On exact solution of unsteady MHD flow of a viscous fluid in an orthogonal rheometer

Boundary value problems

Muhammad Afzal Rana¹  Saima Noor²  Sadia Siddiqa³ 

[1] Department of Basic Sciences, Riphah International University, Islamabad, Pakistan;Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan;Department of Mathematics, COMSATS Institute of Information Technology, Attock, Pakistan

关键词: viscous fluid;    MHD flow;    orthogonal rheometer;    eccentric rotation;    exact solutions;   

DOI  :  10.1186/s13661-014-0146-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper studies the unsteady MHD flow of a viscous fluid in which each point of the parallel planes are subject to the non-torsional oscillations in their own planes. The streamlines at any given time are concentric circles. Exact solutions are obtained and the loci Γ of the centres of these concentric circles are discussed. It is shown that the motion so obtained gives three infinite sets of exact solutions in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks. These solutions reduce to a single unique solution when symmetric solutions are looked for. Some interesting special cases are also obtained from these solutions.

【 授权许可】

CC BY