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Temperature And Heat Transfer Profiles Of A Fluid Film Squeezed Between Two Permeable Isothermal Discs Rotating Within A Magnetic Field


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B. Bhatt & R. Mohais


We consider the case of an electrically conducting fluid squeezed between two permeable, parallel discs placed within a magnetic field. Each disc is maintained at a distinct isothermal temperature and is allowed to rotate independently. The upper disc is then set in motion towards the lower one. Using a similarity solution, analytical and numerical solutions are derived from which the effects of various flow parameters on the temperature and heat transfer profiles are studied. The Hartmann number has an effect on the temperature profiles when the discs are allowed to rotate in the same direction, but the effects are negligible during rotation in the opposite direction. The Prandtl number also affects the temperature and heat transfer profiles for small values of the Squeeze Reynolds number. The effect of permeability on the heat transfer profile varies depending on the speed of rotation of the discs relative to each other. Keywords: heat transfer, permeable discs, electrically conducting fluid. 1 Introduction The problem of a fluid enclosed between two parallel discs has long been a source of intrigue to many mathematicians over the years. von K´arm´an was the first to study the situation where an infinite disc rotated in an unbounded fluid [1]. It was Hamza however who examined the effect of a magnetic field on the radial and axial velocity profiles associated with a fluid film squeezed between two rotating surfaces [2]. He later studied the case of irrotational discs subjected to temperature variations and found that the effect of squeezing was of primary significance, whereas the effect of the magnetic forces was negligible [3]. Further, Hamza and


heat transfer, permeable discs, electrically conducting fluid.