Heat transfer of permeable discs rotating in a magnetic field

Abstract

An electrically conducting Newtonian fluid is squeezed between two parallel infinite axisymmetric discs placed in an orthogonal magnetic field. Both discs are permeable. The upper disc is allowed to rotate in its own plane while moving freely along the z-axis. The lower disc is fixed with respect to the z-axis, but is allowed to rotate within its own plane. This paper addresses two cases, the first where each disc is set at a constant uniform temperature, the temperature of the upper disc being higher than the temperature of the lower disc. Using a similarity solation for small Reynolds numbers, analytical and numerical solutions are derived through which the effects of the permeability on the temperature and heat transfer profiles of the fluid film are studied. In the first case, the heat transfer profile is affected by the disc permeability up to the limiting where the discs rotate at the same speed. The temperature profile however is unaffected. In the second case considered, the lower disc is subjected to a heat flux whilst keeping the upper disc at a uniform constant temperature. In the second case, analytical and numerical solutions show that although the temperature and heat transfer profiles are influenced by the temperature ratio of the disc, they however remain unaffected by disc rotation and disc permeability.