Thermodynamic analysis of a magnetohydrodyamic oldroyd 8-constant fluid in a vertical channel with heat source and slippage

Document Type : Full Length Research Article

Authors

1 Mathematics, Physical sciences, university of Ilorin kwara state nigeria

2 Mathematics, physical sciences, University of Ilorin, kwara state Nigeria

Abstract

Thermodynamic analysis of a steady state flow and heat transfer of an Oldroyd 8-constant fluid with effect of heat source, velocity slip and buoyancy force under tranverse a magnetic field is is carried out in this paper. The model for momentum and energy balance is tackled numerically using Method of Weighted Residual (MWR). Partition method is used to minimize the associated residuals. The results obtained were compared with that obtained using inbuilt numerical solver in MAPLE 18 to validate the method used and the convergence of the method is discussed. The results obtained from the momentum and energy balance were used to compute the entropy generation rate and the irreversibility ratio. The effects of controlling parameters such as non-Newtonian parameters, slip parameters, Grashoff number parameter, Brinkmann number, Hartmann, heat source parameter on the non dimensional velocity, temperature, entropy generation rate and irreversibility ratio are presented graphically and discussed. It is observed that irreversibility due to fluid friction dominates over the heat transfer when the non Newtonian parameter is kept constant for various values of , while irreversibility due to heat transfer dominate over fluid friction for various values of with fixed value .

Keywords

Main Subjects

References

References
[1]. J.G, Oldroyd, ‘‘On the formulation of rheological equation of state’’, Proc. Roy. soc. Londo. A, 200, 523-541, (1950).
[2]. R.B. Bird, R.C. Armstrong, O. Hassager, ‘‘Dynamics of polymeric liquids’’, Fluid Mech.1, PP. 354, New York: Wiley, (1987).
[3]. T. Hayat, M. Khan, and S. Asghar, ‘‘Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid’’, Acta Mechanica, 168, 213–232, (2004).
[4]. T. Hayat, M. Khan, S. Asghar, ‘‘Megnetohydrodynamic flow of an Oldroyd 6-constant fluid’’, Applied Mathematics and Computation, 155, 417-425, (2004).
[5].T. Hayat, M. Khan, M. Ayub, ‘‘Effect of slip condition on flow of an Oldroyd 6-constant fluid’’, Journal of computation and Applied Mathematics, 202, 402-413, (2007).
[6].R. Ellahi,T. Hayat, T. Javed, S. Asghar, ‘‘On the analytic solution of nonlinear flow problem involving Oldroyd 8-constant fluid’’,  Mathematical and Computer Modeling, 48, 1191-1200, (2008).
[7].S. Baris, ‘‘Flow of an Oldroyd 8-constant fluid in a convergent channel’’, Acta Mechanica, 148, 47-127, (2001).
[8]. M. Khan, Qurrat-ul-Ain, M. Sajid, ‘‘Heat transfer analysis of the steady flow of an Oldroyd 8-constant fluid due to suddenly moved plate’’, Commun Nonlinear Sci Numer Simulat, 16, 1347-1355, (2011).
[9]. M. Khan, T. Hayat, M. Ayub, ‘‘Numerical study of partial slip on the MHD flow of an Oldroyd 8-constant fluid’’, Computers and Mathematics with Applications, 53, 1088-1097, (2007).
[10].          M. Khan, T. Hayat, W. Wang, ‘‘Slip effects on shearing flows in a porous medium’’, Acta Mech Sin, 24, 51-59, (2008).
[11].          S. Das, R.N, Jana, ‘‘Entropy generation due to MHD flow in a channel with Navier slip’’, Ain Shams Eng. J., 5, 575-584, (2014).
[12].           J.A. Gbadeyan, T.A. Yusuf, M.S Dada, J.O. Akinremi, ‘‘Effects Of slippage and couple stresses on entropy generation in a porous channel filled with highly porous medium’’, Ilorin Journal of Science 2(1), 48-67, (2015).
[13].           J.A. Gbadeyan, T.A. Yusuf, ‘‘Second law analysis of radiative unsteady MHD fluid flow with partial slip and convective boundary cooling’’, Asian Journal of Mathematics and computer research, 17(4), 212-236, (2017).
[14].          A.S. Eegunjobi, O.D. Makinde, ‘‘Combined effect of buoyancy force and Navier slip on entropy generation in a vertical porous channel’’, Entropy, 14, 1028-1044, (2012).
[15].          A. Bejan. ‘‘Entropy generation minimization’’. New York, NY, USA, (1996) CRC Press.
[16].          A. Bejan. ‘‘Second Law Analysis in heat transfer’’, Energy Int J., 5(7), 21-23, (1980).
[17].          A. Bejan. ‘‘Second Law Analysis in heat transfer and thermal design’’, Adv. Heat Transf., 15, 1-58, (1982).
[18].           P. Vyas, A. Rai, ‘‘Entropy regime for radiation MHD Couette flow inside a channel with naturally permeable base’’, International Journal of energy and Technology, 5(19), 1-9, (2013).
[19].           S.O Adesanya, S.O. Kareem, J.A. Falade and S.A. Arekete, ‘‘Entropy generation analysis for a reactive couple stress fluid flow through a channel saturated with porous material’’,  Energy, 93, 1239-1245, (2015).
[20].           S.O. Adesanya, J.A. Falade, ‘‘Thermodynamics analysis of hydromagnetic third grade fluid flow through a channel filled with porous medium’’, Alexandria engineering journal, 54, 615-622, (2015).
[21].           S.O. Adesanya, ‘‘Second law analysis for third-grade fluid with variable properties’’, Journal of thermodynamics. Article ID 452168, 8 pages http://dx.doi.org/10.1155/2014/452168, (2014).
[22].           S.O. Adesanya, O.D. Makinde, ‘‘Entropy generation in couple stress fluid through porous channel with fluid slippage’’, Int J. Exergy 15(3), 344-362, (2014).
[23].           A.O. Ajibade, B.K. Jha, A. Omame, ‘‘Entropy Generation Under the effects of suction/injection’’ Applied Mathematical Modelling., 35, 4630-4046, (2011).
[24].           Y.A.S. Aregbesola, ‘‘Numerical solution of Bratu problems using the method of weighted residuals’’, Electronic Journal of Southern African Math. Sci. Association (SAMSA), 3, 1-7, (2003).
[25].           P.M. Ghesemi, M. Abbasi, M. Khaki, ‘‘New Analytic Solution of MHD fluid flow of fourth grade fluid through the channel with slip condition via collocation method’’, Int. J. Adv. Appl. Math and Mech., 2(3), 87-94, (2015).
[26].          S.T. Ledari, H. Mirgolbabaee, D.D. Ganji, ‘‘Heat transfer analysis of a fin with temperature dependent thermal conductivity and heat transfer coefficient’’, New Trends in Mathematical Sciences. 3(2), 55-69, (2015).
[27].          S.A. Odejide, Y.A.S. Aregbesola,‘‘Applications of Method of Weighted Residuals to Problems with Infinite Domain’’,  Rom. Journ Phys., 56(2), (2011) 14-24, (2011).

Files

History

  • Receive Date: 22 April 2017
  • Revise Date: 06 October 2017
  • Accept Date: 12 October 2017

Share

How to cite

Statistics