Journal of Applied and Computational Mechanics

Free Convection Flow of an Electrically-Conducting Micropolar Fluid between Parallel Porous Vertical Plates Using Differential Transform

Document Type : Research Paper

Authors

1 Department of Mathematics, Gulbarga University, Gulbarga Karnataka-585 106, India

2 Mechanical Engineering Department, Prince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Saudi Arabia

3 RAK Research and Innovation Center, American University of Ras Al Khaimah, United Arab Emirates

Abstract

In the present study, the effect of temperature-dependent heat sources on the fully developed free convection flow of an electrically conducting micropolar fluid between two parallel porous vertical plates in the presence of a strong cross magnetic field is analyzed. The micropolar fluid fills the space inside the porous plates when the rate of suction at one boundary is equal to the rate of injection at the other boundary. The coupled nonlinear governing differential equations are solved using the differential transform method (DTM). Moreover, the Runge-Kutta shooting method (RKSM), which is a numerical method, is used for the validity of DTM method and an excellent agreement is observed between the solutions of DTM and RKSM. Trusting this validity, the effects of Hartmann number, Reynolds number, micropolar parameter, and applied electric field load parameter are discussed on the velocity, microrotation velocity, and temperature. The skin friction, the couple stress, and Nusselt numbers at the plates are shown in graphs. It is observed that the Hartmann number and the micropolar parameter decreases the skin friction and the couple stress at both plates for suction and injection.

Keywords

Main Subjects

[1] A.C. Eringen, Theory of micropolar fluids, Journal of Mathematics and Mechanics, 16, 1966, 1–18.
[2] A.C. Eringen, Theory of thermomicrofluids, Journal of Mathematical Analysis and Applications, 38, 1972, 480–496.
[3] G. Lukaszewicz, Micropolar fluids: theory and applications, Birkhauser, Basel, 1999.
[4] A.C. Eringen, Microcontinuum field theories, II. Fluent media, Springer, New York, 2001.
[5] T. Ariman, M.A. Turk, N.D. Sylvester, Micro continuum fluid mechanics – A review, International Journal of Engineering Science, 11, 1973, 905–930.
[6] R.S. Agarwal, C. Dhanapal, Numerical solution of free convection micropolar fluid flow between two parallel porous vertical plates, International Journal of Engineering Science, 26, 1988, 1247–1255.
[7] D. Srinivasacharya, J.V. Ramana Murthy, D. Venugopalam, Unsteady stokes flow of micropolar fluid between two parallel porous plates, International Journal of Engineering Science, 39, 2001, 1557–1563.
[8] M.F. El-Amin, Magnetohydrodynamic free convection and mass transfer flow in micropolar fluid with constant suction, Journal of Magnetism and Magnetic Materials, 234, 2001, 567–574.
[9] M.F. El-Amin, Combined effect of internal heat generation and magnetic field on free convection and mass transfer flow in a micropolar fluid with constant suction, Journal of Magnetism and Magnetic Materials, 270, 2004, 130–135.
[10] M. Emad, A.F. Abo-Eldahab, Ghonaim, Convective heat transfer in an electrically conducting micropolar fluid at a stretching surface with uniform free stream, Applied Mathematics and Computation, 137, 2003, 323–336.
[11] A.A. Joneidi, D.D. Ganji, M. Babaelahi, Micropolar flow in a porous channel with high mass transfer, International Communications in Heat and Mass Transfer, 36, 2009, 1082-1088.
[12] J. Prathap Kumar, J.C. Umavathi, Ali J. Chamkha, Ioan Pop, Fully-developed free-convective flow of micropolar and viscous fluids in a vertical channel, Applied Mathematical Modelling, 34, 2010, 1175–1186.
[13] R. Mahmood, M. Sajid, Flow of a micropolar fluid through two parallel porous boundaries, Numerical Methods for Partial Differential Equations, 27, 2011, 637–643.
[14] M.A. El-Haikem, A.A. Mohammadein, S.M.M. El-Kabeir, Joule heating effects on magnetohydrodynamic free convection flow of a micropolar fluid, International Communications in Heat and Mass Transfer, 2, 1999, 219.
[15] M.F. El-Amin, Magnetohydrodynamic free convection and mass transfer flow in micropolar fluid with constant suction, Journal of Magnetism and Magnetic Materials, 234, 2001, 567.
[16] R. Bhargava, L. Kumar, H.S. Takhar, Numerical solution of free convection MHD micropolar fluid flow between two parallel porous vertical plates, International Journal of Engineering Science, 41, 2003, 123–136.
[17] J. Zueco, P. Eguía, L.M. López-Ochoa, J. Collazo, D. Patiño, Unsteady MHD free convection of a micropolar fluid between two parallel porous vertical walls with convection from the ambient, International Communications in Heat and Mass Transfer, 36, 2009, 203–209
[18] J.C. Umavathi, I.C. Liu, J. Prathap Kumar, Magnetohydrodynamic Poseuille-Coutte flow and heat transfer in an inclined channel, Journal of Mechanics, 26, 2010, 525-532.
[19] A.T. Akinshilo, J.O. Olofinkua, O. Olaye, Flow and heat transfer analysis of the Sodium Alginate conveying Copper Nanoparticles between two parallel plates, Journal of Applied and Computational Mechanics, 3, 2017, 258-266.
[20] A.T. Akinshilo, G.M. Sobamowo, Perturbation solutions for the study of MHD blood as a third grade nanofluid transporting gold nanoparticles through a porous channel, Journal of Applied and Computational Mechanics, 3, 2017, 103-113.
[21] E. Ghahremani, R. Ghaffari,  H. Ghadjari, J. Mokhtari, Effect of variable thermal expansion coefficient and nanofluid properties on steady natural convection in an enclosure, Journal of Applied and Computational Mechanics, 3, 2017, 240-250
[22] A. Noghrehabadi, R. Pourrajab, M. Ghalambaz, Effect of partial slip boundary condition on the flow and heat transfer of nanofluids past stretching sheet prescribed constant wall temperature, International Journal of Thermal Sciences, 54, 2012, 253-261.
[23] A. Noghrehabadi, M.R. Saffarian, R. Pourrajab, M. Ghalambaz, Entropy analysis for nanofluid flow over a stretching sheet in the presence of heat generation/absorption and partial slip, Journal of Mechanical Science and Technology, 27, 2013, 927-937.
[24] H. Zargartalebi, A. Noghrehabadi, M. Ghalambaz, I. Pop, Natural convection boundary layer flow over a horizontal plate embedded in a porous medium saturated with a nanofluid: case of variable thermophysical properties, Transport in Porous Media, 107, 2015, 153-170.
[25] A. Noghrehabadi, M. Ghalambaz, A. Ghanbarzadeh, A new approach to the electrostatic pull-in instability of nanocantilever actuators using the ADM- Padé technique, Computers and Mathematics with Applications, 64, 2012, 2806-2815.
[26] J.K. Zhou, Differential transformation and its applications for electrical circuits, Huazhong University Press, 1986.
[27] C.K. Chen, S.H. Ho, Solving partial differential equations by two dimensional differential transform method, Applied Mathematics and Computation, 106, 1999, 171–179.
[28] F. Ayaz, Solutions of the systems of differential equations by differential transform method, Applied Mathematics and Computation, 147, 2004, 547–567.
[29] A.S.V. Ravi Kanth, K. Aruna, Solution of singular two-point boundary value problems using differential transformation method, Physics Letters A, 372, 2008, 4671–4673.
[30] I.H. Abdel-Halim Hassan, Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems, Chaos, Solitons and Fractals, 36, 2008, 53–65.
[31] M.J. Jang, C.L. Chen, Y.C. Liu, Two-dimensional differential transform for partial differential equations, Applied Mathematics and Computation, 121, 2001, 261–270.
[32] D.D. Ganji, H. Bararnia, S. Soleimani, E. Ghasemi, Analytical solution of the magneto-hydrodynamic flow over a nonlinear stretching sheet, Modern Physics Letters B, 23, 2009, 2541–2556.
[33] A. Kurnaz, G. Oturnaz, M.E. Kiris, n-Dimensional differential transformation method for solving linear and nonlinear PDE’s, International Journal of Computer Mathematics, 82, 2005, 369–380.
[34] M.M. Rashidi, E. Erfani, New analytical method for solving Burgers’ and nonlinear heat transfer equations and comparison with HAM, Computer Physics Communications, 180, 2009, 1539–1544.
[35] J.C. Umavathi, A.S.V. Ravi Kanth, and M. Shekar, Comparison study of differential transform method with finite difference method for magneto convection in a vertical channel, Heat Transfer-Asian Research, 42(3), 2013, 243–258.
Journal of Applied and Computational Mechanics
Volume 4, Issue 4
October 2018
Pages 286-298