Analysis of heat transfer transition of thermally driven flow within a square enclosure under effects of inclined magnetic field

Abstract

This research pertains to the numerical study on natural convection induced by thermally driven flow under influences of slanted magnetic field with a comprehensive parametric analysis. The influences of Rayleigh number (Ra), Hartmann number (Ha), and oblique angles of magnetic field (θ) are considered in details. The results present that the magnetic field direction has significant influences on streamlines and isotherms in a square enclosure, and the average Nusselt number (NuMean) and maximum streamline function (SMax) are decreased with the magnetic field intensity. Based on the curves of normalized Nusselt number Nu∗ with θ, four heat transfer patterns can be observed and called, respectively, Type-1 (single-peak), Type-2 (peak & trough), Type-3 (transition zone), and Type-4 (double-peak). The dimensionless parameter Ha2/Ra is found not to be adequate in determining the heat transfer modes of changing inclined angle. Numerical experiments with a wide range of Ra and Ha are carried out to explore the heat transfer pattern, and a correlated expression for heat transfer transition is proposed to indicate the switching of heat transfer pattern dominated by the inclined magnetic field. By increasing the Ra number, Ha number is examined to interpret the conditions for transition between these four heat transfer patterns.