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Arrhenius Activation Energy Effect on Free Convection About a Permeable Horizontal Cylinder in Porous Media

  • Chuo-Jeng HuangEmail author
Article
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Abstract

This study numerically analyzed the Arrhenius activation energy effect on free convection about a permeable horizontal cylinder in porous media. The surface of the horizontal cylinder is maintained at uniform wall temperature and uniform wall concentration. Non-similar transformed governing equations are solved by Keller box method. Comparisons with previous works showed good agreement. Numerical data of the Nusselt number and the Sherwood number are presented for dimensionless reaction rate, temperature difference parameter, fitted rate constant, dimensionless activation energy, blowing/suction parameter, dimensionless coordinate, buoyancy ratio, and Lewis number. Generally, the Nusselt (Sherwood) number reduces (increases) with decreasing dimensionless activation energy or increasing dimensionless reaction rate, temperature difference parameter, and fitted rate constant.

Keywords

Arrhenius activation energy Free convection Permeable horizontal cylinder Porous media 

List of Symbols

a

Radius of the horizontal circular cylinder (m)

C

Volume-averaged concentration (kg/m3)

DM

Mass diffusivity (m2/s)

E

Dimensionless activation energy defined in Eq. (27)

Ea

Activation energy (eV)

f

Dimensionless stream function defined in Eq. (14)

fw

Blowing/suction parameter defined in Eq. (25)

g

Gravitational acceleration (m/s2)

h

Local convective heat transfer coefficient (W/m2K)

hm

Local convective mass transfer coefficient (m/s)

K

Permeability of the porous medium (m2)

k

Equivalent thermal conductivity (W/mK)

kr2

Reaction rate (1/s)

Le

Lewis number defined in Eq. (26)

mw

Wall mass flux (kg/m2s)

N

Buoyancy ratio defined in Eq. (26)

n

Fitted rate constant

Nu

Nusselt number defined in Eq. (28)

p

Pressure (N/m2)

qw

Wall heat flux (W/m2)

Ra

Modified Rayleigh number for the flow through the porous medium defined in Eq. (17)

Sh

Sherwood number defined in Eq. (29)

T

Volume-averaged temperature (K)

u

Volume-averaged velocity component in the x-direction (m/s)

v

Volume-averaged velocity component in the y-direction (m/s)

Vw

Uniform blowing/suction velocity (m/s)

x

Streamwise coordinate (m)

y

Transverse coordinate (m)

Greek Symbols

α

Equivalent thermal diffusivity (m2/s)

βC

Coefficient of concentration expansion (m3/kg)

βT

Coefficient of thermal expansion (1/K)

δ

Temperature difference parameter defined in Eq. (27)

δC

Concentration boundary layer thickness (m)

δT

Thermal boundary layer thickness (m)

η

Pseudo-similarity variable defined in Eq. (13)

θ

Dimensionless temperature defined in Eq. (15)

κ

Boltzmann constant (eV/K)

μ

Absolute viscosity of the fluid (kg/ms)

ξ

Dimensionless coordinate defined in Eq. (12)

σ

Dimensionless reaction rate defined in Eq. (27)

ρ

Density of the fluid (kg/m3)

ϕ

Dimensionless concentration defined in Eq. (16)

ψ

Stream function (m2/s)

Subscripts

w

Condition at the wall

Condition at infinity

Notes

Acknowledgements

The author gratefully acknowledges Professor Kuo-Ann Yih at the Air Force Institute of Technology for assistance in preparing this manuscript.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Aircraft EngineeringAir Force Institute of TechnologyKaohsiungTaiwan, ROC

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