This paper is aimed at studying an unsteady hydromagnetic flow of a viscous incompressible electrically conducting reactive fluid in a permeable channel with asymmetrical convective boundary conditions in a rotating reference frame under the Arrhenius kinetics with neglect of the reactant consumption. Asymmetrical convective heat exchange with the surrounding medium at the channel surfaces follows the Newton law of cooling. A chemical reaction in the flow system is exothermic and assumed to follow the Arrhenius rate law. The heat transfer characteristics of the flow are considered with viscous and Joule dissipations taken into account. The expressions for the velocity components obtained in closed form are used to calculate the wall shear stresses. The energy equation is tackled numerically with using MATLAB. The effects of the pertinent parameters on the flow dynamics are analyzed graphically. The results reveal that the combined effects of magnetic field, rotation, suction/injection, and convective heating substantially affect the flow characteristics in the channel.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. S. Berman, Laminar flow in channels with porous walls, J. Appl. Phys., 24, 1232–1235 (1953).
J. R. Sellars, Laminar flow in channels with porous walls at high suction Reynolds numbers, J. Appl. Phys., 26, 489–490 (1955).
G. Radhakrishnamacharya and M. K. Maiti, Heat transfer to pulsatile flow in a porous channel, Int. J. Heat Mass Transf., 20, 171–173 (1977).
R. Moreau, Magnetohydrodynamics, Kluwer Academic Publishers, Dordrecht (1990).
J. Hartmann, Hg-Dynamics I: Theory of the laminar flow of an electrically conductive liquid in a homogeneous magnetic field, Det. Kgl. Danske Vid. Sels. Math.-Fys. Medd., 15, No. 6, 1–27 (1937).
K. R Cramer and S. I. Pai, Magnetofl uid Dynamics for Engineers and Applied Physicists, McGraw Hill, New York (1973).
H. A. Attia, Effect of Hall current on transient hydromagnetic Couette–Poiseuille flow of a viscoelastic fluid with heat transfer, Appl. Math. Model., 32, 375–388 (2008).
K. Michaeli, K. S. Tikhonov, and A. M. Finkelstein, Hall effect in superconducting films, Phys. Rev., B86, 014515 (2012).
A. S. Gupta, Heat transfer in hydromagnetic Couette flow with Hall effects, Math. Student, XL, 103–106 (1972).
V. M. Soundalgekar, G. A. Dessai, and A. S. Gupta, Hall effects on generalized MHD Couete fl ow with heat transfer, Bull. Classe Sci., LX, 332–345 (1974).
A. J. Chamkha, Unsteady laminar hydromagnetic flow and heat transfer in porous channels with temperature-dependent properties, Int. J. Numer. Meth. Heat Fluid Flow, 11, 430–448 (2001).
O. A. Bég, J. Zueco, and H. S. Takhar, Unsteady magnetohydrodynamic Hartmann–Couette flow and heat transfer in a Darcian channel with Hall current, ion slip, viscous and Joule heating effects: Network numerical solutions, Commun. Nonlinear Sci. Numer. Simul., 14, 1082–1097 (2009).
O. D. Makinde and T. Chinyoka, Numerical investigation of transient heat transfer to hydromagnetic channel flow with radiative heat and convective cooling, Commun. Nonlinear Sci. Numer. Simul., 15, 3919–3930 (2010).
B. K. Jha and C. A. Apere, Time-dependent MHD Couette flow in a rotating system with suction/injection, Z. Angew. Math. Mech., 91, 832–842 (2011).
R. N. Jana, N. Datta, and B. S. Mazumder, Magnetohydrodynamic Couette flow and heat transfer in a rotating system, J. Phys. Soc. Jpn., 42, 1034–1039 (1977).
S. K. Ghosh, O. A. Bég, and M. Narahari, Hall effects on MHD flow in a rotating system with heat transfer characteristics, Meccanica, 44, 741–765 (2009).
G. S. Seth, R. Nandkeolyar, and M. S. Ansari, Hall effects on oscillatory hydromagnetic Couette flow in a rotating system, Int. J. Acad. Res., 1, 6–17 (2009).
S. Das, S. L. Maji, M. Guria, and R. N. Jana, Unsteady MHD Couette flow in a rotating system, Math. Comput. Model., 50, 1211–1217 (2009).
B. C. Sarkar, S. Das, and R.N. Jana, Combined effects of Hall currents and rotation on steady hydromagnetic Couette flow, Res. J. Appl. Sci. Eng. Technol., 5, No. 6, 1864–1875 (2013).
O. D. Makinde, T. Iskander, F. Maboodc, W. A. Khan, and M. S. Tshehl, MHD Couette–Poiseuille flow of variable viscosity nanofl uids in a rotating permeable channel with Hall effects, J. Mol. Liq., 221, 778–787 (2016).
S. K. Ghosh, MHD rotating fl ow and heat transfer through a channel with Hall effects, J. Magn. Magn. Mater., 404, 221–229 (2016).
A. O. Ali, O. D. Makinde, and Y. Nkansah-Gyekye, Numerical study of unsteady MHD Couette flow and heat transfer of nanofluids in a rotating system with convective cooling, Int. J. Numer. Meth. Heat Fluid Flow, 26, No. 5, 1567 –1579 (2016).
O. D. Makinde, On thermal stability of a reactive third-grade fl uid in a channel with convective cooling the walls, Appl. Math. Comput., 213, 170–176 (2009).
L. Rundora and O. D. Makinde, Analysis of unsteady MHD reactive flow of non-Newtonian fl uid through a porous saturated medium with asymmetric boundary conditions, Iran J. Sci. Technol. Trans. Mech. Eng., 40, 189–201 (2016).
S. Das, R. R. Patra, R. N. Jana, and O. D. Makinde, Hall effects on unsteady MHD reactive flow through a porous channel with convective heating at the Arrhenius reaction rate, J. Eng. Phys. Thermophys., 90, No. 5, 1240–1253 (2017).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 94, No. 3, pp. 722–733, May–June, 2021
Rights and permissions
About this article
Cite this article
Das, S., Patra, R.R. & Jana, R.N. Hydromagnetic Oscillatory Reactive Flow through a Porous Channel in a Rotating Frame Subject to Convective Heat Exchange under Arrhenius Kinetics. J Eng Phys Thermophy 94, 702–713 (2021). https://doi.org/10.1007/s10891-021-02347-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-021-02347-0