Unsteady magnetohydrodynamic casson nanofluid flow through a moving cylinder with brownian and thermophoresis effects

Unsteady magnetohydrodynamic casson nanofluid flow through a moving cylinder with brownian and thermophoresis effects

Tanmoy Sarker S. M. Arifuzzaman Sk. Reza-E-Rabbi Rubel Ahmed Md. Shakhaoath Khan Sarder Firoz Ahmmed 

Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh

School of Engineering, RMIT University,VIC- 3001, Australia

Corresponding Author Email: 
30 June 2018
| Citation



The aim of this study is to analysis of finite difference scheme of unsteady MHD flow of Casson nano-fluid attribute of Brownian motion and thermophoresis through a moving cylinder. The governing model for the flow is metamorphosed into non-dimensional impetus, strength and mass-diffusion equations and evolved numerically by employing explicit finite difference fetch with the aid of a computer programming language Compact visual FORTRAN 6.6a. In order to optimize the strait parameters and exactness of the strait, the stability and convergence test have sustained. It is clear that with primary boundary postulates, U=V=T=C=0, and small difference time Δt=0.0005, ΔX=0.202, and ΔR= 0.251, the strait has converged for Prandtl number, Pr ≥0.02   and Lewis number, Le ≥  0.018. The acquired results of this study are discussed for several values of natural parameters viz. Prandtl number, Casson fluid parameter, Lewis number, magnetic parameter, Brownian motion and thermophoresis number on the impetus, strength, mass-diffusion, skin friction, Nusselt number by means of several time steps. Moreover, the graphical representations of the solution are shown by conducting tecplot 9.0


casson fluid, nano particles, EFDM, MHD and Moving cylinder

1. Introduction
2. Mathematical model
3. Numerical technique
4. Stability and convergence analysis
5. Results and discussions
6. Conclusions

Boyd J., Buick J. M., Green S. (2007). Analysis of Casson and carreau – yasuda non-Newtonian blood models in steady and oscillatory flow using the lattice Boltzmann method. Phys. Fluids, Vol. 19, pp. 93-103. https://doi.org/10.1063/1.2772250

Buongiorno J. (2006). Convective transport in nano-fluids. Journal of Heat Transfer, Vol. 128, pp. 240-250. https://doi.org/10.1115/1.2150834

Casson N. (1959). A flow equation for pigment oil suspensions of the printing ink type. In: Rheology of Disperse Systems, Mill, C. C. (Ed.), Advances in Mechanical Engineering, Pergamon Press, Oxford, pp. 84-104. 

Chevalley J. (1991). An adaptation of Casson equationfor the rheology of chocolate. J. Texture Stude., Vol. 22, pp. 219-229. https://doi.org/10.1111/j.1745-4603.1991.tb00015.x

Choi S. (1995). Enhancing thermal conductivity of fluids with nano-particles. ASME-Publi. Fed, Vol. 231, pp. 99-105. https://www.osti.gov/servlets/purl/196525

Cokelet G., Shin H., Britten A., Wells R. E. (1963). Rheology of human blood – measurement near and at zero shear rate. Trans. Soc. Rheol., Vol. 7, pp. 303-317. https://doi.org/10.1122/1.548959

Eldabe N. T. M., Salwa M. G. E. (1995). Heat transfer of MHD non-Newtonian Casson fluid flow between two rotating cylinder. J. Phys. Soc, Jpn., Vol. 64, pp. 41-64.

Emmanuel M. A., Ibrahim Y. S., Letis B. B. (2015). Analysis of Casson fluid flow over a vertical porous surface with chemical reaction in the presence of magnetic field. Journal of Applied Mathematics, Vol. 3, pp. 713-723. https://doi.org/10.4236/jamp.2015.36085

Garcia-Ochoa F., Casa J. A. (1994). Apparent yield stress in xanthium gum solutions at low concentrations. Chem. Eng. J., Vol. 53, pp. B41-B46. https://doi.org/10.1016/0923-0467(93)06043-P

Hayat T., Bilal A. M., Shehzad S. A., Alsaedi A. (2015). Mixed convection flow of Casson nanofluid over a stretching sheet with convectively heated chemical reaction and heat source/sink. Journal of Applied Fluid Mechanics, Vol. 8, pp. 803-811. https://doi.org/10.18869/acadpub.jafm.67.223.22995

Hussanan A., Zukhi S. M., Tahar R. M., Khan I. (2014). Unsteady boundary layer flow and heat and mass transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating. PLOS ONE, Vol. 9, pp. e108763. https://doi.org/10.1371/journal.pone.0108763

Kataria H. R., Patal H. R. (2016). Soret and heat generation effects on MHD Casson fluid flow past an oscillating vertical plate embedded through porous medium. Alexandria Engineering Journal, Vol. 55, pp. 2125-2137. https://doi.org/10.1016/j.aej.2016.06.024

Kataria H. R., Patel H. R. (2016). Radiation and chemical reaction effects on MHD Casson fluid flow past an oscillating vertical plate embedded in porous medium. Alexandria Engineering Journal, Vol. 55, pp. 583-595. https://doi.org/10.1016/j.aej.2016.01.019

Khan M. S., Karim I., Ali L. E., Islam A. (2012). Unsteady MHD free convection boundary-layer flow of a nanofluid along a stretching sheet with thermal radiation and viscous dissipation effects. International Nano Letters, Vol. 2, pp. 24. https://doi.org/10.1186/2228-5326-2-24

Kumari P. K., Murthy M. V., Reddy M., Kumar Y. V. K. (2011). Peristaltic pumping of a magnetohydrodynamic Casson fluid in an inclined channel. Adv. Appl. Sci. Res., Vol. 2, pp. 428-436.   

Mahabaleshwar U., Lorenzini G. (2017). Combined effect of heat source/sink and stress work on MHD Newtonian fluid flow over a stretching porous sheet. International Journal of Heat and Technology, Vol. 35, pp. 330-S335. https://doi.org/10.18280/ijht.35Sp0145

Makanda G., Shaw S., Sibanda P. (2015). Effects of radiation on MHD free convection of a Casson fluid from a horizontal circular cylinder with partial slip in non-Darcy porous medium with viscous dissipation. Boundary Value Problems, pp. 75. https://doi.org/10.1186/s13661-015-0333-5

Malik M. Y., Naseer M., Nadeem S., Rehman A. (2014). The boundary layer flow of Casson nanofluid over a vertical exponentially stretching cylinder. Applied Nanoscience, Vol. 4, pp. 869-873. https://doi.org/10.1007/s13204-013-0267-0

Nadeem S., Haq R. U., Lee C. (2012). MHD flow of Casson fluid over an exponentially shrinking sheet. Scientia Iranica, Vol. 19, pp. 1550-1553. https://doi.org/10.1016/j.scient.2012.10.021

Okay S. (1979). Non-Newtonian blood flow in capillary with a permeable wall. In: Proc. Festschrift of Harold Wayland Symposium, Calyfornia Inst. Of Tech., Pasadena, USA. 

Sakiadis B. C. (1961). Boundary layer behavior on continuous solid surface: 1. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE Journal, Vol. 7, No. 1, pp. 26-28. https://doi.org/10.1002/aic.690070108 

Sreenadh S., Pallavi A. R., Satynarayana B. (2011). Flow of a Casson fluid through an inclined tube of mom-uniform cross section with multiple stenosis. Adv. Appl. Sci. Res., Vol. 2, No. 5, pp. 340-349.

Walwander W. P., Chen T. Y., Cala D. F. (1975). An approximate Casson fluid model for tube flow of blood. Biorheology, Vol. 12, pp. 111-119. https://doi.org/10.3233/BIR-1975-12202