### Hall Current and Joule Heating Effects on Flow of Couple Stress Fluid with Entropy Generation

#### Abstract

In this work, an analytical study of the effects of Hall current and Joule heating on the entropy generation rate of couple stress fluid is performed. It is assumed that the applied pressure gradient induces fluid motion. At constant velocity, hot fluid is injected at the lower wall and sucked off at the upper wall. The obtained equations governing the flow are transformed to dimensionless form and the resulting nonlinear coupled boundary value problems for velocity and temperature profiles are solved by Adomian decomposition method. Analytical expressions for fluid velocity and temperature are used to obtain the entropy generation and the irreversibility ratio. The effects of Hall current, Joule heating, suction/injection and magnetic field parameters are presented and discussed through graphs. It is found that Hall current enhances both primary and secondary velocities and entropy generation. It is also interesting that Joule heating raises fluid temperature and encourages entropy production. On the other hand Hartman number inhibited fluid motion while increase in suction/injection parameter resulted into a shift in flow symmetry.

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G. K. Batchelor, “On the spontaneous magnetic field in a conducting liquid in turbulent motion”, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 21, No. 1066, pp. 406-416, 1950

J. C. R. Hunt, J. A. Shercliff, “Magnetohydrodynamics at high Hartmann number”, Annual Review of Fluid Mechanics, Vol. 3, pp. 37-62, 1971

S. Gupta, “Magnetohydrodynamic Ekmann layer”, Acta Mechanica, Vol. 13, pp. 155-160, 1972

D. R. V. Prasada Rao, D. V. Krishna, L. Debnath, “Combined effect of free and forced convection on MHD flow in a rotating porous channel”, International Journal of Mathematics and Mathematical Sciences, Vol. 5, No. 1, pp. 165-182, 1982

J. A. Gbadeyan, A. S. Idowu, “Radiation effect of magnetohydrodynamic flow of gas between concentric spheres”, Journal of the Nigerian Association of Mathematical Physics, Vol. 10, pp. 305-314, 2006

O. Areo, P. O. Olaleye, J. A. Gbadeyan, “The radiative effect on velocity, magnetic and temperature fields of a magneto hydrodynamic oscillatory flow past a limiting surface with variable suction”, European Journal of Applied Sciences, Vol. 3, No. 3, pp. 102-112, 2011

S. O. Adesanya, E. O. Oluwadare, J. A. Falade, O. D. Makinde, “Hydromagnetic natural convection flow between vertical parallel plates with time-periodic boundary conditions”, Journal of Magnetism and Magnetic Materials, Vol. 396, pp. 295–303, 2015

I. Olajuwon, “Convection heat and mass transferr in a hydromagnetic flow of second grade fluid in the presence of thermal radiation and thermal diffusion”, International Communications in Heat and Mass Transfer, Vol. 38, No. 3, pp. 377–382, 2011

Raptis, P. C. Ram, “Effects of hall current and rotation”,”Astrophysics and Space Science, Vol. 106, No. 2, pp. 257-264, 1984

M. Abd El-Aziz1, T. Nabil, “Homotopy analysis solution of hydromagnetic mixed convection flow past an exponentially stretching sheet with hall current”, Mathematical Problems in Engineering, Vol. 2012, Article ID 454023, 2012

S. Das, S. L. Maji, R. N. Jana, “Hall Effects on unsteady hydromagnetic flow induced by a porous plate”, International Journal of Computer Applications (0975 – 8887), Vol. 57, No. 18, pp. 37-44, 2012

K. Jha, C. A. Apere, “Combined effect of hall and ion-slip currents on unsteady MHD Couette flows in a rotating system”, Journal of the Physical Society of Japan, Vol. 79, No. 10, 2010

Pal, B. Talukdar, I. S. Shivakumara, K. Vajravelu, “Effects of Hall current and chemical reaction on oscillatory mixed convection-radiation of a micropolar fluid in a rotating system”, Chemical Engineering Communications, Vol. 199, pp. 943–965, 2012

S. Asghar, M. R. Mohyuddin, T. Hayat, “Effects of Hall current and heat transfer on flow due to a pull of ecentric rotating disks”, International Journal of Heat and Mass Transfer, Vol. 48, No. 3-4, pp. 599-607, 2005

M. Aboeldahab, E. M. E. Elbarbary, “Hall current effect on magnetohydrodynamic free convection flow past a semi-infinite vertical plate with mass transfer”, International Journal of Engineering Science, Vol. 39, No. 14, pp, 1641-1652, 2001

Arikoglu, I. Ozkol, G. Komurgoz, “Effect of slip on entropy generation in a single rotating disk in MHD flow”, Applied Energy, Vol. 85, No. 12, pp. 1225-1236, 2008

M. M. Rashidi, N. Freidooni Mehr, “Effects of velocity slip and temperature jump on the entropy generation in MHD flow over a porous rotating disk”, Journal of Mechanical Engineering, Vol. 1, No. 3, pp. 3-14. 2012

M. M. Rashidi, M. M. Bhatti, M. A. Abbas, M. E. Ali, “Entropy generation on MHD blood flow of nanofluid due to peristaltic waves”, Entropy, Vol. 18, No. 4, 2016

S. O. Adesanya, J. A. Falade, “Thermodynamics analysis of hydromagnetic third grade fluid flow through a channel filled with porous medium”, Alexandria Engineering Journal, Vol. 54, No. 3, pp. 615–622, 2015

A. Opanuga, J. A. Gbadeyan, S. A. Iyase, H. I. Okagbue, “Effect of thermal radiation on entropy generation of hydromagnetic flow through porous channel”, Pacific Journal of Science and Technology, Vol. 17, No. 2, pp. 59-68, 2016

S. O. Adesanya, J. A. Falade, S. Jangili, O. A Beg, “Irreversibility analysis for reactive third-grade fluid flow and heat transfer with convective wall cooling”, Alexandria Engineering Journal, Vol. 56, No. 1, pp. 153–160, 2017

S. O. Adesanya, O. D. Makinde, “Irreversibility analysis in a couple stress film flow along an inclined heated plate with adiabatic free surface”, Physica A, Vol. 432, pp. 222–229, 2015

A. Opanuga, H. I. Okagbue, O. O. Agboola, “Irreversibility analysis of a radiative MHD Poiseuille flow through porous medium with slip condition”, Proceedings of the World Congress on Engineering, London, UK, Vol. 1, pp. 167-171, July 5-7, 2017

M. Pakdemirli, B. S. Yilbas, “Entropy generation in a pipe due to non-Newtonian fluid flow: Constant viscosity case”, Sadhana, Vol. 31, No. 1, pp. 21–29, 2006

A. Opanuga, H. I. Okagbue, O. O. Agboola, O. F. Imaga, “Entropy generation analysis of buoyancy effect on hydromagnetic poiseuille flow with internal heat generation”, Defect and Diffusion, Vol. 378, pp. 102-112, 2017

L. B. Erbay, Z. Altac, B. Sulus, “An analysis of the entropy generation in a square enclosure”, Entropy, Vol. 5, No. 5, pp. 496-505, 2003

A. Opanuga, E. A. Owoloko, O. O. Agboola, H. I. Okagbue, “Application of homotopy perturbation and modified Adomian decomposition methods for higher order boundary value problems”, Proceedings of the World Congress on Engineering, London, UK, Vol. 1, July 5-7, 2017

M. C. Agarana, M. E. Emetere, “Solving non-linear damped driven simple pendulum with small amplitude using a semi analytical method”, ARPN Journal of Engineering and Applied Sciences, Vol. 11, No. 7, pp. 4478-4484, 2016

M. C. Agarana, A. N. Ede, “Application of differential transform method to vibration analysis of damped railway bridge on Pasternak foundation under moving train”, Proceedings of The World Congress on Engineering and Computer Science 2016, London, UK, June 29–July 1, 2016, 2016

O. O. Agboola, J. A. Gbadeyan, A. A. Opanuga, M. C. Agarana, S. A. Bishop, J. G. Oghonyon, “Variational Iteration Method for Natural Frequencies of a Cantilever Beam with Special Attention to the Higher Modes”, Proceedings of The World Congress on Engineering and Computer Science 2017, London, UK, July 5-7, 2017

A. A. Opanuga, E. A. Owoloko, H. I. Okagbue, O. O. Agboola, “Finite difference method and Laplace transform for boundary value problems”, Proceedings of The World Congress on Engineering and Computer Science 2017, London, UK, July 5-7, 2017

V. Daftardar-Gejj H. Jafari, “Solving a multi-order fractional differential equation using Adomian Decomposition”, Applied Mathematics and Computation, Vol. 189, No. 1, pp. 541-548, 2007

A. M. Wazwaz, “Analytical solution for the time-dependent Emden–Fowler type of equations by Adomian decomposition method”, Applied Mathematics and Computation, Vol. 166, No. 3, pp. 638-651, 2005

K.Haldar, “Application of Adomian's approximations to the Navier-Stokes equations in cylindrical coordinates”, Applied Mathematics Letters, Vol. 9, No. 4, pp. 109-113, 1996

B. Zhang, Q.-B. Wu, X.-G. Luo, “Experimentation with two-step Adomian decomposition method to solve evolution models”, Applied Mathematics and Computation, Vol. 175, No. 2, pp. 1495-1502, 2006

A. M. Wazwaz, “Padé approximants and Adomian decomposition method for solving the Flierl–Petviashivili equation and its variants”, Applied Mathematics and Computation, Vol. 182, No. 2, pp. 1812-1818, 2006

H. Haddadpour, “An exact solution for variable coefficients fourth-order wave equation using the Adomian method”, Mathematical and Computer Modelling, Vol. 44, No. 11–12, pp. 1144-1152, 2006

S.Nadeem, N. S. Akbar, “Effects of heat transfer on the peristaltic transport of MHD Newtonian fluid with variable viscosity: Application of Adomian decomposition method”, Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 11, pp. 3844-3855, 2009

M. Tataria, M. Dehghana, M. Razzaghi, “Application of the Adomian decomposition method for the Fokker–Planck equation”, Mathematical and Computer Modelling, Vol. 45, No. 5–6, pp. 639-650, 2007

S. O. Adesanya, E. S. Babadipe, S.A. Arekete, “A new result on Adomian decomposition method for solving Bratu’s problem”, Mathematical Theory and modeling, Vol. 3, No. 2, pp. 116-120, 2013

T. G. Cowling, Magnetohydrodynamics, Interscience, Inc, New York, 1957

R. C. Meyer, “On Reducing Aerodynamic Heat-Transfer Rates by MagnetohydrodynamicTechniques”, Journal of the Aerospace Sciences, Vol. 25, No. 9, pp. 561-566, 1958

S. Das, R. N. Jana, “Effects of hall current on entropy generation in a porous channel with suction/injection”, International Journal of Energy & Technology, Vol. 5, No. 25, pp. 1–11, 2013

S. O. Adesanya, 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

A. Bejan, Entropy Generation through Heat and Fluid Flow, Wiley, New York, 1982

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