Abstract
A boundary layer analysis was carried out to investigate the coupled phenomena of heat and mass transfer by natural convection from concentrated heat and mass sources embedded in saturated porous media. Both line and point source problems were treated. The boundary layer equations based on Darcy's law and Boussinesq approximation were solved by means of similarity transformation to obtain the details of velocity, temperature and concentration distributions above a concentrated heat source. Two important parameters, namely the Lewis number Le and the buoyancy ratioN were identified to conduct a series of numerical integrations. For the case of small Le, a substance diffuses further away from the plume centerline, such that the mass transfer influences both velocity and temperature profiles over a wide range. For large Le, on the other hand, the substance diffuses within a narrow range along the centerline. Naturally, the influence of mass transfer is limited to the level of the centerline velocity, so that a peaky velocity profile appears for positiveN whereas a velocity defect emerges along the centerline for negativeN. For such cases of large Le, the temperature profiles are found to be fairly insensitive to Le.
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Abbreviations
- c :
-
concentration
- C :
-
dimensionless concentration
- c p :
-
specific heat of convective fluid at constant pressure
- D :
-
effective mass diffusivity in a saturated porous medium
- f :
-
dimensionless stream function
- g :
-
acceleration due to gravity
- K :
-
permeability
- Le:
-
Lewis number, α/D
- \(\dot m, \dot M\) :
-
strength of mass source
- N :
-
buoyancy ratio, defined in Eqs. (21) and (32)
- \(\dot q, \dot Q\) :
-
strength of heat source
- r :
-
radial coordinate
- Ra xq :
-
Rayleigh number, defined in Eq. (12)
- Ra Q :
-
Rayleigh number, defined in Eq. (36)
- T :
-
temperature
- u,v :
-
Darcian velocities
- x,y :
-
Cartesian coordinates
- α :
-
effective thermal diffusivity in a saturated porous medium
- β :
-
coefficient of thermal expansion
- β c :
-
coefficient of concentration expansion
- η :
-
similarity variable
- ϑ :
-
dimensionless temperature
- μ :
-
viscosity
- ρ :
-
density of convective fluid
- ψ :
-
stream function
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Nakayama, A., Ashizawa, T. A boundary layer analysis of combined heat and mass transfer by natural convection from a concentrated source in a saturated porous medium. Appl. Sci. Res. 56, 1–11 (1996). https://doi.org/10.1007/BF02282918
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DOI: https://doi.org/10.1007/BF02282918