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Uniform transpiration effect on coupled heat and mass transfer in mixed convection about inclined surfaces in porous media: The entire regime

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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.

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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

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Author notes

  1. K. A. Yih

    Present address: , F. 3 No. 11 Lane 53 Min Zhi Road, 73011, Hsin-ying City, Tainan County, Taiwan, R.O.C.

Authors and Affiliations

  1. Air Force Aeronautical and Technical School, Kang-shan, 90395-2, Kaohsiung, Taiwan, R.O.C.

    K. A. Yih

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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

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  • DOI: https://doi.org/10.1007/BF01186970

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