Document Type: Research Paper


Department of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran


The entropy generation analysis of non-Newtonian fluid in rotational flow between two concentric cylinders is examined when the outer cylinder is fixed and the inner cylinder is revolved with a constant angular speed. The viscosity of non-Newtonian fluid is considered at the same time interdependent on temperature and shear rate. The Nahme law and Carreau equation are used to modeling dependence of viscosity on temperature and shear rate, respectively. The viscous dissipation term is adding elaboration to the formerly highly associate set of governing motion and energy equations. The perturbation method has been applied for the highly nonlinear governing equations of base flow and found an approximate solution for narrowed gap limit. The effect of characteristic parameter such as Brinkman number and Deborah number on the entropy generation analysis is investigated. The overall entropy generation number decays in the radial direction from rotating inner cylinder to stationary outer cylinder. The results show that overall rate of entropy generation enhances within flow domain as increasing in Brinkman number. It, however, declines with enhancing Deborah number. The reason for this is very clear, the pseudo plastic fluid between concentric cylinders is heated as Brinkman number increases due to frictional dissipation and it is cooled as Deborah number increases which is due to the elasticity behavior of the fluid. Therefore, to minimize entropy need to be controlled Brinkman number and Deborah number.

Graphical Abstract


Main Subjects

[1] Andereck, C.D.; Liu, S.S.; Swinney, H.L.. "Flow regimes in a circular Couette system with independently rotating cylinders". Journal of Fluid Mechanics, Vol. 164, pp. 155-183, (1986).

[2] N. Ashrafi, A. Hazbavi, “Flow pattern and stability of pseudoplastic axial Taylor–Couette flow”, International Journal of Non-Linear Mechanics, Vol. 47, No. 8, pp. 905-917, (2012).

[3] Tasnim, S. H., Mahmud S. and Mamun, M. A. H., Entropy generation in a porous channel with hydromagnetic effect, Exergy, an Int. J., Vol. 2, No. 4, pp. 300-308, (2002).

[4] Mahmud, S. and Fraser R. A., The second law analysis in fundamental convective heat transfer problems, Int. J. of Therm. Sci., Vol. 42, No. 2, pp. 177–186, (2003).

[5] Carrington, C. G. and Sun, Z. F., Second law analysis of combined heat and mass transfer in internal flow and external flows. Int. J. Heat and Fluid Flow, Vol. 13, No. 1, pp. 65–70, (1992).

[6] Arpaci, V.S. and Selamet A., Entropy production in boundary layers, J. Thermo phys. Heat Transfer, Vol. 4, No. 3, pp. 404–407, (1990).

[7] Abu-Hijleh, B. A. K., entropy generation in laminar convection from an isothermal cylinder in cross flow, energy, Vol. 23, No. 10, pp. 851-857, (1998).

[8] Khalkhali, H. Faghri, A. and Zuo, Z. J., Entropy generation in a heat pipe system, Applied Thermal Eng., Vol. 19, No. 10, pp. 1027-1043, (1999).

[9] N. Ashrafi, A. Hazbavi, “Heat transfer in flow of nonlinear fluids with viscous dissipation”, Archive of Applied Mechanics, Vol. 83, No. 12, pp. 1739-1754, (2013).

[10] A. Hazbavi, “Second Law Analysis of Magnetorheological Rotational Flow with Viscous Dissipation”, Journal of Thermal Science and Engineering Applications, Vol. 8, No. 2, 021020, (2016).

[11] Abbas Kosarineia and Sajad Sharhani, Second Law Analysis of Magneto-Micropolar Fluid Flow Between Parallel Porous Plates. Journal of Thermal Science and Engineering Applications, Vol. 10, No. 4, 041017, (2018).

[12] J.R.A. Pearson, Mechanics of Polymer Processing, Elsevier, London,1985.

[13] R.B. Bird, R.C. Armstrong, Dynamics of Polymeric Liquids, Wiley, New York (1987).

[14] J. V. Ramana Reddy, V. Sugunamma, N. Sandeep, Dual solutions for heat and mass transfer in chemically reacting radiative non-Newtonian fluid with aligned magnetic field. Journal of Naval Architecture and Marine Engineering, Vol. 14, No. 1, pp. 25-38.

[15] Jayachandra Babu M., Sandeep N., Ali M.E., Nuhait A.O., Magneto-hydrodynamic dissipative flow across the slendering stretching sheet with temperature dependent variable viscosity. Results in physics, Vol. 7, pp. 1801-1807.

[16] Ramana Reddy J.V., Sugunamma V., Sandeep N., Enhanced heat transfer in the flow of dissipative non-Newtonian Casson fluid flow over a convectively heated upper surface of a paraboloid of revolution. Journal of Molecular Liquids, Vol. 229, pp. 380-388.

[17] Ramandevi B., Reddy J.V.R., Sugunamma V., Sandeep N., Combined influence of viscous dissipation and non-uniform heat source/sink on MHD non-Newtonian fluid flow with Cattaneo-Christov heat flux. Alexandria Engineering Journal.

[18] Kumar K., Reddy R., Sugunamma V., Sandeep N., Impact of Frictional Heating on MHD Radiative Ferrofluid Past a Convective Shrinking Surface. Defect and Diffusion Forum, Vol. 378, pp. 157-174, (2017).

[19] Kumar K., Reddy R., Sugunamma V., Sandeep N., Magnetohydrodynamic Cattaneo-Christov flow past a cone and a wedge with variable heat source/sink. Alexandria Engineering Journal, Vol. 57, No. 1, pp. 435–443.

[20] Kumar K., Reddy R., Sugunamma V., Sandeep N., Impact of cross diffusion on MHD viscoelastic fluid flow past a melting surface with exponential heat source, Multidiscipline Modeling in Materials and Structures, Vol. 14, No. 5, pp. 1573-6105, (2018).

[21] A. Bejan, A study of entropy generation in fundamental convective heat transfer, J. Heat Transfer, Vol. 101, No. 4, 718–725, (2010).

[22] R. Keunings, M. J. Crochet, Numerical simulation of the flow of a viscoelastic fluid through an abrupt contraction, J. Non-Newtonian Fluid Mech, Vol. 14, pp. 279–299, (1984).

[23]F. T. Pinho, P. J. Oliveira, Axial annular flow of non-linear viscoelastic fluid an analytical solution, J. Non-Newtonian Fluid Mech., Vol. 93, pp. 325–33, (2000).