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Effects of Viscous Dissipation and Radiation on MHD Natural Convection in Oblique Porous Cavity with Constant Heat Flux

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Thermodynamics and heat transfer Flows in porous media; filtration; seepage

Published online by Cambridge University Press:  09 January 2017

Ammar I. Alsabery ,
Habibis Saleh  and
Ishak Hashim
Ammar I. Alsabery*
Affiliation:
School of Mathematical Sciences, Faculty of Science & Technology, University Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia
Habibis Saleh
Affiliation:
School of Mathematical Sciences, Faculty of Science & Technology, University Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia
Ishak Hashim
Affiliation:
School of Mathematical Sciences, Faculty of Science & Technology, University Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia Research Institute, Center for Modeling & Computer Simulation, King Fahd University of Petroleum & Minerals, Dhahran-31261, Saudi Arabia
*
*Corresponding author. Email:ammar_e_2011@yahoo.com (A. I. Alsabery)
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Abstract

Effects of viscous dissipation and radiation on MHD natural convection in oblique porous cavity with constant heat flux is studied numerically in the present article. The right inclined wall is maintained at a constant cold temperature Tc and the left inclined wall has a constant heat flux q with length S, while the remainder of the left wall is adiabatic. The horizontal walls are assumed to be adiabatic. The governing equations are obtained by applying the Darcy model and Boussinesq approximations. COMSOL's finite element method is used to solve the non-dimensional governing equations together with specified boundary conditions. The governing parameters of this study are Rayleigh number (Ra=10,100,200,250,500 and 1000), Hartmann number (0≤ Ha ≤20), inclination angle of the magnetic field (0° ≤ ω ≤ π/2), Radiation (0≤R≤15), the heater flux length (0.1≤H≤1) and inclination angle of the sloping wall (–π/3≤ϕ≤π/3). The results are considered for various values of the governing parameters in terms of streamlines, isotherms and averageNusselt number. It is found that the intensity of the streamlines and the isotherm patterns decrease with an increment in Hartmann number. The overall heat transfer is significantly increased with the increment of the viscous dissipation and the radiation parameters.

Keywords

Heat transferMHD natural convectionporous mediaviscous dissipationradiation

MSC classification

Secondary: 65M06: Finite difference methods 80A20: Heat and mass transfer, heat flow 76S05: Flows in porous media; filtration; seepage
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 2 , April 2017 , pp. 463 - 484
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Nield, D. A. and Bejan, A., Convection in Porous Media, Springer, 2006.Google Scholar
[2] Ingham, D. and Pop, I., Transport Phenomena in Porous Media III, Volume 3, Elsevier, 2005.Google Scholar
[3] Bejan, A., Porous and Complex Flow Structures in Modern Technologies, Springer, 2004.CrossRefGoogle Scholar
[4] Ingham, D. and Pop, I., Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media, Elsevier, 2001.Google Scholar
[5] Walker, K. L. and Homsy, G. M., Convection in a porous cavity, J. Fluid Mech., 87(03) (1978), pp. 449–474.CrossRefGoogle Scholar
[6] Bejan, A., On the boundary layer regime in a vertical enclosure filled with a porous medium, Lett. Heat Mass Transfer, 6(2) (1979), pp. 93–102.CrossRefGoogle Scholar
[7] Gross, R. J., Bear, M. R. and Hickox, C. E., The application of flux-corrected transport (fct) to high rayleigh number natural convection in a porous medium, in Proc. 8th Int. Heat Transfer Conf., San Francisco, CA, 1986.CrossRefGoogle Scholar
[8] Beckermann, C., Viskanta, R. and Ramadhyani, S., A numerical study of non-darcian natural convection in a vertical enclosure filled with a porous medium, Numer. Heat Transfer, 10(6) (1986), pp. 557–570.CrossRefGoogle Scholar
[9] Moya, S., Ramos, E. and Sen, M., Numerical study of natural convection in a tilted rectangular porous material, Int. J. Heat Mass Transfer, 30(4) (1987), pp. 741–756.CrossRefGoogle Scholar
[10] Manole, D. and Lage, J., Numerical benchmark results for natural convection in a porous medium cavity, ASME-PUBLICATIONS-HTD, 216 (1993), pp. 55–55.Google Scholar
[11] Goyeau, B., Songbe, J-P. and Gobin, D., Numerical study of double-diffusive natural convection in a porous cavity using the darcy-brinkman formulation, Int. J. Heat Mass Transfer, 39(7) (1996), pp. 1363–1378.CrossRefGoogle Scholar
[12] Saeid, N. H. and Pop, I., Natural convection from a discrete heater in a square cavity filled with a porous medium, J. Porous Media, 8(1) (2005).CrossRefGoogle Scholar
[13] Sivasankaran, S., Kandaswamy, P. and Ng, C. O., Double diffusive convection of anomalous density fluids in a porous cavity, Transport in Porous Media, 71(2) (2008), pp. 133–145.CrossRefGoogle Scholar
[14] Baytas, A. C. and Pop, I., Free convection in oblique enclosures filled with a porous medium, Int. J. Heat Mass Transfer, 42(6) (1999), pp. 1047–1057.CrossRefGoogle Scholar
[15] Baytas, A. C. and Pop, I., Natural convection in a trapezoidal enclosure filled with a porous medium, Int. J. Eng. Sci., 39(2) (2001), pp. 125–134.CrossRefGoogle Scholar
[16] Rathish Kumar, B. V. and Kumar, B., Parallel computation of natural convection in trapezoidal porous enclosures, Math. Comput. Simulation, 65(3) (2004), pp. 221–229.CrossRefGoogle Scholar
[17] Varol, Y., Oztop, H. F. and Pop, I., Numerical analysis of natural convection in an inclined trapezoidal enclosure filled with a porous medium, Int. J. Thermal Sci., 47(10) (2008), pp. 1316–1331.CrossRefGoogle Scholar
[18] Grosan, T., Revnic, C., Pop, I. and Ingham, D., Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium, Int. J. Heat Mass Transfer, 52(5) (2009), pp. 1525–1533.CrossRefGoogle Scholar
[19] Mansour, M. A., Chamkha, A. J., Mohamed, R. A., Abd El-Aziz, M. M and Ahmed, S. E., MHD natural convection in an inclined cavity filled with a fluid saturated porous medium with heat source in the solid phase, Nonlinear Analysis: Modelling and Control, 15(1) (2010), pp. 55–70.CrossRefGoogle Scholar
[20] Revnic, C., Grosan, T., Pop, I. and Ingham, D. B., Magnetic field effect on the unsteady free convection flow in a square cavity filled with a porous medium with a constant heat generation, Int. J. Heat Mass Transfer, 54(9) (2011), pp. 1734–1742.CrossRefGoogle Scholar
[21] Saleh, H., Roslan, R. and Hashim, I., Natural convection in a porous trapezoidal enclosure with an inclined magnetic field, Comput. Fluids, 47(1) (2011), pp. 155–164.CrossRefGoogle Scholar
[22] Altawallbeh, A. A., Saeid, N. H. and Hashim, I., Magnetic field effect on natural convection in a porous cavity heating from below and salting from side, Adv. Mech. Eng., (2013).CrossRefGoogle Scholar
[23] Ahmed, S. E., Numerical study of MHD natural convection in an inclined rectangular cavity with internal heat generation filled with a porous medium under the influence of joule heating, Latin American Applied Research, 43(1) (2013), pp. 67–71.Google Scholar
[24] Saeid, N. H. and Pop, I., Viscous dissipation effects on free convection in a porous cavity, Int. Commun. Heat Mass Transfer, 31(5) (2004), pp. 723–732.CrossRefGoogle Scholar
[25] Hossain, A., Saha, S. C. and Rama, G. S., Viscous dissipation effects on natural convection from a vertical plate with uniform surface heat flux placed in a thermally stratified media, Int. J. Fluid Mech. Research, 32(3) (2005).CrossRefGoogle Scholar
[26] Badruddin, I. A., Zainal, Z. A. Aswatha Narayana, P. A. and Seetharamu, K. N., Heat transfer in porous cavity under the influence of radiation and viscous dissipation, Int. Commun. Heat Mass Transfer, 33(4) (2006), pp. 491–499.CrossRefGoogle Scholar
[27] Israel-Cookey, C., Ogulu, A. and Omubo-Pepple, V. B., Influence of viscous dissipation and radiation on unsteady MHD free-convection flow past an infinite heated vertical plate in a porous medium with time-dependent suction, Int. J. Heat Mass Transfer, 46(13) (2003), pp. 2305–2311.CrossRefGoogle Scholar
[28] Osalusi, E., Side, J., Harris, R. and Johaston, B., On the effectiveness of viscous dissipation and joule heating on steady MHD flow and heat transfer of a bingham fluid over a porous rotating disk in the presence of hall and ion-slip currents, Int. Commun. Heat Mass Transfer, 34(9) (2007), pp. 1030–1040.CrossRefGoogle Scholar
[29] Sharma, P. R. and Singh, G., Effects of variable thermal conductivity, viscous dissipation on steady MHD natural convection flow of low prandtl fluid on an inclined porous plate with ohmic heating, Meccanica, 45(2) (2010), pp. 237–247.CrossRefGoogle Scholar
[30] Ahmed, S. E., Kadhim, H. A., Mohammed, H. A., Adegun, I. K., Xiaohui, Z., Lioua, K., Arman, H. and Sivasankaran, S., Viscous dissipation and radiation effects on MHD natural convection in a square enclosure filled with a porous medium, Nuclear Eng. Design, 266 (2014), pp. 34–42.CrossRefGoogle Scholar
[31] Raptis, A., Radiation and free convection flow through a porous medium, Int. Commun. Heat Mass Transfer, 25(2) (1998), pp. 289–295.CrossRefGoogle Scholar
[32] Prasad, V. and Kulacki, F. A., Natural convection in a rectangular porous cavity with constant heat flux on one vertical wall, J. Heat Transfer, 106(1) (1984), pp. 152–157.CrossRefGoogle Scholar