Free Convection MHD Couette Flow with Application of Periodic Temperature and Constant Heat Flux on Walls
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.
Keywords:magnetohydrodynamics (MHD), Couette flow, free convection
A. Singh, “Natural convection in unsteady Couette motion”, Defence Science Journal, Vol. 38, No. 1, pp. 35-41, 1988 DOI: https://doi.org/10.14429/dsj.38.4823
B. Jha, “Natural convection in unsteady MHD Couette flow”, Heat and Mass Transfer, Vol. 37, No. 4, pp. 329-331, 2001 DOI: https://doi.org/10.1007/PL00013295
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 DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2013.11.058
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 DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.025
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 DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2015.08.066
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 DOI: https://doi.org/10.9734/ARJOM/2018/44702
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 DOI: https://doi.org/10.5556/j.tkjm.38.2007.97
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 DOI: https://doi.org/10.5251/ajsir.2010.1.2.326.331
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 DOI: https://doi.org/10.26634/jfet.6.4.1480
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 DOI: https://doi.org/10.4236/ojfd.2012.21002
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 DOI: https://doi.org/10.1515/ijame-2017-0068
How to Cite
MetricsAbstract Views: 525
PDF Downloads: 256
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.