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Buoyant plumes due to mass diffusion

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Abstract

This paper presents the results of a numerical study of laminar axisymmetric plumes that emanate from a point source of mass diffusion. Various flow configurations that arise in mass diffusion plumes are identified. In the ambient, the cases of constant concentration and stable density stratification are considered. The governing conservation equations of mass, momentum, and species diffusion are cast in finite-difference form using an explicit scheme. Boundary layer and Boussinesq approximations are incorporated. Upwind-differencing is employed for convective terms. Velocity and concentration fields are obtained for various values of Schmidt number, and concentration stratification levels in the ambient. The results are explained in terms of the basic physical mechanisms that govern these flows. The complex interactions between the buoyancy and the Schmidt number, and the stratification parameter are discussed.

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Abbreviations

c :

concentration of diffusing species

C :

concentration excess ratio, (c−c∞,x)/(c0−c∞,0)

C*:

concentration excess ratio based on centerline concentration, (c−c ∞,x )/(c c−c∞,x)

D :

diffusion coefficient

g :

gravitational acceleration

p :

pressure

S*:

concentration stratification parameter, 1/ΔC 0dc ∞,x /dX

t :

temperature

u, v :

velocity components

U, V :

non-dimensional velocity components

x, r :

axial and radial space coordinates

X, R :

non-dimensional space coordinates

β*:

coefficient of expansion with concentration, 1/ρ(∂ρ/∂c) t,p

ρ :

density

τ :

time

τ*:

non-dimensional time

ν :

kinematic viscosity

Sc:

Schmidt number,ν/D

∞:

location indicating far away from the axis of the plume

0 :

location indicating the source

c :

location indicating centerline

x :

location alongX-axis

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Author information

Correspondence to D. Angirasa.

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Jagannadham, M., Subba Reddi, K. & Angirasa, D. Buoyant plumes due to mass diffusion. Appl. Sci. Res. 49, 135–146 (1992). https://doi.org/10.1007/BF01799249

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Keywords

  • Boundary Layer
  • Stratification
  • Schmidt Number
  • Mass Diffusion
  • Explicit Scheme