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Coupled heat and mass transfer by free convection over a truncated cone in porous media: VWT/VWC or VHF/VMF

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Summary

The heat and mass transfer characteristics of natural convection about a truncated cone embedded in a saturated porous medium subjected to the coupled effects of thermal and mass diffusion is numerically analyzed. The surface is maintained at variable wall temperature/concentration (VWT/VWC) or variable heat/mass flux (VHF/VMF). The transformed governing equations are solved by Keller box method. Numerical data for the dimensionless temperature profiles, the dimensionless concentration profiles, the local Nusselt number and the local Sherwood number are presented for wide range of dimensionless distance ξ, the Lewis number Le, the exponent λ, and buoyancy ratioN (orN *). In general, it has been found that when the buoyancy ratio is increasing both the local Nusselt number and the local Sherwood number increase. Increasing the value of λ and ξ increases the local surface heat and mass transfer rates. The local Nusselt (Sherwood) number increases (decreases) with decreasing the Lewis number. Furthermore, it is shown that the local Nusselt number and the local Sherwood number of the truncated cone approach those of inclined plate (full cone) for the case of ξ=0 (ξ→∞).

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Abbreviations

a 1,a 2 :

Constants

b 1,b 2 :

Constants

C :

Dimensionless concentration

c :

Concentration

D :

Mass diffusivity

f :

Dimensionless stream function

g :

Gravitational acceleration

h :

Local heat transfer coefficient

K :

Permeability of the porous medium

k :

Thermal conductivity

Le:

Lewis number, α/D

m :

Local mass flux

N :

Buoyancy ratio for VWT/VWC

N * :

Buoyancy ratio for VHF/VMF

Nu x * :

Local Nusselt number,hx */k

q w :

Local heat flux

Ra x * :

Modified local Rayleigh number,gcosγβ T (T w −T ∞)K x */(να)

Ra * x :

Modivied local Rayleigh number,gcosγβ T q w K(x *)2/(ναk)

r :

Local radius of the truncated cone

Sh x * :

Local Sherwood number,mx */[D(c ω−c ∞)]

T :

Temperature

u :

Darcy velocity in the x-direction

v :

Darcy velocity in the y-direction

x :

Streamwise coordinate

x * :

Distance measured from the leading edge of the truncated cone,x−x 0

x 0 :

Distance of the leading edge of truncated cone measured from the origin

y :

Transverse coordinate

α:

Thermal diffusivity

β c :

Coefficient of concentration expansion

β T :

Coefficient of thermal expansion

γ:

Half angle of the truncated cone

η:

Pseudosimilarity variable

θ:

Dimensionless temperature

λ:

Exponent for VWT/VWC or VHF/VMF

ν:

Kinematic viscosity of convective fluid

ξ:

Dimensionless distance

ψ:

Stream function

ω:

Condition at the wall

∞:

Condition at infinity

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  1. K. A. Yih

    Present address: , F 3 No. 11 Lane 53 Min Zhi Road, 73011, Hsin-ying City, Tainan County, Taiwan Republic of China

Authors and Affiliations

  1. Air Force Aeronautics Technology School, Kang-shan, 90395-2, Kaohsiung, Taiwan Republic of China

    K. A. Yih

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Yih, K.A. Coupled heat and mass transfer by free convection over a truncated cone in porous media: VWT/VWC or VHF/VMF. Acta Mechanica 137, 83–97 (1999). https://doi.org/10.1007/BF01313146

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  • DOI: https://doi.org/10.1007/BF01313146

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