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Analysis of Heat and Mass Transfer in a Vertical Annular Porous Cylinder Using FEM

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Abstract

The present study is intended to study heat and mass transfer in a vertical annular cylinder embedded with saturated porous medium. The inner surface of cylinder is maintained at uniform wall temperature and uniform wall concentration. The governing partial differential equations are non-dimensionalised and solved by using finite element method (FEM). The porous medium is discritised using triangular elements with uneven element size. Large number of smaller-sized elements are placed near the walls of the annulus to capture the smallest variation in solution parameters. The results are reported for both aiding and opposing flows. The effects of various non-dimensional numbers such as buoyancy ratio, Lewis number, Rayleigh number, aspect ratio, etc on heat and mass transfer are discussed. The temperature and concentration profiles are presented.

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Abbreviations

A:

Area of an element

A r :

Aspect ratio

C p :

Specific heat

\({C,\bar{{C}}}\) :

Species concentration (dimensional and non-dimensional, respectively)

D :

Mass diffusivity

g :

Gravitational acceleration

H :

Height of cylinder

k :

Thermal conductivity

K :

Permeability of porous media

L :

 = r o − r i

Le :

Lewis number

M :

Shape function

n :

Refractive index

N :

Buoyancy ratio

\({Nu_{z } ,\bar{{N}}u}\) :

Local and average Nusselt number

p :

Pressure

q r :

Radiation flux

r, z :

Cylindrical coordinates

\({\bar{r}, \bar{z}}\) :

Non-dimensional coordinates

\({\bar{{R}}}\) :

Mean radial distance of an element

R :

Radius ratio

Ra :

Rayleigh number

Rd :

Radiation parameter

\({Sh_z ,\bar{S}h}\) :

Local and average Sherwood number

\({T, \bar{T}}\) :

Dimensional and non-dimensional temperature, respectively

u, w :

Velocity in r and z directions

α :

Thermal diffusivity

β C :

Coefficient of concentration expansion

β T :

Coefficient of thermal expansion

β R :

Rosseland extinction coefficient

ρ :

Density

v :

Coefficient of kinematic viscosity

μ :

Coefficient of dynamic viscosity

σ :

Stefan Boltzmann’s constant

ψ :

Stream function

\({\bar{{\psi }}}\) :

Non-dimensional stream function

w :

Wall

∞:

Conditions at infinity

i :

Inner

o :

Outer

References

  • Angirasa D., Peterson G.P., Pop I.: Combined heat and mass transfer by natural convection with opposing buoyancy effects in a saturated porous medium. Int. J. Heat Mass Trans. 40, 2755–2773 (1997)

    Article  Google Scholar 

  • Badruddin I.A., Zainal Z.A., Aswatha Narayana P.A., Seetharamu K.N.: Heat transfer by radiation and natural convection through a vertical annulus embedded in porous medium. Int. Comm. Heat Mass Trans. 33, 500–507 (2006)

    Article  Google Scholar 

  • Badruddin I.A., Zainal Z.A., Aswatha Narayana P.A., Seetharamu K.N.: Thermal non-equilibrium modeling of heat transfer through vertical annulus embedded with porous medium. Int. J. Heat Mass Trans. 49, 4955–4965 (2006)

    Article  Google Scholar 

  • Badruddin I.A., Zainal Z.A., Zahid A.K., Zulquernain M.: Effect of viscous dissipation and radiation on natural convection in a porous medium embedded within vertical annulus. Int. J. Thermal Sci. 46(3), 221–227 (2007)

    Article  Google Scholar 

  • Bejan A.D.K., (eds): Heat Transfer Handbook. Wiley, New York (2003)

    Google Scholar 

  • Cheng C.-Y.: Free convection heat and mass transfer from a horizontal cylinder of elliptic cross section in micropolar fluids. Int. Comm. Heat Mass Trans. 33, 311–318 (2006)

    Article  Google Scholar 

  • Cheng C.-Y.: Fully developed natural convection heat and mass transfer in a vertical annular porous medium with asymmetric wall temperatures and concentrations. Appl. Thermal Eng. 26, 2442–2447 (2006)

    Article  Google Scholar 

  • Cheng C.-Y.: Natural convection heat and mass transfer near a vertical wavy surface with constant wall temperature and concentration in a porous medium. Int. Comm. Heat Mass Trans. 26, 431–440 (2000)

    Google Scholar 

  • Cheng C.-Y.: Soret and Dufour effects on natural convection heat and mass transfer from a vertical cone in a porous medium. Int. Comm. Heat Mass Trans. 36, 1020–1024 (2009)

    Article  Google Scholar 

  • El-Amin M.F.: Double dispersion effects on natural convection heat and mass transfer in non-Darcy porous medium. Appl. Math. Comput. 156, 1–17 (2004)

    Article  Google Scholar 

  • Hossain M.A., Alim M.A.: Natural convection radiation interaction on boundary layer flow along a thin vertical cylinder. Heat Mass Trans. 32, 515–520 (1997)

    Article  Google Scholar 

  • Hossain M.A., Vafai K., Khanafer K.M.N.: Non-Darcy natural convection heat and mass transfer along a vertical permeable cylinder embedded in a porous medium. Int. J. Thermal Sci. 38, 854–862 (1999)

    Article  Google Scholar 

  • Ingham, D.B., Pop, I. (eds): Transport Phenomena in Porous Media. Pergamon, Oxford (1998)

    Google Scholar 

  • Kairi R.R., Murthy P.V.S.N.: Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium. Appl. Math. Comput. 217, 8100–8114 (2011)

    Article  Google Scholar 

  • Lewis R.W., Nithiarasu P., Seetharamu K.N.: Fundamentals of the Finite Element Method for Heat and Fluid Flow. Wiley, Chichester (2004)

    Book  Google Scholar 

  • Nakayama A., Hossain M.A.: An integral treatment for combined heat and mass transfer by natural convection in a porous medium. Int. J. Heat Mass Trans. 38, 761–765 (1995)

    Article  Google Scholar 

  • Nield D., Bejan A.: Convection in Porous Media. 3rd edn. Springer, New York (2006)

    Google Scholar 

  • Pop I., Ingham D.B.: Convective Heat Transfer: Mathematical and Computational Modeling of Viscous Fluids and Porous Media. Pergamon, Oxford (2001)

    Google Scholar 

  • Rajamani R., Srinivasa C., Nithiarasu P., Seetharamu K.N.: Convective heat transfer in axisymmetric porous bodies. Int. J. Numer. Methods Heat Fluid Flow 5, 829–837 (1995)

    Article  Google Scholar 

  • Raptis A.: Radiation and free convection flow through a porous medium. Int. Comm. Heat Mass Trans. 25, 289–295 (1998)

    Article  Google Scholar 

  • Salman Ahmed N.J., Badruddin I.A., Jeevan K., Zainal Z.A., Nazim Ahamed K.S.: Study of mixed convection in an annular vertical cylinder filled with saturated porous medium, using thermal non-equilibrium model. Int. J. Heat Mass Trans. 54(17-18), 3822–3825 (2011)

    Article  Google Scholar 

  • Salman Ahmed N.J., Badruddin I.A., Zainal Z.A., Khaleed H.M.T., Jeevan K.: Heat transfer in a conical cylinder with porous medium. Int. J. Heat Mass Trans. 52(13–14), 3070–3078 (2009)

    Article  Google Scholar 

  • Segerland L.J.: Applied Finite Element Analysis. Wiley, New York (1982)

    Google Scholar 

  • Singh B.B., Chandarki I.M.: Integral treatment of coupled heat and mass transfer by natural convection from a cylinder in porous media. Int. Comm. Heat Mass Trans. 36, 269–273 (2009)

    Article  Google Scholar 

  • Thomas H.R., Ferguson W.J.: A fully coupled heat and mass transfer model incorporating contaminant gas transfer in an unsaturated porous medium. Comput. Geotech. 24, 65–87 (1999)

    Article  Google Scholar 

  • Trevisan O.V., Bejan A.: Mass and heat transfer by high Rayleigh number convection in a porous medium heated from below. Int. J. Heat Mass Trans. 30, 2341–2356 (1987)

    Article  Google Scholar 

  • Vafai, K. (eds): Hand Book of Porous Media. Marcel Dekker, New York (2000)

    Google Scholar 

  • Yang Y.-C.: Simultaneously estimating the contact heat and mass transfer coefficients in a double-layer hollow cylinder with interface resistance. Appl. Thermal Eng. 27, 501–508 (2007)

    Article  Google Scholar 

  • Yih K.A.: Coupled heat and mass transfer in mixed convection about a vertical cylinder in a porous medium: The entire regime. Mech. Rea. Commun. 25, 623–630 (1998)

    Article  Google Scholar 

  • Yih K.A.: Coupled heat and mass transfer by natural convection adjacent to a permeable horizontal cylinder in a saturated porous medium. Int. Comm. Heat Mass Trans. 26, 431–440 (1999)

    Article  Google Scholar 

  • Yih K.A.: Radiation effect on natural convection over a vertical cylinder embedded in a porous media. Int. Comm. Heat Mass Trans. 26, 1025–1035 (1999)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia

    Irfan Anjum Badruddin, N. J. Salman Ahmed & Sarfaraz Kamangar

  2. Public Authority for Applied Education and Training, Industrial Training Institute, 13092, Adiliya, Kuwait

    Abdullah A. A. A. Al-Rashed

  3. Department of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia

    Jeevan Kanesan

  4. Department of Mechanical Engineering, Anjuman Engineering College, Bhatkal, 581320, India

    H. M. T. Khaleed

Authors
  1. Irfan Anjum Badruddin
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  2. N. J. Salman Ahmed
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  3. Abdullah A. A. A. Al-Rashed
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  4. Jeevan Kanesan
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  5. Sarfaraz Kamangar
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  6. H. M. T. Khaleed
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Correspondence to Irfan Anjum Badruddin.

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Badruddin, I.A., Salman Ahmed, N.J., Al-Rashed, A.A.A.A. et al. Analysis of Heat and Mass Transfer in a Vertical Annular Porous Cylinder Using FEM. Transp Porous Med 91, 697–715 (2012). https://doi.org/10.1007/s11242-011-9867-x

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  • DOI: https://doi.org/10.1007/s11242-011-9867-x

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