Summary
A boundary layer analysis is used to investigate the effect of uniform transpiration velocity on the heat and mass transfer characteristics of mixed convection about inclined surfaces in saturated porous media under the coupled effects of thermal and mass diffusion. The surfaces are maintained at variable wall temperature (VWT) and variable wall concentration (VWC). Nonsimilar governing equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results are presented for the local Nusselt number as well as the local Sherwood number. The local Nusselt number and the local Sherwood number increase (decrease) due to the effect of suction (blowing). Increasing the buoyancy ratio N increases the local Nusselt number and the local Sherwood number. It is apparent that the Lewis number has a pronounced effect on the local Sherwood number than it does on the local Nusselt number. Furthermore, increasing the Lewis number decreases (increases) the local heat (mass) transfer rate.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- a, B, b :
-
constant
- C :
-
dimensionless concentration defined in Eq. (6.5)
- c :
-
concentration
- D :
-
mass diffusivity
- f :
-
dimensionless stream function defined in Eq. (6.3)
- g :
-
gravitational acceleration
- h :
-
local heat transfer coefficient
- K :
-
Darcy permeability
- k :
-
effective thermal conductivity
- Le:
-
Lewis number,α/D
- m :
-
local mass flux
- N :
-
buoyancy ratio defined in Eq. (15)
- Nu x :
-
local Nusselt number,hx/k
- Pe x :
-
local Péclet number defined in Eq. (14)
- Ra x :
-
modified local Rayleigh number defined in Eq. (14)
- Sh x :
-
local Sherwood number,mx/[D(cω−c∞)]
- T :
-
temperature
- U ∞ :
-
velocity of the potential flow outside the boundary layer
- u, v :
-
Darcy velocity in the x-direction, y-direction
- V o :
-
uniform transpiration velocity
- x, y :
-
streamwise coordinate, transverse coordinate
- α:
-
thermal diffusivity
- β c,β T :
-
coefficient of concentration expansion, coefficient of thermal expansion
- η:
-
pseudosimilarity variable defined in Eq. (6.2)
- θ:
-
dimensionless temperature defined in Eq. (6.4)
- λ:
-
exponent of wall temperature/concentration
- ν:
-
kinematic viscosity of convective fluid
- ξ:
-
transpiration parameter defined in Eq. (6.1)
- χ:
-
combined convection parameter defined in Eq. (13)
- ψ:
-
stream function
- ω:
-
condition at the wall
- ∞:
-
condition at infinity
References
Cheng, P.: The influence of lateral mass flux on free convection boundary layers in a saturated porous medium. Int. J. Heat Mass Transfer20, 201–206 (1977).
Minkowycz, W. J., Cheng, P.: Local non-similar solutions for free convective flow with uniform lateral mass flux in porous medium. Lett. Heat Mass Transfer9, 159–168 (1982).
Yücel, A.: The influence of injection or withdrawal of fluid on free convection about a vertical cylinder in a porous medium. Numer. Heat Transfer7, 483–493 (1984).
Cheng, P.: Combined free and forced convection flow about inclined surfaces in porous media. Int. J. Heat Mass Transfer20, 807–814 (1977).
Lai, F. C., Kulacki, F. A.: The influence of lateral mass flux on mixed convection over inclined surfaces in saturated porous media. ASME J. Heat Transfer112, 515–518 (1990).
Hooper, W. B., Chen, T. S., Armaly, B. F.: Mixed convection from a vertical plate in porous media with surface injection or suction. Numer. Heat Transfer Part A25, 317–329 (1994).
Kumari, M., Gorla, R. S. R.: Combined convection along a non-isothermal wedge in a porous medium. Heat Mass Transfer32, 393–398 (1997).
Bejan, A., Khair, K. R.: Heat and mass transfer by natural convection in a porous medium. Int. J. Heat Mass Transfer28, 909–918 (1985).
Lai, F. C., Kulacki, F. A.: Coupled heat and mass transfer by natural convection from vertical surfaces in porous media. Int. J. Heat Mass Transfer34, 1189–1194 (1991).
Lai, F. C.: Coupled heat and mass transfer by mixed convection from a vertical plate in a saturated porous medium. Int. Comm. Heat Mass Transfer18, 93–106 (1991).
Cebeci, T., Bradshaw, P.: Physical and computational aspects of convective heat transfer, p. 385. New York: Springer 1984.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yih, K.A. Uniform transpiration effect on coupled heat and mass transfer in mixed convection about inclined surfaces in porous media: The entire regime. Acta Mechanica 132, 229–240 (1999). https://doi.org/10.1007/BF01186970
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01186970