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

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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/m

^{3})*D*_{M}Mass diffusivity (m

^{2}/s)*E*Dimensionless activation energy defined in Eq. (27)

*E*_{a}Activation energy (eV)

*f*Dimensionless stream function defined in Eq. (14)

*f*_{w}Blowing/suction parameter defined in Eq. (25)

*g*Gravitational acceleration (m/s

^{2})*h*Local convective heat transfer coefficient (W/m

^{2}K)*h*_{m}Local convective mass transfer coefficient (m/s)

*K*Permeability of the porous medium (m

^{2})*k*Equivalent thermal conductivity (W/mK)

*k*_{r}^{2}Reaction rate (1/s)

*Le*Lewis number defined in Eq. (26)

*m*_{w}Wall mass flux (kg/m

^{2}s)*N*Buoyancy ratio defined in Eq. (26)

*n*Fitted rate constant

*Nu*Nusselt number defined in Eq. (28)

*p*Pressure (N/m

^{2})*q*_{w}Wall heat flux (W/m

^{2})*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)*V*_{w}Uniform blowing/suction velocity (m/s)

*x*Streamwise coordinate (m)

*y*Transverse coordinate (m)

## Greek Symbols

*α*Equivalent thermal diffusivity (m

^{2}/s)*β*_{C}Coefficient of concentration expansion (m

^{3}/kg)*β*_{T}Coefficient of thermal expansion (1/K)

*δ*Temperature difference parameter defined in Eq. (27)

*δ*_{C}Concentration boundary layer thickness (m)

*δ*_{T}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/m

^{3})*ϕ*Dimensionless concentration defined in Eq. (16)

*ψ*Stream function (m

^{2}/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.

## References

- Bestman, A.R.: Natural convection boundary layer with suction and mass transfer in a porous medium. Int. J. Energy Res.
**14**(4), 389–396 (1990)CrossRefGoogle Scholar - Cebeci, T., Bradshaw, P.: Physical and computational aspects of convective heat transfer. Springer, New York (1984)CrossRefGoogle Scholar
- Chamkha, A.J., Quadri, M.M.A.: Heat and mass transfer from a permeable cylinder in a porous medium with magnetic field and heat generation/absorption effects. Numer. Heat Transf. Part A Appl.
**40**(4), 387–401 (2001)CrossRefGoogle Scholar - Chamkha, A.J., El-Kabeir, S.M.M., Rashad, A.M.: Heat and mass transfer by non-Darcy free convection from a vertical cylinder embedded in porous media with a temperature-dependent viscosity. Int. J. Numer. Methods Heat Fluid Flow
**21**(7), 847–863 (2011)CrossRefGoogle Scholar - Cheng, C.Y.: Natural convection heat and mass transfer from a horizontal cylinder of elliptic cross section with constant wall temperature and concentration in saturated porous media. J. Mech.
**22**(3), 257–261 (2006)CrossRefGoogle Scholar - Cheng, C.Y.: Integral solutions for free convection heat and mass transfer from horizontal cylinders in porous media. J. South. Taiwan Univ.
**39**(1), 107–118 (2014)Google Scholar - Hassanien, I.A., Rashed, Z.Z.: Non-Darcy free convection flow over a horizontal cylinder in a saturated porous medium with variable viscosity, thermal conductivity and mass diffusivity. Commun. Nonlinear Sci. Numer. Simul.
**16**(4), 1931–1941 (2011)CrossRefGoogle Scholar - Ingham, D.B., Pop, I.: Natural convection about a heated horizontal cylinder in a porous medium. J. Fluid Mech.
**184**(1), 157–181 (1987)CrossRefGoogle Scholar - Maleque, KhA: Unsteady natural convection boundary layer flow with mass transfer and a binary chemical reaction. Br. J. Appl. Sci. Technol.
**3**(1), 131–149 (2013)CrossRefGoogle Scholar - Mansour, M.A., El-Anssary, N.F., Aly, A.M., Gorla, R.S.R.: Chemical reaction and magnetohydrodynamic effects on free convection flow past an inclined surface in a porous medium. J. Porous Media
**13**(1), 87–96 (2010)CrossRefGoogle Scholar - Merkin, J.H.: Free convection boundary layers on axi-symmetric and two-dimensional bodies of arbitrary shape in a saturated porous medium. Int. J. Heat Mass Transf.
**22**(10), 1461–1462 (1979)CrossRefGoogle Scholar - Mustafa, M., Khan, J.A., Hayat, T., Alsaedi, A.: Buoyancy effects on the MHD nanofluid flow past a vertical surface with chemical reaction and activation energy. Int. J. Heat Mass Transf.
**108**(Part B), 1340–1346 (2017)CrossRefGoogle Scholar - Nield, D.A., Bejan, A.: Convection in Porous Media, 5th edn. Springer, New York (2017)CrossRefGoogle Scholar
- Oahimire, J.I., Olajuwon, B.I.: Effect of Hall current and thermal radiation on heat and mass transfer of a chemically reacting MHD flow of a micropolar fluid through a porous medium. J. King Saud Univ. Eng. Sci.
**26**(2), 112–121 (2014)Google Scholar - Pop, I., Kumari, M., Nath, G.: Free convection about cylinders of elliptic cross section embedded in a porous medium. Int. J. Eng. Sci.
**30**(1), 35–45 (1992)CrossRefGoogle Scholar - Postelnicu, A.: Heat and mass transfer by natural convection at a stagnation point in a porous medium considering Soret and Dufour effects. Heat Mass Transf.
**46**(8–9), 831–840 (2010)CrossRefGoogle Scholar - Shafique, Z., Mustafa, M., Mushtaq, A.: Boundary layer flow of Maxwell fluid in rotating frame with binary chemical reaction and activation energy. Results Phys.
**6**(1), 627–633 (2016)CrossRefGoogle Scholar - Srinivasacharya, D., Swamy Reddy, G.: Chemical reaction and radiation effects on mixed convection heat and mass transfer over a vertical plate in power-law fluid saturated porous medium. J. Egypt. Math. Soc.
**24**(1), 108–115 (2016)CrossRefGoogle Scholar - Yih, K.A.: Coupled heat and mass transfer by natural convection adjacent to a permeable horizontal cylinder in a saturated porous medium. Int. Commun. Heat Mass Transf.
**26**(3), 431–440 (1999)CrossRefGoogle Scholar