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Unsteady MHD Non-Darcian Flow Over a Vertical Stretching Plate Embedded in a Porous Medium with Thermal Non-Equilibrium Model

Published online by Cambridge University Press:  21 December 2015

D. Prakash ,
M. Muthtamilselvan  and
Xiao-Dong Niu
D. Prakash
Affiliation:
Department of Applied Mathematics, Bharathiar University, Coimbatore-641 046, India
M. Muthtamilselvan*
Affiliation:
Department of Applied Mathematics, Bharathiar University, Coimbatore-641 046, India
Xiao-Dong Niu
Affiliation:
Department of Mechatronics Engineering, Shantou University, Shantou 515063, China
*
*Corresponding author. Email:muthtamil1@yahoo.co.in (M.Muthtamilselvan), dsprakash86@gmail.com (D. Prakash)
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Abstract

An analysis is performed to study the influence of local thermal non-equilibrium (LTNE) on unsteady MHD laminar boundary layer flow of viscous, incompressible fluid over a vertical stretching plate embedded in a sparsely packed porous medium in the presence of heat generation/absorption. The flow in the porous medium is governed by Brinkman-Forchheimer extended Darcy model. A uniform heat source or sink is presented in the solid phase. By applying similarity analysis, the governing partial differential equations are transformed into a set of time dependent non-linear coupled ordinary differential equations and they are solved numerically by Runge-Kutta Fehlberg method along with shooting technique. The obtained results are displayed graphically to illustrate the influence of different physical parameters on the velocity, temperature profile and heat transfer rate for both fluid and solid phases. Moreover, the numerical results obtained in this study are compared with the existing literature in the case of LTE and found that they are in good agreement.

Keywords

76D1076S0576W05MHDBrinkman-Forchheimer modelheat generationlocal thermal non-equilibrium (LTNE)
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 1 , February 2016 , pp. 52 - 66
Copyright
Copyright © Global-Science Press 2016 

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References

[1]Vajravelu, K., Flow and heat transfer in a saturated porous medium over a stretching surface, Z. Angew. Math. Mech., 74 (1994), pp. 605–614.Google Scholar
[2]Nield, D. A. and Bejan, A., Convection in Porous Media, Springer, New York, 2013.CrossRefGoogle Scholar
[3]Vafai, K., Handbook of Porous Media, Taylor & Francis, New York, 2005.Google Scholar
[4]Ingham, D. B. and Pop, I., Transport Phenomena in Porous Media, Vol. III. Elsevier, Oxford, 2005.Google Scholar
[5]Vafai, K. and Tien, C. L., Boundary and inertia effects onflow and heat transfer in porous media, Int. J. Heat Mass Transfer, 24 (1981), pp. 195–203.Google Scholar
[6]Chen, C. H. and Chen, C. K., Non-Darcian mixed convection along a vertical plate embedded in a porous medium, Appl. Math. Model., 14 (1990), pp. 482–488.CrossRefGoogle Scholar
[7]Elbashbeshy, E. M. A. and Bazid, M. A. A., The mixed convection along a vertical plate with variable surface heat flux embedded in porous medium, Appl. Math. Comput., 125 (2002), pp. 317–324.Google Scholar
[8]Cheng, C. Y., Non-Darcy natural convection heat and mass transfer from a vertical wavy surface in saturated porous media, Appl. Math. Comput., 182 (2006), pp. 1488–1500.Google Scholar
[9]Hassanien, I. A. and Al-Arabi, T. H., Non-Darcy unsteady mixed convection flow near the stagnation point on a heated vertical surface embedded in a porous medium with thermal radiation and variable viscosity, Commun. Nonlinear Sci. Numer. Simulat., 14 (2009), pp. 1366–1376.Google Scholar
[10]Rosali, H., Ishak, A. and Pop, I., Mixed convection stagnation-point flow over a vertical plate with prescribed heat flux embedded in a porous medium: brinkman-extended darcy formulation, Transp Porous Med., 90 (2011), pp. 709–719.CrossRefGoogle Scholar
[11]Prakash, D., Muthtamilselvan, M. and Doh, Deog-Hee, Unsteady MHD non-Darcian flow over a vertical stretching plate embedded in a porous medium with non-uniform heat generation, Appl. Math. Comput., 236 (2014), pp. 480–492.Google Scholar
[12]Kaviany, M., Principles of Heat Transfer in Porous Media, Second ed., Springer, New York, 1999.Google Scholar
[13]Sanjuan, N., Simal, S., Bon, J. and Mulet, A., Modelling of broccoli stems rehydration process, J. Food Eng., 42 (1999), pp. 27–31.CrossRefGoogle Scholar
[14]Zorrilla, S. E. and Rubiolo, A. C., Mathematical modeling for immersion chilling and freezing of foods. Part I. Model development, J. Food. Eng., 66 (2005), pp. 329–338.CrossRefGoogle Scholar
[15]Dincov, D. D., Parrott, K. A. and Pericleous, K. A., Heat and mass transfer in two-phase porous materials under intensive microwave heating, J. Food Eng., 65 (2004), pp. 403–412.CrossRefGoogle Scholar
[16]Calmidi, V. V. and Mahajan, R. L., Forced convection in high porosity foams, ASME J. Heat Transfer, 122 (2000), pp. 557–565.Google Scholar
[17]Zhao, C. Y., Lu, T.J. and Hodson, H. P., Thermal radiation in ultralight metal foams with open cells, Int. J. Heat Mass Transfer, 47 (2004), pp. 2927–2939.Google Scholar
[18]Saeid, N. H., Analysis of free convection about a horizontal cylinder in a porous media using a thermal non-equilibrium model, Int. Commun. Heat Mass Transfer, 33 (2006), pp. 158–165.CrossRefGoogle Scholar
[19]Baytas, A. C. and Pop, I., Free convection in a square porous cavity using a thermal nonequilibrium model, Int. J. Thermal. Sci., 41 (2002), pp. 861–870.Google Scholar
[20]Baytas, A. C., Thermal non-equilibrium natural convection in a square enclosure filled with a heat-generating solid phase, non-Darcy porous medium, Int. J. Energy Res., 27 (2003), pp. 975–988.Google Scholar
[21]Borujerdi, A. N., Noghrehabadi, A. R. and Rees, D. A. S., Onset of convection in a horizontal porous channel with uniform heat generation using a thermal nonequilibrium model, Transport Porous Media, 69 (2007), pp. 343–357.CrossRefGoogle Scholar
[22]Wong, K. C. and Saeid, N. H., Numerical study of mixed convection on jet impingement cooling in a horizontal porous layer under local thermal non-equilibrium conditions, Int. J. Thermal Sci., 48 (2009), pp. 860–870.Google Scholar
[23]Rees, D. A. S. and Pop, I., Vertical free convection boundary layer flow in a porous medium using a thermal non-equilibrium model, J. Porous Media, 3 (2001), pp. 31–44.Google Scholar
[24]Saeid, N. H., Analysis of mixed convection in a vertical porous layer using non-equilibrium model, Int. J. Heat Mass Transfer, 47 (2004), pp. 5619–5627.Google Scholar
[25]Nouri-Borujerdi, A., Noghrehabadi, A. R. and Rees, D. A. S., The effect of local thermal non-equilibrium on conduction in porous channels with a uniform heat source, Transp Porous Med., 69 (2007), pp. 281–288.Google Scholar
[26]Nazari, M. and Kowsary, F., Analytical solution of non-equilibrium heat conduction in porous medium in-corporating a variable porosity model with heat generation, J. Heat Transfer, 131 (2009), 014503.CrossRefGoogle Scholar
[27]Barletta, A. and Celli, M., Local thermal non-equilibrium flow with viscous dissipation in a plane horizontal porous layer, Int. J. Thermal. Sci., 50 (2011), pp. 53–60.CrossRefGoogle Scholar
[28]Muthtamilselvan, M., Prakash, D. and Doh, Deog-Hee, Effect of thermal non-equilibrium on transient hydromagnetic flow over a moving surface in a nanofluid saturated porous media, J. Mech. Sci. Tech., 28 (2014), pp. 3709–3718.Google Scholar
[29]Saeid, N. H. and Mohamad, A. A., Periodic free convection from a vertical plate in a saturated porous medium-Non-equilibrium model, Int. J. Heat Mass Transfer, 48 (2005), pp. 3855–3863.CrossRefGoogle Scholar
[30]Malashetty, M. S., Pop, I. and Heera, R., Linear and nonlinear double diffusive convection in a rotating sparsely packed porous layer using a thermal non-equilibrium model, Continuum. Mech. Thermodyn., 21 (2009), pp. 317–339.Google Scholar
[31]Ishak, A., Nazar, R. and Pop, I., Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature, Nonlinear Anal. Real World Appl., 10 (2009), pp. 2909–2913.Google Scholar
[32]Muthtamilselvan, M. and Prakash, D., Unsteady hydromagnetic slip flow and heat transfer of nanofluid over a moving surface with prescribed heat and mass fluxes, Proc. I Mech. E Part C J. Mech. Eng. Sci., 229 (2015), pp. 703–715.CrossRefGoogle Scholar
[33]Pantokratoras, A., A common error made in investigation of boundary layer flows, Appl. Math-emat. Model., 33 (2009), pp. 413–422.Google Scholar
[34]Ishak, A., Nazar, R. and Pop, I., Boundarylayer flow andheat transfer over an unsteady stretching vertical surface, Meccanica, 44 (2009), pp. 369–375.Google Scholar
[35]Vajravelu, K., Prasad, K. V. and Chiu-On, NG., Unsteady convective boundary layer flow of a viscous fluid at a vertical surface with variable fluid properties, Nonlinear Anal. Real World Appl., 14 (2013), pp. 455–464.Google Scholar