Free Convection MHD Couette Flow with Application of Periodic Temperature and Constant Heat Flux on Walls

M. R. Abdullah, N. Saada


Numerical analysis and analytical solution were performed to study the free convection in transient Couette flow of an electrically conducting fluid confined between two vertical parallel plates. Constant heat flux on the wall with uniform vertical motion in its own plane and periodic temperature on the stationary wall were applied. The dimensionless governing momentum and energy equations are solved numerically using a fully implicit finite difference method. An analytical solution using eigenfunction expansion method is carried out for temperature profile in case of constant plate temperature. Analytical and numerical results converge at a satisfactory degree. The effect of different physical parameters on the transient velocity and temperature, such as Grashof’s number (Gr), magnetic parameter (M), Prandtl number (Pr) and temperature frequency are also studied. It is found that the velocity increases with an increase in Gr and temperature frequency, while it decreases with an increase in Pr and M.


magnetohydrodynamics (MHD); Couette flow; free convection

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A. Singh, “Natural convection in unsteady Couette motion”, Defence Science Journal, Vol. 38, No. 1, pp. 35-41, 1988

B. Jha, “Natural convection in unsteady MHD Couette flow”, Heat and Mass Transfer, Vol. 37, No. 4, pp. 329-331, 2001

M. M. Rashidi, N. Kavyani, S. Abelman, “Investigation of entropy generation in MHD and slip over a rotating porous disk with variable properties”, International Journal of Heat and Mass Transfer, Vol. 70, pp. 892-917, 2014

A. M. Rashad, M. M. Rashidi, G. Lorenzini, S. E. Ahmed, A. M. Aly, “Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium saturated with Cu–water nanofluid”, International Journal of Heat and Mass Transfer, Vol. 104, pp. 878–89, 2017

M. Sheikholeslami, K. Vajravelu, M. M. Rashidi, “Forced convection heat transfer in a semi annulus under the influence of a variable magnetic field”, International Journal of Heat and Mass Transfer, Vol. 92, pp. 339–348, 2016

R. Chaudhary, P. Jain, “Exact solutions of incompressible couette flow with constant temperature and constant heat flux on walls in the presence of radiation”, Turkish Journal of Engineering and Environmental Sciences, Vol. 31, No. 5, pp. 297–304, 2007

M. Narahari, “Effects of thermal radiation and free convection currents on the unsteady couette flow between two vertical parallel plates with constant heat flux at one boundary”, Wseas Transactions on Heat and Mass Transfer, Vol. 5, No. 1, pp. 21-30, 2010

K. Bunonyo, E. Amos, I. C. Eli, “Unsteady oscillatory couette flow between vertical parallel plates with constant radiative heat flux”, Asian Research Journal of Mathematics, Vol. 11, No. 2, pp. 1-11, 2018

P. Sharma, B. Sharma, R. C. Tamkang, “Unsteady free covection oscillatory couette flow through a porous medium with periodic wall temperature”, Journal of Mathematics, Vol. 38, No. 1, pp. 93-102, 2007

C. Israel-Cookey, E. Amos, C. Nwaigwe, “MHD oscillatory couette flow of a radiating viscous fluid in a porous medium with periodic wall temperature”, American Journal of Scientific and Industrial Research, Vol. 1, No. 2, pp. 326-331, 2010

M. Narahari, B. Dutta, “Free convection flow and heat transfer between two vertical parallel plates with variable temperature at one boundary”, Acta Technica, Vol. 56, pp. 103–113, 2011

M. Raju, S. Varma, “Unsteady mhd free convection oscillatory couette flow through a porous medium with periodic wall temperature”, I-Manager’s Journal on Future Engineering & Technology, Vol. 6, No. 4, pp. 7-12, 2011

N. Ahmed, K. Sarma, D. P. Barua, “Magnetic field effect on free convective oscillatory flow between two vertical parallel plates with periodic plate temperature and dissipative heat”, Applied Mathematical Sciences, Vol. 6, No. 39, pp. 1913-1924, 2012

S. Das, B. Sarkar, R. N. Jana, “Radiation effects on free convection mhd couette flow started exponentially with variable wall temperature in presence of heat generation”, Open Journal of Fluid Dynamics, Vol. 2, No. 1, pp. 14-27, 2012

H. K. Mandal, S. Das, R. N. Jana, “Transient free convection in a vertical channel with variable temperature and mass diffusion”, Chemical and Process Engineering Research, Vol. 23, pp. 38-54, 2014

B. Zigta, P. Koya, “The effect of mhd on free convection with periodic temperature and concentration in the presence of thermal radiation and chemical reaction”, International Journal of Applied Mechanics and Engineering, Vol. 22, No.4, pp. 1059-1073, 2017

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