modeled as spheres. Neighboring absorbing spheres compete for diffusing species and thereby reduce each other's rate of absorption. Levich's well-known asymptotic (high Péclet number) theory of convection-diffusion considers only the inner region of the concentration boundary layer; it does not describe the wake zone accurately. An extension of the Levich model is constructed for the wake zone. This is used to model intersphere competitive effects. The model demonstrates that for two neighboring spheres aligned along the flow direction, the absorption of the downstream sphere is substantially reduced vis-à-vis the upstream sphere. The model is verified by comparison to numerical simulation studies. Both single-sphere simulations (reported in this paper) and multisphere simulations (taken from existing literature) are considered. In the single-sphere case, the discrepancy between the analytical model and the numerical results is maximally 10% at Pe = 10 and much lower at higher Péclet numbers. An appreciable part of the error stems from the original Levich model itself, rather than from our method of extending the Levich model. In the multisphere case, the difference between the analytical model and the numerical studies is generally less than 30%. At small intersphere separations (say, center-to-center distances < 5 sphere radii), the model tends to overestimate the interference effects. This is related to the fact that flow stagnancy in the space between two closely packed spheres is not taken into account in the model. Key words. diffusion convection mass-transfer AMS subject classifications. 76R50, 76M45DOI. 10.1137/15M10393891. Introduction. Consider a steady-state model of mass transport in which a microscopic species moves toward a collection of macroscopic immobile absorption centers. The motion of the microscopic species consists of a combination of stochastic movements (diffusion) and externally imposed motion by a carrier fluid (convection). The macroscopic absorption centers are assumed to be spheres of which the locations are known and fixed; they are assumed to be all of equal size.In a recent paper [6] we developed an approximate analytical theory for such a system in the case of pure diffusion and in the case of diffusion combined with a relatively weak convective component. It was found that the range of applicability of the former theory in the convection-diffusion (CD) case was very limited; beyond Péclet numbers of about 0.6, our theory was found to be unreliable. (The Péclet number measures the ratio between convective and diffusive fluxes.) As will be shown below (and as is intuitively quite plausible), the reason for this failure at high Péclet numbers is that CD-concentration profiles around a sphere exhibit an extreme degree of fore/aft asymmetry. At the front side of the sphere, the solute is swept up extremely close to the boundary of t...

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“…Below, we compare the output of the model with a number of numerical simulation studies [3,8,14,16,17]. Interpretation and discussion of the results is postponed to section 4.2.1 below.…”

Section: 2mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%