Finite Element Analysis of Heater Length in a Porous Annulus - Part B

Abstract:

The present study is undertaken to investigate the effect of geometrical and physical parameters on discrete heating of an annular vertical porous cylinder heated isothermally at center portion of inner radius. Finite element method is employed to convert the governing partial differential equations into matrix form of equations by employing 3 noded triangular elements. Darcy model is assumed to represent the flow behavior inside the porous medium. Two temperature model is used to describe energy flow in the medium. The study is conducted for different lengths of heater corresponding to 20%, 35% and 50% of the total height of the cylinder. It is found that the flow pattern for aspect ratio 1 is smoother than that of the 0.5.

• Periodical: Applied Mechanics and Materials (Volume 786)
• Pages: 199-204
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.786.199
• Online since: August 2015
• Authors: Abdullah A.A.A. Al-Rashed, S.N.J. Ahmed, Ghulam Abdul Quadir*, H.M.T. Khaleed, I.A. Badruddin, Y.T.M. Khan, S. Kamangar
• Keywords: Darcy Law, Discrete Heating, FEM, Porous Annulus

References

[1] D.A. Nield, A. Bejan, 1999. Convection in porous media, second ed, Springer-Verlag, New York.

[2] K. Vafai, 2000. Hand book of porous media, Marcel Dekker, New York.

[3] I. Pop, D.B. Ingham, 2001. Convective heat transfer: Mathematical and computational modeling of viscous fluids and porous media, Pergamon, Oxford.

[4] V. Prasad, F. A Kulacki, Natural convection in a vertical porous annulus, Int. J. Heat Mass Transfer 27 (1984) 207-219.

DOI: 10.1016/0017-9310(84)90212-6

[5] R.C. Rajamani, C. Srinivas, P. Nithiarasu, K.N. Seetharamu, Convective Heat-Transfer in Axisymmetrical Porous Bodies. International Journal of Numerical Methods for Heat & Fluid Flow 5(9) (1995) 829-837.

DOI: 10.1108/eum0000000004126

[6] I.A. Badruddin, Abdullah A.A. A Al-Rashed, N. J. Salman Ahmed, S. Kamangar, Investigation of heat transfer in square porous-annulus. International Journal of Heat and Mass Transfer  55(7-8) (2012) 2184-2192.

DOI: 10.1016/j.ijheatmasstransfer.2011.12.023

[7] N.J. Salman Ahmed, I.A. Badruddin, Z.A. Zainal, H.M.T. Khaleed, Jeevan Kanesan, Heat transfer in a conical cylinder with porous medium. International Journal of Heat and Mass Transfer 52(13-14) (2009) 3070-3078.

DOI: 10.1016/j.ijheatmasstransfer.2008.12.030

[8] I.A. Badruddin, Z.A. Zainal, P. Narayana, K.N. Seetharamu, L.W. Siew, Free convection and radiation for a vertical wall with varying temperature embedded in a porous medium. International Journal of Thermal Sciences 45(5) (2006) 487-493.

DOI: 10.1016/j.ijthermalsci.2005.05.008

[9] I.A. Badruddin, Z.A. Zainal, P.A. Narayana, K.N. Seetharamu, Heat transfer in porous cavity under the influence of radiation and viscous dissipation. International Communications in Heat and Mass Transfer 33(4) (2006) 491-499.

DOI: 10.1016/j.icheatmasstransfer.2006.01.015

[10] I.A. Badruddin, Z.A. Zainal, Zahid A. Khan, Zulquernain Mallick, Effect of viscous dissipation and radiation on natural convection in a porous medium embedded within vertical annulus. International Journal of Thermal Sciences 46 (3) (2007).

DOI: 10.1016/j.ijthermalsci.2006.05.005

[11] A. Raptis, Radiation and free convection flow through a porous medium. International Communications in Heat and Mass Transfer 25(2) (1998) 289-295.

DOI: 10.1016/s0735-1933(98)00016-5

[12] Irfan Anjum Badruddin, Z.A. Zainal, P.A. Aswatha Narayana, K.N. Seetharamu, Heat transfer by radiation and natural convection through a vertical annulus embedded in porous medium, International Communications in Heat and Mass Transfer 33( 4) (2006).

DOI: 10.1016/j.icheatmasstransfer.2006.01.008

[13] N.J.S. Ahmed, S. Kamangar, I.A. Badruddin, A. A. A. A. Al-Rashed, G.A. Quadir, H.M.T. Khaleed, T.M.Y. Khan, Conjugate heat transfer in porous annulus, J. Porous Media. 17(12) (2014) 1109-1119.

DOI: 10.1615/jpormedia.v17.i12.70

[14] N.H. Saeid, Analysis of free convection about a horizontal cylinder in a porous media using a thermal non-equilibrium model. International Communications in Heat and Mass Transfer 33(2) (2006) 158-165.

DOI: 10.1016/j.icheatmasstransfer.2005.09.009

[15] Tiew Wei Ting, Yew Mun Hung, Ningqun Guo, Entropy generation of viscous dissipative nanofluid flow in thermal non-equilibrium porous media embedded in microchannelsOriginal Research Article International Journal of Heat and Mass Transfer 81 (2015).

DOI: 10.1016/j.ijheatmasstransfer.2014.11.006

[16] Yasser Mahmoudi, Effect of thermal radiation on temperature differential in a porous medium under local thermal non-equilibrium conditionOriginal Research Article International Journal of Heat and Mass Transfer 76 (2014) 105-121.

DOI: 10.1016/j.ijheatmasstransfer.2014.04.024

[17] I.A. Badruddin, Z.A. Zainal, P.A. Narayana, K.N. Seetharamu, Thermal non-equilibrium modeling of heat transfer through vertical annulus embedded with porous medium. International Journal of Heat and Mass Transfer 49(25-26) (2006) 4955-4965.

DOI: 10.1016/j.ijheatmasstransfer.2006.05.043

[18] N.J. Salman Ahmed, I.A. Badruddin, Jeevan Kanesan, Z.A. Zainal, K.S. Nazim Ahamed, Study of mixed convection in an annular vertical cylinder filled with saturated porous medium, using thermal non-equilibrium model. International Journal of Heat and Mass Transfer 54(17-18) (2011).

DOI: 10.1016/j.ijheatmasstransfer.2011.05.001

[19] I.A. Badruddin, Z.A. Zainal, P.A. Narayana, P. A, K.N. Seetharamu, Numerical analysis of convection conduction and radiation using a non-equilibrium model in a square porous cavity. International Journal of Thermal Sciences 46(1) (2007) 20-29.

DOI: 10.1016/j.ijthermalsci.2006.03.006

[20] P. Bera, Sarita Pippal, Abhishek K. Sharma, A thermal non-equilibrium approach on double-diffusive natural convection in a square porous-medium cavity Original Research Article International Journal of Heat and Mass Transfer 78 (2014) 1080-1094.

DOI: 10.1016/j.ijheatmasstransfer.2014.07.041

[21] I.A. Badruddin, Abdullah A.A.A. Al-Rashed, N.J. Salman Ahmed, Sarfaraz Kamangar, K. Jeevan, Natural convection in a square porous annulus, International Journal of Heat and Mass Transfer 55(23-24) ( 2012) 7175-7187.

DOI: 10.1016/j.ijheatmasstransfer.2012.07.034

[22] U. Akdag, Numerical investigation of pulsating flow around a discrete heater in a channel. International Communications in Heat and Mass Transfer 37(7) (2010) 881-889.

DOI: 10.1016/j.icheatmasstransfer.2010.04.001

[23] E. Bilgen, and A. Muftuoglu, Conjugate heat transfer in open cavities with a discrete heater at its optimized position. International Journal of Heat and Mass Transfer 51(3-4) (2008) 779-788.

DOI: 10.1016/j.ijheatmasstransfer.2007.04.017

[24] Fu-Yun Zhao, Di Liu, and G. -F. Tang.,. Resonant response of fluid flow subjected to discrete heating elements. Energy Conversion and Management 48(9) (2007) 2461–2472.

DOI: 10.1016/j.enconman.2007.04.008

[25] N.H. Saeid, and I. Pop, Maximum density effects on natural convection from a discrete heater in a cavity filled with a porous medium. Acta Mechanica 171(3-4) (2004) 203-212.

DOI: 10.1007/s00707-004-0142-x

[26] G. Saha, Finite element simulation of magnetoconvection inside a sinusoidal corrugated enclosure with discrete isoflux heating from below. International Communications in Heat and Mass Transfer 37(4) (2010) 393-400.

DOI: 10.1016/j.icheatmasstransfer.2009.12.001

[27] M. Sankar, and Y. Do, Numerical simulation of free convection heat transfer in a vertical annular cavity with discrete heating. International Communications in Heat and Mass Transfer 37(6) (2010) 600-606.

DOI: 10.1016/j.icheatmasstransfer.2010.02.009

[28] G.F. Tang, F.Y. Zhao, and D. Liu, Natural convection in a porous enclosure with a partial heating and salting element. International Journal of Thermal Sciences 47(5) (2008) 569-583.

DOI: 10.1016/j.ijthermalsci.2007.04.006

[29] S.K.W. Tou, and X.F. Zhang, Three-dimensional numerical simulation of natural convection in an inclined liquid-filled enclosure with an array of discrete heaters. International Journal of Heat and Mass Transfer 46(1) (2003) 127-138.

DOI: 10.1016/s0017-9310(02)00253-3

[30] W.M. Yan, and T.F. Lin, Natural convection heat transfer in vertical open channel flows with discrete heating, International Communications in Heat and Mass Transfer 14(2) (1987) 187-200.

DOI: 10.1016/s0735-1933(87)81009-6