Entropy generation analysis of MHD forced convective flow through a horizontal porous channel

Sharma, Pooja; Sharma, Tarun; Kumar, Navin

doi:10.22061/jcarme.2019.5039.1615

Document Type : Research Paper

Authors

¹ Department of Mathematics & Statistics; Faculty of Basic Sciences, Manipal University Jaipur, Jaipur, India

² Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, Rajasthan

³ Department of Mathematics, Indian Military Academy, Dehradun, Uttarakhand,24800, India

https://doi.org/10.22061/jcarme.2019.5039.1615

Abstract

Entropy generation due to viscous incompressible MHD forced convective dissipative fluid flow through a horizontal channel of finite depth in the existence of an inclined magnetic field and heat source effect has been examined. The governing non-linear partial differential equations for momentum, energy and entropy generation are derived and solved by using the analytical method. In addition; the skin friction coefficient and Nusselt number are calculated numerically and their values are presented through the tables for the upper and the bottom wall of the channel. It was concluded that; total entropy generation rate and Bejan number are reduced due to rise in the inclination angle of the magnetic field. Also, an increment in the heat source prop ups the fluid temperature and total entropy generation rate. This study will help to reduce the energy loss due to reversible process and heat dissipation. The results are very useful for chemical and metallurgy industries.

Graphical Abstract

Keywords

20.1001.1.22287922.2020.10.1.3.8

Main Subjects

Heat and Mass Transfer

References

[1] A.A. Raptis, “Unsteady free convective flow through a porous medium”, International Journal of Engineering Science, Vol. 21, No 4, pp. 345-348, (1983).

[2] S.P. Vanka and R.K. Ahluwalia, “Three-dimensional flow and thermal development in magnetohydrodynamic channels”, Journal of Energy, Vol. 6, No. 3, pp. 218-224, (1982).

[3] S.K. Ghosh and P.K. Bhattacharjee, “Hall effects on steady hydromagnetic flow in a rotating channel in the presence of an inclined magnetic field”, Czechoslovak Journal of Physics, Vol. 50, No. 6, pp. 759-767, (2010).

[4] D.V. Krishna, D.R.V. Prasad Rao, and A.S. Ramachandra Murthy, “Hydromagnetic convection flows through a porous medium in a rotating channel”, Journal of Engineering Physics and Thermophysics, Vol. 75, No. 2, pp. 281-291, (2002).

[5] A.K. Singh, “ MHD free convective flow through a porous medium between two vertical parallel plates”, Indian Journal of Pure and Applied Physics, Vol. 40, pp. 709-713,(2002).

[6] P.Y. Mhone and O.D. Makinde, “Unsteady MHD flow with heat transfer in a diverging channel”, Romanian Journal of Physics, Vol. 51, No. 9, pp. 967-979, (2006).

[7]. G.S. Seth, Raj Nandkeoylar, N. Mahto and S.K. Singh, “MHD couette flows in a rotating system in the presence of an inclined magnetic field”, Applied Mathematical Sciences, Vol. 3, No. 59, pp. 2919-2932, (2009).

[8] G.S. Seth, Raj Nandkeolyar and Md. S. Ansari, “Hartmann flow in a rotating system in the presence of inclined magnetic field with hall effects”, Tamkang Journal of Science and Engineering, Vol. 13, No. 3, pp. 243-252, (2010).

[9] W.A. Manyonge, D.W. Kiema and C.C.W. Lyaya, “Steady MHD Poiseuille flow between two infinite parallel porous plates in an inclined magnetic field”, International Journal of Pure and Applied Mathematics, Vol. 76, No. 5, pp. 661-668, (2012).

[10] K.M. Joseph, S. Daniel and G.M. Joseph, “Unsteady MHD couette flow between two infinite parallel porous plates in an inclined magnetic field with heat transfer”, International Journal of Mathematics and Statistics Invention, Vol. 2, No. 3, pp. 103-110, (2014).

[11] K.V.S. Raju, T.S. Reddy, M.C. Raju, P.V. Satya Narayana and S. Venkataramana, “ MHD convective flow through a porous medium in a horizontal channel with insulated and impermeable bottom wall in the presence of viscous dissipation and joule heating”, Ain Shams Engineering Journal, Vol. 4, No. 2, pp. 543-551, (2014).

[12] A. Mburu and J. Kwanza, “Magnetohydrodynamic fluid flow between two parallel infinite plates subjected to an inclined magnetic field under pressure gradient”, Journal of Multidisciplinary Engineering Science and Technology (JMEST), Vol. 3, No. 11, pp. 5910-5914, (2016).

[13] P. Sharma and R. Saboo, “A theoretical study of heat and mass transfer in forced convective chemically reacting radiating MHD flow though saturated porous medium over fixed horizontal channel”, AMSE-IIETA publication, Modelling, Measurement and Control C, Vol. 78, No. 1, pp. 100-115, (2017).

[14] A. Bejan, “A study of entropy generation in fundamental convective heat transfer”, Journal of Heat Transfer, Vol. 101, No. 4, pp. 718-725, (1979).

[15] A. Bejan, “Entropy generation minimization: the new thermodynamics of finite-size device and finite time processes”, Journal of Applied Physics, Vol. 79, No. 3, pp. 1191-1218, (1996).

[16] S. Mahmud and R.A, Fraser, “Magnetohydrodynamic free convection and entropy generation in a square porous cavity”, International Journal of Heat and Mass Transfer, Vol. 47, No. 14-17, pp. 3245-3256, (2004).

[17] S. Mahmud and R.A. Fraser, “Flow, thermal and entropy generation characteristics inside a porous channel with viscous dissipation”, International Journal of Thermal sciences, Vol. 44, No. 1, pp. 21-32, (2005).

[18] R.A. Damesh, M.Q. Al-Odat and M.A. Al-Nimr, “Entropy generation during fluid flow in a channel under the effect of the transverse magnetic field”, Heat and Mass Transfer, Vol. 44, No. 8, pp. 897-904, (2008).

[19] M. Bouabid, N. Hidouri, M. Magherbi and A.B. Brahim, “Analysis of the magnetic field effect on entropy generation at thermosolutal convection in a square cavity”, Entropy, Vol. 13, No. 5, pp. 1034-1054, (2011).

[20] A. S. Eegunjobi and O.D. Makinde, “Effects of Navier slip on entropy generation in a porous channel with suction/injection” Journal of Thermal Science and Technology, Vol. 7, No. 4, pp. 522-535,(2012).

[21]. A. S. Eegunjobi and O.D. Makinde, “Combined effect of buoyancy force and Navier slip on entropy generation in a vertical porous channel”, Entropy, Vol. 14 No. 6, pp. 1028-1044, (2012).

[22] O.D. Makinde, and A.S. Eegunjobi, “Analysis of inherent irreversibility in a variable viscosity MHD generalized Couette flow with permeable walls.”, Journal of Thermal Science and Technology, Vol. 8, No. 1, pp. 240-254, (2013).

[23] Z. Mehrez, M. Bouterra, A.E. Cafsi and A. Belghith, “ Heat transfer and entropy generation analysis of nanofluids flow in an open cavity”, Computers and Fluids, Vol. 88, pp. 363-373, (2013).

[24] S.O. Adesanya O.D. Makinde, “Entropy generation in couple stress fluid flow through porous channel with fluid slippage”, International Journal of Exergy, Vol. 15, No. 3, pp. 344-362. (2014).

[25] S.O. Adesanya and O.D. Makinde, “Effects of couple stresses on entropy generation rate in a porous channel with convective heating”, Computational and Applied Mathematics, Vol. 34, No. 1, pp. 293-307, (2015).

[26] O.D. Makinde, and A.S. Eegunjobi, “Entropy analysis of thermally radiating magnetohydrodynamic slip flow of Casson fluid in a microchannel filled with saturated porous media”, Journal of Porous Media, Vol. 19, No. 9, pp.799-810, (2016).

[27] P. Sharma, T. Sharma and N. Kumar, “Entropy analysis in MHD forced convective flow through a circular channel filled with the porous medium in the presence of thermal radiation”, International Journal of Heat Technology, Vol. 34, No. 2, pp. 311-318, (2016).

[28] K. Yamamoto and N. Iwamura, “Flow with convective acceleration through a porous medium”, Journal of Engineering Mathematics, Vol. 10, No. 1, pp. 41-54, (1976).

[29] L.C. Woods, “The thermodynamics of fluid systems”, Oxford Engineering Science Series, Clarendon press (1975).

[30] A. Bejan, “Entropy generation through heat and fluid flow”, Wiley, (1982).

[31] S. Das and R.N. Jana, “Entropy generation due to MHD flow in a porous channel with navier slip”, Ain Shams Engineering Journal, Vol. 5, No. 2, pp. 575-584, (2014).