# THERMODYNAMIC ANALYSIS OF VISCOELASTIC FLUID IN A POROUS MEDUIM WITH PRESCRIBED WALL HEAT FLUX OVER STRETCHING SHEET SUBJECTED TO A TRANSITIVE MAGNETIC FIELD

## Main Article Content

## Abstract

An analysis is performed for entropy generation in a steady laminar boundary layer flow of an electrically conducting second grade fluid in a porous medium prescribed wall heat flux (PHF) subject to a transverse uniform magnetic field past a semi-infinite stretching sheet, The effects of viscous dissipation, internal heat generation of absorption due to deformation are considered in the energy equation. Kummer's functions are used to obtain temperature field. The velocity, temperature are used to compute the entropy generation number with a change in various dimensionless parameters.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2419>. Date accessed: 20 feb. 2018. doi: https://doi.org/10.2298/TSCI160919028C.

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Accepted 2017-03-15

Published 2017-03-15

## References

[2] Bhattacharya, S.; Pal, A. & Gupta, A. S. Heat transfer in the flow of a viscoelastic fluid over a stretching surface, Heat mass Transfer, 34 (1998) , pp. 41-45.

[3] Datti, P. S.; Prasad, K. V.; Abel, M. S. & Joshi, A. MHD viscoelastic fluid flow over a non- isothermal stretching sheet, Int. J. Eng. Sci, 42 ( 2004), pp. 935-946.

[4] Idrees, M.K. & Abel, M. S. Viscoelastic flow past a stretching sheet in porous media and heat transfer with internal heat source, Indian J. Theory. Phys, 44 (1996), pp. 233-244.

[5] Lawrence, P.S. &Rao, B. N. Heat transfer in the flow of viscoelastic fluid over stretching sheet, Acta Mech , 93 (1992), pp. 53-61.

[6] Prasad, K.V.; Abel, M. S. & Khan, S. K. Momentum and heat transfer in viscoelastic fluid flow in a porous medium over a non-isothermal stretching sheet, Int. J. Numer. Method Heat flow, 10 (2000), pp. 786-801.

[7] Prasad, K.V.; Abel, M. S.; Khan, S.K. &Datti, P. S. Non-Darcy forced convective heat transfer in a viscoelastic fluid flow over a non-Isothermal stretching sheet, J. Porous Media , 5 (2002), pp. 41-47.

[8] Khan, S. K. &Sanjayanand, E. Viscoelastic boundary layer flow and heat transfer over an exponential stretching sheet, Int. J. Heat Mass Transfer, 48 (2005), pp. 1534-1542.

[9] Cortell, R. A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet, Int. J. Non-Linear Mech, 41 (2006), pp. 78-85.

[10] Abel, M. S.; Siddheshwar, P. G. &Nandeppanavar, M. M. Heat transfer in a viscoelastic boundary layer low over a stretching sheet with viscous dissipation and non-uniform heat source, Int. J. Heat Mass Transfer, 50 ( 2007), pp. 960-966.

[11] I-Chung Liu, Flow and heat transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet subject to a transverse magnetic field , Int. J. Non- Linear Mech, 40 ( 2005), pp.465 – 474.

[12] Khan, S. K.Heat transfer in a viscoelastic fluid over a stretching surface with source/sink, suction/blowing and radiation, Int. J. Heat Mass Transfer,49 ( 2006), pp. 628- 639.

[13] Abel, M. S.; Sanjayanand, E. & Nandeppanavar; M. M. Viscoelastic MHD flow and heat heat transfer over a stretching sheet with viscous and ohmic dissipation, Comm. Nonlinear. Sci. and Num. Simulation, 13 (2008), pp. 1808-1821.

[14] Hsiao, K. L. Conjugate heat transfer of magnetic mixed convection with viscous dissipation effects for second-grade viscoelastic fluid past a stretching sheet, Appl.Therm. Eng, 27 (2007), pp. 1895-1903.

[15] Abbas, Z.; Wang, Y.; Hayat, T. & Oberlack M. Hydromagnetic flow of a viscoelastic fluid due to the oscillatory stretching surface, Int. J. Non-Linear Mech, 43 (2008), pp. 783-793.

[16] Singh, A. K. Heat source and radiation effects on magneto-convection flow of a viscoelastic fluid past a stretching sheet: Analysis with Kummer’s functions, Int. Comm. Heat Mass Transfer, 35 (2008), pp. 637-642.

[17] Prasad, K.V.; Pal, D.; Umesh, V. &PrasannaRao, N. S. The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet, Comm. Nonlinear Sci. and Num. Simulation, 15 (2010) , pp. 331-344.

[18] Abel, M. S. &Mahesha, N.Heat transfer in MHD viscoelastic fluid over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation, Appl. Math. Modelling, 32 (2008), pp. 1965-1983.

[19] Hayat, T.; Sajid, M. & Pop, I. Three-dimensional flow over a stretching sheet in a viscoelastic fluid, Nonlinear. Ana. Real World Appl, 9 (2008), pp. 1811-1822.

[20] Misra, J. C., & Shit, G. C. Biomagnetic viscoelastic fluid flow over a stretching sheet, Appl. Math. And Compu, 210 (2009), pp. 350-361.

[21] Abel, M. S. &Nandeppanavar, M. M. Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with non-uniform heat source/sink, Comm. NonLinear Sci. and Num. Simu,14 (2009), pp. 2120-2131.

[22] Nandeppanavar, M. M.; Abel, M. S. &Vajravelu, K. Flow and heat transfer characteristics of a viscoelastic fluid in a porous medium over an impermeable stretching sheet with viscous dissipation, Int. J. Heat Mass Transfer, 53 (2010), pp. 4707-4713.

[23] Chen, C. H. On the analytic solution of MHD flow and heat transfer for two types of viscoelastic fluid over a stretching sheet with energy dissipation internal heat source and thermal radiation, Int. J. Heat mass Transfer, 53 (2010), pp. 4264-4273.

[24] Nandeppanavar, M. M.; Vajravelu, K. & Abel, M. S. Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink, Comm. Nonlinear. Sci. and Num. Simulation, 16 (2011), pp.3578-3590.

[25] Cortell R. Flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/ absorption and suction/blowing. Fluid Dyn Res, 37 ( 2005), pp.231–45

[26] Rashidi MM, Rostami B, Navid F, Abbasbandy S. Free convective heat and mass transfer for MHD fluid flow over a permeable vertical stretching sheet in the presence of the radiation and buoyancy effects. Ain Shams Eng J, 5 (2014), pp.901–912.

[27] Rashidi MM, Vishnu Ganesh N, Abdul Hakeem AK, Ganga B. Buoyancy effect on MHD flow of nanofluid over a stretching sheet in the presence of thermal radiation. J Mol Liq, 198 (2014),pp.234–238.

[28] Bejan, A. A study of entropy generation in fundamental convective heat transfer, J.Heat Transfer, 101 (1979), pp. 718-725.

[29] Bejan, A. Second-law analysis in heat transfer and thermal design, Adv. Heat Transfer 15 (1982), pp.1-58.

[30] Bejan, A. Entropy generation minimization. CRC Press, Boca Raton, New York, USA,(1996).

[31] Sahin, A. Z. Second law analysis of laminar viscous flow through a duct subjected to constant wall temperature, J. Heat Transfer,120(1998),pp. 76-83.

[32] Sahin, A. Z. Effect of variable viscosity on the entropy generation and pumping power in a laminar fluid flow through a duct subjected to constant heat flux, Heat Mass Transfer, 35(1999), pp. 499-506.

[33] Sahin, A. Z. A second law comparison for optimum shape of duct subjected to constant wall temperature and laminar flow, Heat Mass Transfer,33 (1998), pp.425-430.

[34] Narusawa, U. The second-law analysis of mixed convection in rectangular ducts, Heat Mass Transfer, 37 (1998), pp. 197-203.

[35] Mahmud, S. & Fraser, R. A.Thermodynamic analysis of flow and heat transfer inside channel with two parallel plates, Exergy,2 (2002), pp. 140-146.

[36] Mahmud, S. & Fraser, R. A.. Inherent irreversibility of channel and pipe flows for non- Newtonian fluids, Int. Comm. Heat Mass Transfer,29 (2002), pp.577-587.

[37] Mahmud, S. & Fraser, R. A. The second law analysis in fundamental convective heat transfer problems, Int. J. Therm. Sci, 42 (2003), 42, pp. 177-186.

[38] Saouli, S. &Aïboud-Saouli, S. Second law analysis of laminar falling liquid film along an inclined heated plate, Int. Comm. Heat Mass Transfer, 31 (2004), pp. 879-886.

[39] Aïboud-Saouli, S.; Saouli, S.; Settou, N. & Meza, N. Thermodynamic analysis of gravity- driven liquid film along an inclined heated plate with hydromagnetic and viscous dissipation effects, Entropy, 8(2006), pp. 188-199.

[40] Aïboud-Saouli, S.; Settou, N.; Saouli, S. &Meza, N. Second-law analysis of laminar fluid flow in a heated channel with hydromagnetic and viscous dissipation effects, Applied Energy,84(2007), pp. 279-289.

[41] Aïboud, S., &Saouli, S. Second law analysis of viscoelastic fluid over a stretching sheet subject to a transverse magnetic field with heat and mass transfer, Entopy,12(2010), pp. 1867- 1884.

[42] Aïboud, S., & Saouli, S. Entropy analysis for viscoelastic magnetohydrodynamics flow over a stretching surface, Int. J. Non-Linear Mech,45(2010), pp. 482-489,

[43] Adesanya SO, Makinde OD. Irreversibility analysis in a couple stress film flow along an inclined heated plate with adiabatic free surface. Physica A ,5(2015), pp. 115–124

[44] Akbar NS. Entropy generation and energy conversion rate for the peristaltic flow in a tube with magnetic field. Energy, 82(2015), pp. 23–30.

[45] Makinde OD. Entropy analysis for MHD boundary layer flow and heat transfer over a flat plate with a convective surface boundary condition. Int J Exergy, 10(2012),pp. 142–154.

[46] Abolbashari MH, Freidoonimehr N, Nazari F, Rashidi MM. Entropy analysis for an unsteady MHD flow past a stretching permeable surface in nano-fluid. Powder Technol, 267(2014),pp. 256–267.

[47] Tripathy RS, Dash GC, Mishra SR, Baag S. Chemical reaction effect on MHD free convective surface over a moving vertical plane through porous medium. Alexandria Eng J, 54(2015), pp. 673–679.

[48] Woods, L. C. Thermodynamics of fluid systems, Oxford University Press, Oxford, UK. (1975).

[49] Elbashbeshy EMA Heat transfer over a stretching surface with variable surface heat flux. J Phys D Appl Phys, 31(1998),pp.1951–1954.

[50] Liu IC .A note on heat and mass transfer for a hydromagnetic flow over a stretching sheet. Int Comm Heat Mass Transf. 32(2005),pp1075–1084

[51] T. C. Chiam, Magnetohydrodynamic heat transfer over a non-isothermal stretching sheet, Acta Mechanica,122(1997),pp. 169-179