Engineering Transactions, 68, 4, pp. 317–334, 2020

Entropy Analysis of a Variable Viscosity MHD Couette Flow Between Two Concentric Pipes with Convective Cooling

Oluwole Daniel MAKINDE
Stellenbosch University
South Africa

Adetayo Samuel EEGUNJOBI
Namibia University of Science and Technology

This paper addresses the combined effects of the magnetic field, thermal buoyancy force, viscous dissipation, Joule heating and temperature-dependent viscosity on the Couette flow of an incompressible conducting fluid between two concentric vertical pipes. It is assumed that convective cooling occurs at the surface of the outer moving pipe while the surface of the inner fixed pipe is maintained at a constant temperature. The nonlinear equations for momentum and energy are obtained and solved numerically using a shooting method coupled with the Runge-Kutta-Fehlberg integration procedure. Relevant results depicting the effects of
embedded thermophysical parameters on the velocity and temperature profiles, skin friction, the Nusselt number, entropy generation rate and the Bejan number are presented graphically and discussed. It is found that an increase in the magnetic field intensity boosts the entropy generation rate while an increase in convective cooling lessens it.
Keywords: MHD; variable viscosity; Couette flow; concentric pipes; buoyancy force; heat transfer
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Maron D.M., Cohen S., Hydrodynamics and heat/mass transfer near rotating surfaces, Advances in Heat Transfer, 21: 141–183, 1992, doi: 10.1016/S0065-2717(08)70335-6.

Watanabe T., Toya Y., Nakamura I., Development of free surface flow between concentric cylinders with vertical axes, Journal of Physics: Conference Series, 14 (1): 9–19, 2005, doi: 10.1088/1742-6596/14/1/002.

Fénot M., Bertin Y., Dorignac E., Lalizel G., A review of heat transfer between concentric rotating cylinders with or without axial flow, International Journal of Thermal Sciences, 50(7): 1138–1155, 2011, doi: 10.1016/j.ijthermalsci.2011.02.013.

Makinde O.D., Thermal analysis of a reactive generalized Couette flow of power law fluids between concentric cylindrical pipes, The European Physical Journal Plus, 129(12): Article ID: 270 (9 pages), 2014, doi: 10.1140/epjp/i2014-14270-4.

Attia H., Influence of temperature-dependent viscosity on the MHD Couette flow of dusty fluid with heat transfer, International Journal of Differential Equations, 2006: Article ID: 75290 (14 pages), 2006, doi: 10.1155/DENM/2006/75290.

Makinde O.D., Onyejekwe O.O., A numerical study of MHD generalized Couette flow and heat transfer with variable viscosity and electrical conductivity, Journal of Magnetism and Magnetic Materials, 323(22): 2757–2763, 2011, doi: 10.1016/j.jmmm.2011.05.040.

Seth G.S., Ansari Md.S., Nandkeolyar R., Effects of rotation and magnetic field on unsteady Couette flow in a porous channel, Journal of Applied Fluid Mechanics, 4(2): 95–103, 2011.

Ali A.O., Makinde O.D., Nkansah-Gyekye Y., Numerical study of unsteady MHD Couette flow and heat transfer of nanofluids in a rotating system with convective cooling, International Journal of Numerical Methods for Heat & Fluid Flow, 26(5): 1567–1579, 2016, doi: 10.1108/HFF-10-2014-0316.

Samal R.C., Biswal T., Fluctuating flow of a second order fluid between two co-axial circular pipes, International Journal of Engineering Research & Technology (IJERT), 4(2): 433–441, 2015.

Thirumaran V., Weliwita J.A., Ishak M.I.M., An analysis of axial Couette flow in annular region of abruptly stopped pipes, Physical Science International Journal, 17(4): 1–12, 2018, doi: 10.9734/PSIJ/2018/40076 .

Makinde O.D., Iskander T., Mabood F., Khan W.A., Tshehla M.S., MHD Couette-Poiseuille flow of variable viscosity nanofluids in a rotating permeable channel with Hall effects, Journal of Molecular Liquids, 221: 778–787, 2016, doi: 10.1016/j.molliq.2016.06.037.

Bejan A., Second-law analysis in heat transfer and thermal design, Advance in Heat Transfer, 15: 1–58, 1982, doi: 10.1016/S0065-2717(08)70172-2.

Yürüsoy M., Yilbas B.S., Pakdemirli M., Non-Newtonian fluid flow in annular pipes and entropy generation: Temperature-dependent viscosity, Sadhana, 31(6): 683–695, 2006, doi: 10.1007/BF02716888.

Tshehla M.S., Makinde O.D., Okecha G.E., Heat transfer and entropy generation in a pipe flow with temperature dependent viscosity and convective cooling, Scientific Research and Essays, 5(23): 3730–3741, 2010.

Eegunjobi A.S., Makinde O.D., Entropy generation analysis in transient variable viscosity Couette flow between two concentric pipes, Journal of Thermal Science and Technology, 9(2): 1–11, 2014, doi: 10.1299/jtst.2014jtst0008.

Vyas P., Ranjan A., Entropy analysis for MHD generalised Couette flow in a composite duct, Journal of Industrial Mathematics, 2015, Article ID: 895046 (10 pages), 2015, doi: 10.1155/2015/895046.

Jain S., Kumar V., Bohra S., Entropy generation in generalized Couette flow through porous medium with different thermal boundary conditions, International Journal of Energy & Technology, 7: 40–48, 2015, doi: 10.1155/2015/895046.

Eegunjobi A.S., Makinde O.D., Irreversibility analysis of MHD buoyancy-driven variable viscosity liquid film along an inclined heated plate with convective cooling, Journal of Applied and Computational Mechanics, 5(5): 840–848, 2019, doi: 10.22055/jacm.2019.28313.1476.

Mkwizu M.H., Makinde O.D., Nkansah-Gyekye Y., Numerical investigation into entropy generation in a transient generalized Couette flow of nanofluids with convective cooling, Sadhana, 40(7): 2073–2093, 2015, doi: 10.1007/s12046-015-0432-0.

Makinde O.D., Eegunjobi A.S., Tshehla M.S., Thermodynamics analysis of variable viscosity hydromagnetic Couette flow in a rotating system with Hall effects, Entropy, 17(11): 7811–7826, 2015, doi: 10.3390/e17117811.

Eegunjobi A.S., Makinde O.D., Tshehla M.S., Franks O., Irreversibility analysis of unsteady Couette flow with variable viscosity, Journal of Hydrodynamics, 27(2): 304–310, 2015, doi: 10.1016/S1001-6058(15)60485-1.

Makinde O.D., Franks O., Thermal decomposition of unsteady non-Newtonian MHD Couette flow with variable properties, International Journal of Numerical Methods for Heat & Fluid Flow, 25(2): 252–264, 2015, doi: 10.1108/HFF-12-2013-0342.

Cebeci T., Bradshaw P., Physical and computational aspects of convective heat transfer, New York, USA, Springer, 1988.

DOI: 10.24423/engtrans.1104.20200720

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