# A numerical study of laminar axisymmetric plumes due to the combined buoyancy of heat and mass diffusion

- Received:
- Accepted:

DOI: 10.1007/BF00457066

- Cite this article as:
- Angirasa, D. & Sarma, P.K. Appl. Sci. Res. (1988) 45: 339. doi:10.1007/BF00457066

## Abstract

This paper presents the results of a computational study of laminar axisymmetric plumes generated by the simultaneous diffusion of thermal energy and chemical species. Species concentrations are assumed small. The plume is treated as a boundary layer. Boussinesq approximations are incorporated and the governing conservation equations of mass, momentum, energy and species are suitably non-dimensionalised. These equations are solved using one time-step-forward explicit finite-difference method. Upwind differencing is employed for convective terms. The results thus obtained are explained in terms of the basic physical mechanisms that govern these flows. They show many interesting aspects of the complex interaction of the two buoyant mechanisms.

### Nomenclature

*B*Buoyancy ratio,

*β**(*c*_{0}*−c*_{∞})/*β*(*t*_{0}*−t*_{∞})*c*Concentration of diffusing species

*C*Concentration difference ratio, (

*c − c*_{∞})/(*c*_{0}*−c*_{∞})*C**Concentration difference ratio based on centerline concentration, (

*c − c*_{∞})/(*c*_{c}*−c*_{∞})*D*Diffusion coefficient

*g*Acceleration due to gravity

*p*Pressure

*t*Temperature

*T*Temperature excess ratio, (

*t − t*_{∞})/(*t*_{0}*− t*_{∞})*T**Temperature excess ratio based on centerline temperature, (

*t − t*_{∞})/(*t*_{c}*− t*_{∞})*u, v*Velocity components

*U, V*Non-dimensional velocity components

*x, r*Axial and radial space coordinates

*X, R*Non-dimensional space coordinates

### Greek letters

*α*Thermal diffusivity

*β*Volumetric coefficient of thermal expansion, −1/

*ϱ*(*∂ϱ/∂t*)_{p,c}*β**Volumetric coefficient of expansion with concentration, 1/

*ϱ*(*∂ϱ/∂c*)_{t,p}*ϱ*Density

*τ*Time

*τ**Non-dimensional time

*ν*Kinematic viscosity

### Dimensionless parameters

- Pr
Prandtl number

- Sc
Schmidt number

### Subscripts

- ∞
Location far away from the axis of the plume

- 0
Location indicating source