Convective diffusion toward the sphere in laminar flow around the sphere

1979 ◽  
Vol 44 (4) ◽  
pp. 1218-1238
Author(s):  
Arnošt Kimla ◽  
Jiří Míčka
Keyword(s):  
Laminar Flow ◽  
Velocity Profile ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Péclet Number ◽  
Stability Of The Solution

The problem of convective diffusion toward the sphere in laminar flow around the sphere is solved by combination of the analytical and net methods for the region of Peclet number λ ≥ 1. The problem was also studied for very small values λ. Stability of the solution has been proved in relation to changes of the velocity profile.

Convective diffusion to a slowly rotating spherical electrode; Basic model for Re → O, Pe → ∞

1983 ◽  
Vol 48 (6) ◽  
pp. 1571-1578 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Flow Regime ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Creeping Flow ◽  
Péclet Number ◽  
Spherical Electrode ◽  
Basic Model ◽  
Boundary Layer Solution ◽  
Layer Solution

Theory has been formulated of a convective rotating spherical electrode in the creeping flow regime (Re → 0). The currently available boundary layer solution for Pe → ∞ has been confronted with an improved similarity description applicable in the whole range of the Peclet number.

Analysis of Laminar Slip-Flow Thermal Transport in Microchannels With Transverse Rib and Cavity Structured Superhydrophobic Walls at Constant Heat Flux

2011 ◽  
Author(s):  
D. Maynes ◽  
B. W. Webb ◽  
V. Soloviev
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Thermal Transport ◽  
Peclet Number ◽  
Average Nusselt Number ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Péclet Number

This paper presents an analytical investigation of the thermally developing and periodically fully-developed flow in a parallel-plate channel comprised of superhydrophobic walls. The superhydrophobic walls considered in this paper exhibit alternating micro-ribs and cavities positioned perpendicular to the flow direction and the transport scenario analyzed is that of constant wall heat flux through the rib surfaces with negligible thermal transport through the vapor cavity interface. Axial conduction is neglected in the analysis and the problem is one of Graetz flow with apparent slip-flow and periodicity of constant heating. Closed form solutions for the local Nusselt number and wall temperature are presented and are in the form of infinite series expansions. Previously it has been shown that significant reductions in the overall frictional pressure drop can be expected relative to the classical smooth channel laminar flow. The present results reveal that the overall thermal transport is markedly influenced by the relative cavity region (cavity fraction), the relative rib/cavity module width, and the flow Peclet number. The following conclusions can be made regarding thermal transport for a constant heat flux channel exhibiting the superhydrophobic surfaces considered: 1) Increases in the cavity fraction lead to decreases in the average Nusselt number; 2) Increasing the relative rib/cavity module length yields a decrease in the average Nusselt number; and 3) as the Peclet number increases the average Nusselt number increases. For all parameters explored, the limiting upper bound on the fully-developed average Nusselt number corresponds to the limiting case scenario of classical laminar flow through a smooth-walled channel with constant heat flux.

Analysis of Laminar Slip-Flow Thermal Transport in Microchannels With Transverse Rib and Cavity Structured Superhydrophobic Walls at Constant Heat Flux

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
D. Maynes ◽  
B. W. Webb ◽  
J. Crockett ◽  
V. Solovjov
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Thermal Transport ◽  
Peclet Number ◽  
Average Nusselt Number ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Péclet Number

This paper presents an analytical investigation of the thermal transport in a parallel-plate channel comprised of superhydrophobic walls. An analytical solution is obtained for the thermally developing state, however, it is the condition far downstream from the entrance where the temperature field exhibits repeating periodic streamwise variation that is of primary interest here. The superhydrophobic walls considered in this paper exhibit alternating microribs and cavities positioned perpendicular to the flow direction and the transport scenario analyzed is that of constant wall heat flux through the rib surfaces with negligible thermal transport through the vapor cavity interface. Axial conduction is neglected in the analysis and the problem is one of Graetz flow with apparent slip-flow and periodicity of constant heating. Closed form solutions for the local Nusselt number and wall temperature are presented and are in the form of infinite series expansions. Previously, it has been shown that significant reductions in the overall frictional pressure drop can be expected relative to the classical smooth channel laminar flow. The present results reveal that the overall thermal transport is markedly influenced by the relative cavity region (cavity fraction), the relative rib/cavity module width, and the flow Peclet number. The following conclusions can be made regarding thermal transport for a constant heat flux channel exhibiting the superhydrophobic surfaces considered: (1) Increases in the cavity fraction lead to decreases in the average Nusselt number; (2) Increasing the relative rib/cavity module length yields a decrease in the average Nusselt number; and (3) as the Peclet number increases the average Nusselt number increases. For all parameters explored, the limiting upper bound on the fully developed average Nusselt number corresponds to the limiting case scenario of classical laminar flow through a smooth-walled channel with constant heat flux.

Efficient Boundary Element Methods for the Time-Dependent Convective Diffusion Equation

2003 ◽  
Author(s):  
G. F. Dargush ◽  
M. M. Grigoriev
Keyword(s):  
Boundary Element ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Fundamental Solutions ◽  
Higher Order ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Boundary Element Methods ◽  
Time Dependent ◽  
Péclet Number

Higher-order boundary element methods (BEM) are presented for time-dependent convective diffusion in two dimensions. The time-dependent convective diffusion free-space fundamental solutions originally proposed by Carslaw and Jaeger are used to obtain the boundary integral formulation. Boundary element method solutions up to the Peclet number 106 are obtained for an example problem of unsteady convection-diffusion that possesses an exact solution. We investigate the convergence rate and accuracy of the higher-order boundary element formulations. An extremely high accuracy of the BEM solutions for highly convective flows is demonstrated. Moreover, it is shown that the use of time-dependent convective kernels provides an automatic upwinding for the entire range of Peclet numbers and also leads to very efficient algorithms as the Peclet number increases.

Transient convective diffusion to a circular sink at finite Peclet number

2006 ◽  
Vol 49 (23-24) ◽  
pp. 4596-4607 ◽  
Author(s):  
Ondrej Wein ◽  
Valentin V. Tovcigrecko ◽  
Vaclav Sobolik
Keyword(s):  
Peclet Number ◽  
Convective Diffusion ◽  
Péclet Number
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