Spin-up and spin-down of a viscous fluid over a heated disk rotating in a vertical plane in the presence of a magnetic field and a buoyancy force

Autor:	Harmindar S. Takhar, Girishwar Nath, Arezki Slaouti
Rok vydání:	2002
Předmět:	Physics Buoyancy Partial differential equation Steady state Mechanical Engineering Computational Mechanics Vertical plane Mechanics engineering.material Secondary flow Magnetic field Physics::Fluid Dynamics Classical mechanics Flow (mathematics) Heat transfer engineering Mathematics
Zdroj:	Acta Mechanica. 156:109-129
ISSN:	1619-6937 0001-5970
DOI:	10.1007/bf01188745
Popis:	The hydromagnetic spin-up and spin-down of an incompressible electrically conducting fluid on a heated infinite disk rotating in a vertical plane in the presence of a magnetic field and a buoyancy force have been studied. The flow is non- axisymmetric due to the imposition of the buoyancy force. We have considered the situation where there is an initial steady state which is perturbed by suddenly changing the angular velocity of the disk. By using suitable transformations the Navier-Stokes and energy equations with four independent variables (x, y, z, t) are reduced to a system of partial differential equations with two independent variables (eta, t*). Also, these transformations uncouple the momentum and energy equations, resulting in a primary axisymmetric flow with an axial magnetic field, in an energy equation dependent on the primary flow and in a buoyancy induced secondary cross flow dependent on both primary flow and energy. The results indicate that the effect of the step-change in the angular velocity of the disk is more pronounced on the primary flow than on the secondary flow and the temperature field. For both spin-up and spin-down cases the surface shear stress in the non-axial direction normal to gravity for the primary flow and the surface shear stresses for the secondary flow increase with the magnetic parameter, whilst the surface shear stress in the vertical direction and the heat transfer at the surface decrease as the magnetic parameter increases. Also, the secondary flow near the disk dominates the primary flow. We have also developed an asymptotic analysis for large magnetic parameters which complements well the numerical results obtained in the lower magnetic parameter range.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b5b0cc6cf8546dbe16291300e1931817 https://doi.org/10.1007/bf01188745 Zobrazit plný text záznamu Plný text ve formátu PDF