Analysis of Steady Convective Heating for Molten Materials Processing within Trapezoidal Enclosures

Material processing involving natural convection within a trapezoidal enclosure for uniformly and nonuniformly heated bottom wall, insulated top wall, and isothermal sidewalls with inclination angle phi have been investigated. The penalty finite element method is used to obtain isotherm and streamline profiles for model liquids e.g. molten metal, salt water and olive oil. Parametric study for the wide range of Rayleigh number (Ra), 10(3) <= Ra <= 10(5) and Prandtl number (Pr) for model fluids with various tilt angles phi = 45 degrees, 30 degrees, and 0 degrees have been obtained. Secondary circulations were observed during molten metal processing. Streamlines show that the strength of convection is larger for phi = 45 degrees and flow intensities are also found to be larger for olive oil compared to molten metal and salt water. Heat transfer rates are shown via local and average Nusselt number plots. Local heat transfer rates are found to be relatively more for phi = 0 degrees than those with phi = 45 degrees and phi = 30 degrees. Average Nusselt number plots show higher heat transfer rates for phi = 0 degrees except for the nonuniform heating of the bottom wall with Pr = 0.015 (molten metal). Overall, less heat transfer rates are observed for molten metal processing.